diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/share/algebra/browse.daase | 762 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1126 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1292 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8298 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29830 |
5 files changed, 20653 insertions, 20655 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index ed0544b6..3f9d72ac 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2237777 . 3417777697) +(2237767 . 3419169924) (-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."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4247 . T) (-4245 . T) (-4244 . T) ((-4252 "*") . T) (-4243 . T) (-4248 . T) (-4242 . T) (-2137 . T)) +((-4247 . T) (-4245 . T) (-4244 . T) ((-4252 "*") . T) (-4243 . T) (-4248 . T) (-4242 . T) (-4131 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3576) +(-31 R -1730) ((|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 -966) (QUOTE (-525))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4250))) (-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2137 . T)) +((-4131 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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 -3576 UP UPUP -3940) +(-39 -1730 UP UPUP -1233) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4243 |has| (-385 |#2|) (-341)) (-4248 |has| (-385 |#2|) (-341)) (-4242 |has| (-385 |#2|) (-341)) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3321 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3321 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3321 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3321 (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) -(-40 R -3576) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3150 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3150 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3150 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3150 (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +(-40 R -1730) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) @@ -107,7 +107,7 @@ NIL (-44 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4250 . T) (-4251 . T)) -((-3321 (-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|))))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|))))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-788))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -3576) +(-53 |Base| R -1730) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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"))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . 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}"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) -(-59 -2400) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +(-59 -3419) ((|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 -2400) +(-60 -3419) ((|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 -2400) +(-61 -3419) ((|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 -2400) +(-62 -3419) ((|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 -2400) +(-63 -3419) ((|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 -2400) +(-64 -3419) ((|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 -2400) +(-65 -3419) ((|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 -2400) +(-66 -3419) ((|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 -2400) +(-67 -3419) ((|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 -2400) +(-68 -3419) ((|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 -2400) +(-69 -3419) ((|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 -2400) +(-70 -3419) ((|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 -2400) +(-71 -3419) ((|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 -2400) +(-72 -3419) ((|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 -2400) +(-75 -3419) ((|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 -2400) +(-76 -3419) ((|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 -2400) +(-77 -3419) ((|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 -2400) +(-78 -3419) ((|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 -2400) +(-79 -3419) ((|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 -2400) +(-80 -3419) ((|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 -2400) +(-81 -3419) ((|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 -2400) +(-82 -3419) ((|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 -2400) +(-83 -3419) ((|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 -2400) +(-84 -3419) ((|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 -2400) +(-85 -3419) ((|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 -2400) +(-86 -3419) ((|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 -2400) +(-87 -3419) ((|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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-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."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . 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."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3321 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3150 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) (-104) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -361,7 +361,7 @@ NIL ((-4245 . T) (-4244 . T)) NIL (-108) -((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) +((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL (-109 A) @@ -372,7 +372,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -3576 UP) +(-111 -1730 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}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-842))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-951))) (|HasCategory| (-112 |#1|) (QUOTE (-761))) (-3321 (|HasCategory| (-112 |#1|) (QUOTE (-761))) (|HasCategory| (-112 |#1|) (QUOTE (-788)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1065))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-842)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) +((|HasCategory| (-112 |#1|) (QUOTE (-842))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-138))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-112 |#1|) (QUOTE (-951))) (|HasCategory| (-112 |#1|) (QUOTE (-761))) (-3150 (|HasCategory| (-112 |#1|) (QUOTE (-761))) (|HasCategory| (-112 |#1|) (QUOTE (-788)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-1065))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-112 |#1|) (QUOTE (-213))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-286))) (|HasCategory| (-112 |#1|) (QUOTE (-510))) (|HasCategory| (-112 |#1|) (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-112 |#1|) (QUOTE (-842)))) (|HasCategory| (-112 |#1|) (QUOTE (-136))))) (-114 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4251))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-2137 . T)) +((-4131 . 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"))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,20 +414,20 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-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."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-124) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3321 (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-125) (QUOTE (-1018)))) (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-125) (QUOTE (-1018))) (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125)))))) (-3150 (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-125) (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-125) (QUOTE (-1018)))) (|HasCategory| (-125) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-125) (QUOTE (-1018))) (-12 (|HasCategory| (-125) (QUOTE (-1018))) (|HasCategory| (-125) (LIST (QUOTE -288) (QUOTE (-125))))) (|HasCategory| (-125) (LIST (QUOTE -565) (QUOTE (-796))))) (-125) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -444,11 +444,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4252 "*") . T)) NIL -(-129 |minix| -2951 S T$) +(-129 |minix| -2058 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-130 |minix| -2951 R) +(-130 |minix| -2058 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -459,7 +459,7 @@ NIL (-132) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4250 . T) (-4240 . T) (-4251 . T)) -((-3321 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-346))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) (-133 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -484,7 +484,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4247 . T)) NIL -(-139 -3576 UP UPUP) +(-139 -1730 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -498,7 +498,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasAttribute| |#1| (QUOTE -4250))) (-142 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2137 . T)) +((-4131 . T)) NIL (-143 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) @@ -516,7 +516,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-147 R -3576) +(-147 R -1730) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -546,7 +546,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-951))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-341))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasAttribute| |#2| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-788)))) (-154 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4243 -3321 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-842)))) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4246 |has| |#1| (-6 -4246)) (-4249 |has| |#1| (-6 -4249)) (-2182 . T) (-2137 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4243 -3150 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-842)))) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4246 |has| |#1| (-6 -4246)) (-4249 |has| |#1| (-6 -4249)) (-4185 . T) (-4131 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-155 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -558,8 +558,8 @@ NIL NIL (-157 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4243 -3321 (|has| |#1| (-517)) (-12 (|has| |#1| (-286)) (|has| |#1| (-842)))) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4246 |has| |#1| (-6 -4246)) (-4249 |has| |#1| (-6 -4249)) (-2182 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-327)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| 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(QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| |#1| (QUOTE (-984))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-510))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-341)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-213))) (-12 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#1| (QUOTE -4249)) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089))))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-327))))) (-158 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -608,7 +608,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-170 R -3576) +(-170 R -1730) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -712,19 +712,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-196 -3576 UP UPUP R) +(-196 -1730 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-197 -3576 FP) +(-197 -1730 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-198) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3321 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) -(-199 R -3576) +((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3150 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) +(-199 R -1730) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -739,18 +739,18 @@ NIL (-202 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-203 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4247 . T)) NIL -(-204 R -3576) +(-204 R -1730) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-205) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2176 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4173 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-206) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -759,14 +759,14 @@ NIL (-207 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-208 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-209 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-210 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -790,28 +790,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4250))) (-215 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-216) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-217 S -2951 R) +(-217 S -2058 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-734))) (|HasCategory| |#3| (QUOTE (-786))) (|HasAttribute| |#3| (QUOTE -4247)) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (QUOTE (-668))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (QUOTE (-1018)))) -(-218 -2951 R) +(-218 -2058 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}.")) 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T)) NIL -(-219 -2951 A B) +(-219 -2058 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 @@ -826,12 +826,12 @@ NIL NIL (-224 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2137 . T)) +((-4131 . T)) NIL (-225 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-226 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -839,19 +839,19 @@ NIL (-227 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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|#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-786))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-668))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -833) (QUOTE (-1089))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-975)))) (-3150 (|HasCategory| |#3| (QUOTE (-975))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525)))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#3| (QUOTE (-1018)))) (-3150 (|HasAttribute| |#3| (QUOTE -4247)) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-975)))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -565) (QUOTE (-796))))) (-231 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -862,7 +862,7 @@ NIL NIL (-233 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-234) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -903,7 +903,7 @@ NIL (-243 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#3| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#3| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#3| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#3| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-244 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -948,11 +948,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-255 R -3576) +(-255 R -1730) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-256 R -3576) +(-256 R -1730) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -974,7 +974,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018)))) (-261 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-262 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1000,7 +1000,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-268 S R |Mod| -3077 -2131 |exactQuo|) +(-268 S R |Mod| -1466 -3459 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL @@ -1022,21 +1022,21 @@ NIL NIL (-273 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4247 -3321 (|has| |#1| (-975)) (|has| |#1| (-450))) (-4244 |has| |#1| (-975)) (-4245 |has| |#1| (-975))) -((|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-975)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3321 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668)))) (|HasCategory| |#1| (QUOTE (-450))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3321 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-1030)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-281))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-450)))) (-3321 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668)))) (-3321 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-975)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) +((-4247 -3150 (|has| |#1| (-975)) (|has| |#1| (-450))) (-4244 |has| |#1| (-975)) (-4245 |has| |#1| (-975))) +((|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-975)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-975)))) (-3150 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668)))) (|HasCategory| |#1| (QUOTE (-450))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3150 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-1030)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-281))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-450)))) (-3150 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668)))) (-3150 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-975)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) (-274 |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."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-275) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-276 -3576 S) +(-276 -1730 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-277 E -3576) +(-277 E -1730) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL @@ -1084,7 +1084,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-289 -3576) +(-289 -1730) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1095,7 +1095,7 @@ NIL (-291 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-951))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-761))) (-3321 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-761))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-788)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-788))) (-12 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| $ (QUOTE (-136)))) (-3321 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| $ (QUOTE (-136)))))) +((|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-951))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-761))) (-3150 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-761))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-788)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-213))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -288) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (LIST (QUOTE -265) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-286))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-510))) (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-788))) (-12 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| $ (QUOTE (-136)))) (-3150 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-136))) (-12 (|HasCategory| (-1157 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| $ (QUOTE (-136)))))) (-292 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1106,9 +1106,9 @@ NIL NIL (-294 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4247 -3321 (-1213 (|has| |#1| (-975)) (|has| |#1| (-587 (-525)))) (-12 (|has| |#1| (-517)) (-3321 (-1213 (|has| |#1| (-975)) (|has| |#1| (-587 (-525)))) (|has| |#1| (-975)) (|has| |#1| (-450)))) (|has| |#1| (-975)) (|has| |#1| (-450))) (-4245 |has| |#1| (-160)) (-4244 |has| |#1| (-160)) ((-4252 "*") |has| |#1| (-517)) (-4243 |has| |#1| (-517)) (-4248 |has| 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(QUOTE (-975))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))))) (-3150 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-975)))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| $ (QUOTE (-975))) (|HasCategory| $ (LIST (QUOTE -966) (QUOTE (-525))))) +(-295 R -1730) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1119,7 +1119,7 @@ NIL (-297 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-298 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1151,12 +1151,12 @@ NIL (-305 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) -(-306 S -3576) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +(-306 S -1730) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-346)))) -(-307 -3576) +(-307 -1730) ((|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."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL @@ -1176,15 +1176,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-312 S -3576 UP UPUP R) +(-312 S -1730 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-313 -3576 UP UPUP R) +(-313 -1730 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-314 -3576 UP UPUP R) +(-314 -1730 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1204,26 +1204,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-319 S -3576 UP UPUP) +(-319 S -1730 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-341)))) -(-320 -3576 UP UPUP) +(-320 -1730 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."))) ((-4243 |has| (-385 |#2|) (-341)) (-4248 |has| (-385 |#2|) (-341)) (-4242 |has| (-385 |#2|) (-341)) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-321 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) +((-3150 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) (-322 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-323 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-324 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1240,31 +1240,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL -(-328 R UP -3576) +(-328 R UP -1730) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-329 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) +((-3150 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) (-330 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-331 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-332 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) +((-3150 (|HasCategory| (-843 |#1|) (QUOTE (-136))) (|HasCategory| (-843 |#1|) (QUOTE (-346)))) (|HasCategory| (-843 |#1|) (QUOTE (-138))) (|HasCategory| (-843 |#1|) (QUOTE (-346))) (|HasCategory| (-843 |#1|) (QUOTE (-136)))) (-333 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) -(-334 -3576 GF) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +(-334 -1730 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1272,14 +1272,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-336 -3576 FP FPP) +(-336 -1730 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-337 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) +((-3150 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-136)))) (-338 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1334,7 +1334,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4251)) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018)))) (-351 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4250 . T) (-2137 . T)) +((-4250 . T) (-4131 . T)) NIL (-352 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) @@ -1358,7 +1358,7 @@ NIL NIL (-357) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4233 . T) (-4241 . T) (-2176 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4233 . T) (-4241 . T) (-4173 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-358 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1374,11 +1374,11 @@ NIL NIL (-361) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2137 . T)) +((-4131 . T)) NIL (-362) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2137 . T)) +((-4131 . T)) NIL (-363 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) @@ -1408,7 +1408,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-370 -3576 UP UPUP R) +(-370 -1730 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1422,27 +1422,27 @@ NIL NIL (-373) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2137 . T)) +((-4131 . T)) NIL (-374) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2137 . T)) +((-4131 . T)) NIL (-375) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-376 -2400 |returnType| -1235 |symbols|) +(-376 -3419 |returnType| -3638 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-377 -3576 UP) +(-377 -1730 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-378 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2137 . T)) +((-4131 . T)) NIL (-379 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1458,7 +1458,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4233)) (|HasAttribute| |#1| (QUOTE -4241))) (-382) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2176 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4173 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-383 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1471,7 +1471,7 @@ NIL (-385 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4237 -12 (|has| |#1| (-6 -4248)) (|has| |#1| (-429)) (|has| |#1| (-6 -4237))) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-761))) (-3321 (|HasCategory| |#1| (QUOTE (-761))) (|HasCategory| |#1| (QUOTE (-788)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1065))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769))))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4248)) (|HasAttribute| |#1| (QUOTE -4237)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-761))) (-3150 (|HasCategory| |#1| (QUOTE (-761))) (|HasCategory| |#1| (QUOTE (-788)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-1065))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769))))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-769)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-510))) (-12 (|HasAttribute| |#1| (QUOTE -4248)) (|HasAttribute| |#1| (QUOTE -4237)) (|HasCategory| |#1| (QUOTE (-429)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-386 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1492,11 +1492,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-391 R -3576 UP A) +(-391 R -1730 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4247 . T)) NIL -(-392 R -3576 UP A |ibasis|) +(-392 R -1730 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 -966) (|devaluate| |#2|)))) @@ -1515,7 +1515,7 @@ NIL (-396 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1129))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1129)))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) +((|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -288) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -265) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-1129))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-1129)))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-429)))) (-397 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1542,9 +1542,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-346)))) (-403 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4250 . T) (-4240 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4240 . T) (-4251 . T) (-4131 . T)) NIL -(-404 R -3576) +(-404 R -1730) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4237 -12 (|has| |#1| (-6 -4237)) (|has| |#2| (-6 -4237))) (-4244 . T) (-4245 . T) (-4247 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4237)) (|HasAttribute| |#2| (QUOTE -4237)))) -(-406 R -3576) +(-406 R -1730) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1562,17 +1562,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (-408 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4247 -3321 (|has| |#1| (-975)) (|has| |#1| (-450))) (-4245 |has| |#1| (-160)) (-4244 |has| |#1| (-160)) ((-4252 "*") |has| |#1| (-517)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4242 |has| |#1| (-517)) (-2137 . T)) +((-4247 -3150 (|has| |#1| (-975)) (|has| |#1| (-450))) (-4245 |has| |#1| (-160)) (-4244 |has| |#1| (-160)) ((-4252 "*") |has| |#1| (-517)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-517)) (-4242 |has| |#1| (-517)) (-4131 . T)) NIL -(-409 R -3576) +(-409 R -1730) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-410 R -3576) +(-410 R -1730) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-411 R -3576) +(-411 R -1730) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1580,7 +1580,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-413 R -3576 UP) +(-413 R -1730 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 -966) (QUOTE (-47))))) @@ -1598,17 +1598,17 @@ NIL NIL (-417) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2137 . T)) +((-4131 . T)) NIL (-418) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2137 . T)) +((-4131 . T)) NIL (-419 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-420 R UP -3576) +(-420 R UP -1730) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1655,7 +1655,7 @@ NIL (-431 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4252 "*") |has| |#2| (-160)) (-4243 |has| |#2| (-517)) (-4248 |has| |#2| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#2| (QUOTE (-842))) (-3321 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3321 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3321 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4248)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-842))) (-3150 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3150 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3150 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4248)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) (-432 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1720,7 +1720,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-448 |lv| -3576 R) +(-448 |lv| -1730 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1735,11 +1735,11 @@ NIL (-451 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-452 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 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T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-788))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-788))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-453 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4251 . T) (-4250 . T)) @@ -1751,7 +1751,7 @@ NIL (-455 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-456) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1759,16 +1759,16 @@ NIL (-457 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(|HasCategory| (-525) (QUOTE (-788))) (-12 (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (QUOTE (-975)))) (-12 (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089))))) (|HasCategory| |#2| (QUOTE (-668))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525))))) (-3150 (|HasCategory| |#2| (QUOTE (-975))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-1018)))) (|HasAttribute| |#2| (QUOTE -4247)) (|HasCategory| |#2| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (-459 S) ((|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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) -(-460 -3576 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +(-460 -1730 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1779,14 +1779,14 @@ NIL (-462) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3321 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3150 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) (-463 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4250)) (|HasAttribute| |#1| (QUOTE -4251)) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (-464 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2137 . T)) +((-4131 . T)) NIL (-465 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1796,7 +1796,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-467 -3576 UP |AlExt| |AlPol|) +(-467 -1730 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1807,16 +1807,16 @@ NIL (-469 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-470 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-471 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-472 R UP -3576) +(-472 R UP -1730) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1836,7 +1836,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-477 -3576 |Expon| |VarSet| |DPoly|) +(-477 -1730 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-1089))))) @@ -1883,19 +1883,19 @@ NIL (-488 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-489 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((-3321 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) +((-3150 (|HasCategory| (-538 |#1|) (QUOTE (-136))) (|HasCategory| (-538 |#1|) (QUOTE (-346)))) (|HasCategory| (-538 |#1|) (QUOTE (-138))) (|HasCategory| (-538 |#1|) (QUOTE (-346))) (|HasCategory| (-538 |#1|) (QUOTE (-136)))) (-490 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-491 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-492 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -1907,7 +1907,7 @@ NIL (-494 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-495 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1920,7 +1920,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-498 K -3576 |Par|) +(-498 K -1730 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -1940,7 +1940,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-503 K -3576 |Par|) +(-503 K -1730 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -1975,12 +1975,12 @@ NIL (-511 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) -(-512 R -3576) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +(-512 R -1730) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-513 R0 -3576 UP UPUP R) +(-513 R0 -1730 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -1990,7 +1990,7 @@ NIL NIL (-515 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2176 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4173 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-516 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL -(-518 R -3576) +(-518 R -1730) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2012,7 +2012,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-521 R -3576 L) +(-521 R -1730 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 -601) (|devaluate| |#2|)))) @@ -2020,11 +2020,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-523 -3576 UP UPUP R) +(-523 -1730 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-524 -3576 UP) +(-524 -1730 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2036,15 +2036,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-527 R -3576 L) +(-527 R -1730 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 -601) (|devaluate| |#2|)))) -(-528 R -3576) +(-528 R -1730) ((|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 -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-577))))) -(-529 -3576 UP) +(-529 -1730 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2052,27 +2052,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-531 -3576) +(-531 -1730) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-532 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2176 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4173 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-533) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-534 R -3576) +(-534 R -1730) ((|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 -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-263))) (|HasCategory| |#2| (QUOTE (-577))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-263)))) (|HasCategory| |#1| (QUOTE (-517)))) -(-535 -3576 UP) +(-535 -1730 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-536 R -3576) +(-536 R -1730) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2088,15 +2088,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-540 R -3576) +(-540 R -1730) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-541 E -3576) +(-541 E -1730) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL -(-542 -3576) +(-542 -1730) ((|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}."))) ((-4245 . T) (-4244 . T)) ((|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-1089))))) @@ -2123,7 +2123,7 @@ NIL (-548 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3321 (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018)))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (-3150 (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018)))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) (-549 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2131,7 +2131,7 @@ NIL (-550 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-525)) (|devaluate| |#1|)))) (|HasCategory| (-525) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-525)))))) (-551 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4245 |has| |#1| (-517)) (-4244 |has| |#1| (-517)) ((-4252 "*") |has| |#1| (-517)) (-4243 |has| |#1| (-517)) (-4247 . T)) @@ -2144,7 +2144,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-554 R -3576 FG) +(-554 R -1730 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2155,30 +2155,30 @@ NIL (-556 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-557 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL ((|HasAttribute| |#1| (QUOTE -4251)) (|HasCategory| |#2| (QUOTE (-788))) (|HasAttribute| |#1| (QUOTE -4250)) (|HasCategory| |#3| (QUOTE (-1018)))) (-558 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2137 . T)) +((-4131 . T)) NIL (-559 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4247 -3321 (-1213 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4245 . T) (-4244 . T)) -((-3321 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4247 -3150 (-3543 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4245 . T) (-4244 . T)) +((-3150 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-560 |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."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| (-1072) (QUOTE (-788))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| (-1072) (QUOTE (-788))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-561 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 (-562 |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}."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-563 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"))) @@ -2196,7 +2196,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-567 -3576 UP) +(-567 -1730 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2212,7 +2212,7 @@ 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}."))) ((-4244 . T) (-4245 . T) (-4247 . T)) ((|HasCategory| |#1| (QUOTE (-786)))) -(-571 R -3576) +(-571 R -1730) ((|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 @@ -2240,18 +2240,18 @@ 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 -(-578 R -3576) +(-578 R -1730) ((|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 -(-579 |lv| -3576) +(-579 |lv| -1730) ((|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 (-580) ((|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."))) ((-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1221) (QUOTE (-51))))))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1072) (QUOTE (-788))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1568) (QUOTE (-51))))))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-1072) (QUOTE (-788))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) (-581 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2262,8 +2262,8 @@ NIL NIL (-583 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4247 -3321 (-1213 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4245 . T) (-4244 . T)) -((-3321 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) +((-4247 -3150 (-3543 (|has| |#2| (-345 |#1|)) (|has| |#1| (-517))) (-12 (|has| |#2| (-395 |#1|)) (|has| |#1| (-517)))) (-4245 . T) (-4244 . T)) +((-3150 (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (LIST (QUOTE -395) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -345) (|devaluate| |#1|)))) (-584 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 @@ -2275,7 +2275,7 @@ NIL (-586 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 -((-2247 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) +((-3389 (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-341)))) (-587 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4247 . T)) @@ -2295,11 +2295,11 @@ NIL (-591 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-769))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-592 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-593 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2314,9 +2314,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4251))) (-596 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})}."))) -((-2137 . T)) +((-4131 . T)) NIL -(-597 R -3576 L) +(-597 R -1730 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 @@ -2336,11 +2336,11 @@ 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}."))) ((-4244 . T) (-4245 . T) (-4247 . T)) NIL -(-602 -3576 UP) +(-602 -1730 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)))) -(-603 A -2643) +(-603 A -2595) ((|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}}"))) ((-4244 . T) (-4245 . T) (-4247 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) @@ -2374,13 +2374,13 @@ NIL NIL (-611 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}."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL -(-612 -3576) +(-612 -1730) ((|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 -(-613 -3576 |Row| |Col| M) +(-613 -1730 |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 @@ -2391,7 +2391,7 @@ NIL (-615 |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."))) ((-4247 . T) (-4250 . T) (-4244 . T) (-4245 . T)) -((|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (-3321 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3321 (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (-3150 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517))) (-3150 (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-160)))) (-616 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2402,12 +2402,12 @@ NIL NIL (-618 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-2137 . T)) +((-4131 . T)) NIL (-619 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 -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-620 |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 @@ -2446,7 +2446,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-341))) (|HasCategory| |#2| (QUOTE (-517)))) (-629 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"))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-630 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."))) @@ -2455,12 +2455,12 @@ NIL (-631 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."))) ((-4250 . T) (-4251 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-517))) (|HasAttribute| |#1| (QUOTE (-4252 "*"))) (|HasCategory| |#1| (QUOTE (-341))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-632 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 -(-633 S -3576 FLAF FLAS) +(-633 S -1730 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 @@ -2470,11 +2470,11 @@ NIL NIL (-635) ((|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"))) -((-4243 . T) (-4248 |has| (-640) (-341)) (-4242 |has| (-640) (-341)) (-2182 . T) (-4249 |has| (-640) (-6 -4249)) (-4246 |has| (-640) (-6 -4246)) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . 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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}."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-637 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}."))) @@ -2484,13 +2484,13 @@ 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 -(-639 OV E -3576 PG) +(-639 OV E -1730 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 (-640) ((|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}"))) -((-2176 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4173 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-641 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."))) @@ -2520,7 +2520,7 @@ 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 -(-648 S -4196 I) +(-648 S -1796 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 @@ -2540,14 +2540,14 @@ 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."))) 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(LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-327))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-655 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2556,7 +2556,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4245 |has| |#1| (-160)) (-4244 |has| |#1| (-160)) (-4247 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138)))) -(-657 R |Mod| -3077 -2131 |exactQuo|) +(-657 R |Mod| -1466 -3459 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4247 . T)) NIL @@ -2568,7 +2568,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4245 . T) (-4244 . T)) NIL -(-660 -3576) +(-660 -1730) ((|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]]}."))) ((-4247 . T)) NIL @@ -2604,7 +2604,7 @@ 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 -(-669 -3576 UP) +(-669 -1730 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 @@ -2623,7 +2623,7 @@ NIL (-673 |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."))) (((-4252 "*") |has| |#2| (-160)) (-4243 |has| |#2| (-517)) (-4248 |has| |#2| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#2| (QUOTE (-842))) (-3321 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3321 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3321 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4248)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-842))) (-3150 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-160))) (-3150 (|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (QUOTE (-517)))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-798 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341))) (-3150 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#2| (QUOTE -4248)) (|HasCategory| |#2| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) (-674 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2642,7 +2642,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-788)))) (-678 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4240 . T) (-4251 . T) (-2137 . T)) +((-4240 . T) (-4251 . T) (-4131 . T)) NIL (-679 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2756,15 +2756,15 @@ 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 -(-707 -3576) +(-707 -1730) ((|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 -(-708 P -3576) +(-708 P -1730) ((|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 -(-709 UP -3576) +(-709 UP -1730) ((|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 @@ -2780,7 +2780,7 @@ 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."))) (((-4252 "*") . T)) NIL -(-713 R -3576) +(-713 R -1730) ((|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 @@ -2800,7 +2800,7 @@ 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 -(-718 -3576 |ExtF| |SUEx| |ExtP| |n|) +(-718 -1730 |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 @@ -2815,7 +2815,7 @@ NIL (-721 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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . 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(QUOTE -37) (QUOTE (-525))))) (-3389 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-1089)))) (-3389 (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-525))))))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-722 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 @@ -2823,14 +2823,14 @@ NIL (-723 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)}"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4246 |has| |#1| (-341)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-724 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-725 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.}"))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-726 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}."))) @@ -2884,23 +2884,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4244 . T) (-4245 . T) (-4247 . T)) NIL -(-739 -3321 R OS S) +(-739 -3150 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-740 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3321 (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (-3150 (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-510))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-929 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (-741) ((|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 -(-742 R -3576 L) +(-742 R -1730 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 -(-743 R -3576) +(-743 R -1730) ((|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 @@ -2908,7 +2908,7 @@ 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 -(-745 R -3576) +(-745 R -1730) ((|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 @@ -2916,11 +2916,11 @@ 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 -(-747 -3576 UP UPUP R) +(-747 -1730 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 -(-748 -3576 UP L LQ) +(-748 -1730 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 @@ -2928,38 +2928,38 @@ 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 -(-750 -3576 UP L LQ) +(-750 -1730 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 -(-751 -3576 UP) +(-751 -1730 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 -(-752 -3576 L UP A LO) +(-752 -1730 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 -(-753 -3576 UP) +(-753 -1730 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)))) -(-754 -3576 LO) +(-754 -1730 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 -(-755 -3576 LODO) +(-755 -1730 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. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-759 (-1089)) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-758 |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."))) (((-4252 "*") |has| |#2| (-341)) (-4243 |has| |#2| (-341)) (-4248 |has| |#2| (-341)) (-4242 |has| |#2| (-341)) (-4247 . T) (-4245 . T) (-4244 . T)) @@ -3014,7 +3014,7 @@ NIL NIL (-771 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4250 . T) (-4240 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4240 . T) (-4251 . T) (-4131 . T)) NIL (-772) ((|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."))) @@ -3027,7 +3027,7 @@ NIL (-774 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."))) ((-4247 |has| |#1| (-786))) -((|HasCategory| |#1| (QUOTE (-786))) (-3321 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3321 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-786))) (-3150 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3150 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-775 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4245 |has| |#1| (-160)) (-4244 |has| |#1| (-160)) (-4247 . T)) @@ -3055,12 +3055,12 @@ NIL (-781 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."))) ((-4247 |has| |#1| (-786))) -((|HasCategory| |#1| (QUOTE (-786))) (-3321 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3321 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-786))) (-3150 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-510))) (-3150 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-21)))) (-782) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-783 -2951 S) +(-783 -2058 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 @@ -3096,11 +3096,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) -(-792 R |sigma| -2576) +(-792 R |sigma| -3970) ((|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."))) ((-4244 . T) (-4245 . T) (-4247 . T)) ((|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-341)))) -(-793 |x| R |sigma| -2576) +(-793 |x| R |sigma| -3970) ((|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."))) ((-4244 . T) (-4245 . T) (-4247 . T)) ((|HasCategory| |#2| (QUOTE (-160))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-429))) (|HasCategory| |#2| (QUOTE (-341)))) @@ -3147,15 +3147,15 @@ NIL (-804 |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)."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-803 |#1|) (QUOTE (-842))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-803 |#1|) (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-138))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-803 |#1|) (QUOTE (-951))) (|HasCategory| (-803 |#1|) (QUOTE (-761))) (-3321 (|HasCategory| (-803 |#1|) (QUOTE (-761))) (|HasCategory| (-803 |#1|) (QUOTE (-788)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (QUOTE (-1065))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (QUOTE (-213))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -803) (|devaluate| |#1|)) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (QUOTE (-286))) (|HasCategory| (-803 |#1|) (QUOTE (-510))) (|HasCategory| (-803 |#1|) (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-842)))) (|HasCategory| (-803 |#1|) (QUOTE (-136))))) +((|HasCategory| (-803 |#1|) (QUOTE (-842))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-803 |#1|) (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-138))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-803 |#1|) (QUOTE (-951))) (|HasCategory| (-803 |#1|) (QUOTE (-761))) (-3150 (|HasCategory| (-803 |#1|) (QUOTE (-761))) (|HasCategory| (-803 |#1|) (QUOTE (-788)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (QUOTE (-1065))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-803 |#1|) (QUOTE (-213))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -486) (QUOTE (-1089)) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -288) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (LIST (QUOTE -265) (LIST (QUOTE -803) (|devaluate| |#1|)) (LIST (QUOTE -803) (|devaluate| |#1|)))) (|HasCategory| (-803 |#1|) (QUOTE (-286))) (|HasCategory| (-803 |#1|) (QUOTE (-510))) (|HasCategory| (-803 |#1|) (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-803 |#1|) (QUOTE (-842)))) (|HasCategory| (-803 |#1|) (QUOTE (-136))))) (-805 |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)}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-951))) (|HasCategory| |#2| (QUOTE (-761))) (-3321 (|HasCategory| |#2| (QUOTE (-761))) (|HasCategory| |#2| (QUOTE (-788)))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) +((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-951))) (|HasCategory| |#2| (QUOTE (-761))) (-3150 (|HasCategory| |#2| (QUOTE (-761))) (|HasCategory| |#2| (QUOTE (-788)))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -265) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-788))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-842)))) (|HasCategory| |#2| (QUOTE (-136))))) (-806 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 (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))))) (-807) ((|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 @@ -3211,7 +3211,7 @@ NIL (-820 |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 (-2247 (|HasCategory| |#2| (QUOTE (-975)))) (-2247 (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))))) (-12 (|HasCategory| |#2| (QUOTE (-975))) (-2247 (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089))))) +((-12 (-3389 (|HasCategory| |#2| (QUOTE (-975)))) (-3389 (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))))) (-12 (|HasCategory| |#2| (QUOTE (-975))) (-3389 (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089))))) (-821 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 @@ -3220,7 +3220,7 @@ 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 -(-823 R -4196) +(-823 R -1796) ((|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 @@ -3244,7 +3244,7 @@ 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 -(-829 UP -3576) +(-829 UP -1730) ((|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 @@ -3267,7 +3267,7 @@ NIL (-834 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 (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-835 |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 @@ -3283,7 +3283,7 @@ NIL (-838 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."))) ((-4247 . T)) -((-3321 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-788)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-788)))) +((-3150 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-788)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-788)))) (-839 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 @@ -3304,7 +3304,7 @@ 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."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) ((|HasCategory| $ (QUOTE (-138))) (|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-346)))) -(-844 R0 -3576 UP UPUP R) +(-844 R0 -1730 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 @@ -3332,7 +3332,7 @@ 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 -(-851 -3576) +(-851 -1730) ((|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 @@ -3348,11 +3348,11 @@ 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}."))) (((-4252 "*") . T)) NIL -(-855 -3576 P) +(-855 -1730 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-856 |xx| -3576) +(-856 |xx| -1730) ((|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 @@ -3376,7 +3376,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-862 R -3576) +(-862 R -1730) ((|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 @@ -3388,7 +3388,7 @@ 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 -(-865 S R -3576) +(-865 S R -1730) ((|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 @@ -3408,11 +3408,11 @@ 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 -819) (|devaluate| |#1|)))) -(-870 R -3576 -4196) +(-870 R -1730 -1796) ((|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 -(-871 -4196) +(-871 -1796) ((|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 @@ -3435,7 +3435,7 @@ NIL (-876 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-877 |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 @@ -3460,7 +3460,7 @@ 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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) NIL -(-883 E V R P -3576) +(-883 E V R P -1730) ((|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 @@ -3471,8 +3471,8 @@ NIL (-885 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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) -(-886 E V R P -3576) +((|HasCategory| |#1| (QUOTE (-842))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1089) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +(-886 E V R P -1730) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-429)))) @@ -3491,12 +3491,12 @@ NIL (-890 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-891) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-892 -3576) +(-892 -1730) ((|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 @@ -3511,11 +3511,11 @@ NIL (-895 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}"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-126)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248))) (-896 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"))) ((-4247 -12 (|has| |#2| (-450)) (|has| |#1| (-450)))) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668))))) (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-346)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-450)))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668)))) (-12 (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-734))))) (-12 (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-668)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-126))) (|HasCategory| |#2| (QUOTE (-126)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-897) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3530,7 +3530,7 @@ NIL NIL (-900 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-901 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}}"))) @@ -3558,7 +3558,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-517)))) (-907 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."))) -((-4250 . T) (-2137 . T)) +((-4250 . T) (-4131 . T)) NIL (-908 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."))) @@ -3574,7 +3574,7 @@ NIL NIL (-911 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}."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-912 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3592,7 +3592,7 @@ 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 -(-916 K R UP -3576) +(-916 K R UP -1730) ((|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 @@ -3622,7 +3622,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-510))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-951))) (|HasCategory| |#2| (QUOTE (-761))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-1065)))) (-923 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}."))) -((-2137 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4131 . T) (-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-924 |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}."))) @@ -3630,7 +3630,7 @@ NIL NIL (-925 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."))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-926 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}."))) @@ -3647,11 +3647,11 @@ NIL (-929 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.}"))) ((-4243 |has| |#1| (-269)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-510))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-269))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -486) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -265) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-510))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))))) (-930 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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-931 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3660,14 +3660,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-933 -3576 UP UPUP |radicnd| |n|) +(-933 -1730 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4243 |has| (-385 |#2|) (-341)) (-4248 |has| (-385 |#2|) (-341)) (-4242 |has| (-385 |#2|) (-341)) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3321 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3321 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3321 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3321 (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) +((|HasCategory| (-385 |#2|) (QUOTE (-136))) (|HasCategory| (-385 |#2|) (QUOTE (-138))) (|HasCategory| (-385 |#2|) (QUOTE (-327))) (-3150 (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (|HasCategory| (-385 |#2|) (QUOTE (-341))) (|HasCategory| (-385 |#2|) (QUOTE (-346))) (-3150 (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (|HasCategory| (-385 |#2|) (QUOTE (-327)))) (-3150 (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-327))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3150 (|HasCategory| (-385 |#2|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-385 |#2|) (QUOTE (-341)))) (-12 (|HasCategory| (-385 |#2|) (QUOTE (-213))) (|HasCategory| (-385 |#2|) (QUOTE (-341))))) (-934 |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."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3321 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) +((|HasCategory| (-525) (QUOTE (-842))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-1089)))) (|HasCategory| (-525) (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-138))) (|HasCategory| (-525) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-951))) (|HasCategory| (-525) (QUOTE (-761))) (-3150 (|HasCategory| (-525) (QUOTE (-761))) (|HasCategory| (-525) (QUOTE (-788)))) (|HasCategory| (-525) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-1065))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| (-525) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| (-525) (QUOTE (-213))) (|HasCategory| (-525) (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| (-525) (LIST (QUOTE -486) (QUOTE (-1089)) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -288) (QUOTE (-525)))) (|HasCategory| (-525) (LIST (QUOTE -265) (QUOTE (-525)) (QUOTE (-525)))) (|HasCategory| (-525) (QUOTE (-286))) (|HasCategory| (-525) (QUOTE (-510))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-525) (LIST (QUOTE -587) (QUOTE (-525)))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| (-525) (QUOTE (-842)))) (|HasCategory| (-525) (QUOTE (-136))))) (-935) ((|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 @@ -3690,7 +3690,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4251)) (|HasCategory| |#2| (QUOTE (-1018)))) (-940 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}."))) -((-2137 . T)) +((-4131 . T)) NIL (-941 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}}"))) @@ -3700,19 +3700,19 @@ 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}}"))) ((-4243 . T) (-4248 . T) (-4242 . T) (-4245 . T) (-4244 . T) ((-4252 "*") . T) (-4247 . T)) NIL -(-943 R -3576) +(-943 R -1730) ((|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 -(-944 R -3576) +(-944 R -1730) ((|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 -(-945 -3576 UP) +(-945 -1730 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 -(-946 -3576 UP) +(-946 -1730 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 @@ -3743,8 +3743,8 @@ NIL (-953 |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"))) ((-4243 . T) (-4248 . T) (-4242 . T) (-4245 . T) (-4244 . T) ((-4252 "*") . T) (-4247 . T)) -((-3321 (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (QUOTE (-525))))) -(-954 -3576 L) +((-3150 (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-385 (-525)) (LIST (QUOTE -966) (QUOTE (-525))))) +(-954 -1730 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 @@ -3780,14 +3780,14 @@ 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 -(-963 -3576 |Expon| |VarSet| |FPol| |LFPol|) +(-963 -1730 |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"))) (((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-964) ((|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.}"))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (QUOTE (-1089))) (LIST (QUOTE |:|) (QUOTE -1221) (QUOTE (-51))))))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-1089) (QUOTE (-788))) (|HasCategory| (-51) (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (QUOTE (-1089))) (LIST (QUOTE |:|) (QUOTE -1568) (QUOTE (-51))))))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-1089) (QUOTE (-788))) (|HasCategory| (-51) (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) (-965 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 @@ -3832,7 +3832,7 @@ 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."))) ((-4247 . T)) NIL -(-976 |xx| -3576) +(-976 |xx| -1730) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3842,12 +3842,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-286))) (|HasCategory| |#4| (QUOTE (-341))) (|HasCategory| |#4| (QUOTE (-517))) (|HasCategory| |#4| (QUOTE (-160)))) (-978 |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"))) -((-4250 . T) (-2137 . T) (-4245 . T) (-4244 . T)) +((-4250 . T) (-4131 . T) (-4245 . T) (-4244 . T)) NIL (-979 |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}."))) ((-4250 . T) (-4245 . T) (-4244 . T)) -((-3321 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) +((-3150 (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (QUOTE (-341)))) (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (QUOTE (-286))) (|HasCategory| |#3| (QUOTE (-517))) (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|))))) (-980 |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 @@ -3879,7 +3879,7 @@ NIL (-987) ((|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}"))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (QUOTE (-1089))) (LIST (QUOTE |:|) (QUOTE -1221) (QUOTE (-51))))))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (QUOTE (-1018))) (|HasCategory| (-1089) (QUOTE (-788))) (|HasCategory| (-51) (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (QUOTE (-1089))) (LIST (QUOTE |:|) (QUOTE -1568) (QUOTE (-51))))))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-51) (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| (-51) (QUOTE (-1018))) (|HasCategory| (-51) (LIST (QUOTE -288) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (QUOTE (-1018))) (|HasCategory| (-1089) (QUOTE (-788))) (|HasCategory| (-51) (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-51) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (LIST (QUOTE -565) (QUOTE (-796))))) (-988 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 @@ -3906,7 +3906,7 @@ NIL NIL (-994 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}."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-995 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."))) @@ -3916,11 +3916,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-997 |Base| R -3576) +(-997 |Base| R -1730) ((|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 -(-998 |Base| R -3576) +(-998 |Base| R -1730) ((|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 @@ -3935,7 +3935,7 @@ NIL (-1001 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."))) ((-4243 |has| |#1| (-341)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089))))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) +((|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-327))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-327)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-346))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341)))) (|HasCategory| |#1| (QUOTE (-327)))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-327))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (-12 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089))))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341)))) (-12 (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (QUOTE (-341))))) (-1002 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 @@ -3959,7 +3959,7 @@ NIL (-1007 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"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1008 (-1089)) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1008 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 @@ -3978,7 +3978,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1018)))) (-1012 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."))) -((-2137 . T)) +((-4131 . T)) NIL (-1013 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3986,7 +3986,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1018)))) (-1014 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2137 . T)) +((-4131 . T)) NIL (-1015 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3994,7 +3994,7 @@ NIL NIL (-1016 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4240 . T) (-2137 . T)) +((-4240 . T) (-4131 . T)) NIL (-1017 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}."))) @@ -4011,7 +4011,7 @@ NIL (-1020 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)}}"))) ((-4250 . T) (-4240 . T) (-4251 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-346))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-1021 |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 @@ -4038,7 +4038,7 @@ NIL NIL (-1027 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.}"))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-1028) ((|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."))) @@ -4055,12 +4055,12 @@ NIL (-1031 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-160))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-341))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-346))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-734))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-786))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525)))))) (|HasCategory| (-525) (QUOTE (-788))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#3| (QUOTE (-213))) (|HasCategory| |#3| (QUOTE (-975)))) (-12 (|HasCategory| |#3| (QUOTE (-975))) (|HasCategory| |#3| (LIST (QUOTE -833) (QUOTE (-1089))))) (|HasCategory| |#3| (QUOTE (-668))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525))))) (-3150 (|HasCategory| |#3| (QUOTE (-975))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -966) (QUOTE (-525)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#3| (QUOTE (-1018)))) (|HasAttribute| |#3| (QUOTE -4247)) (|HasCategory| |#3| (QUOTE (-126))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1018))) (|HasCategory| |#3| (LIST (QUOTE -288) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -565) (QUOTE (-796))))) (-1032 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-429)))) -(-1033 R -3576) +(-1033 R -1730) ((|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 @@ -4078,7 +4078,7 @@ NIL NIL (-1037 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4250 . T) (-4251 . T) (-2137 . T)) +((-4250 . T) (-4251 . T) (-4131 . T)) NIL (-1038 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4086,7 +4086,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-341))) (|HasAttribute| |#3| (QUOTE (-4252 "*"))) (|HasCategory| |#3| (QUOTE (-160)))) (-1039 |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."))) -((-2137 . T) (-4250 . T) (-4244 . T) (-4245 . T) (-4247 . T)) +((-4131 . T) (-4250 . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL (-1040 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}."))) @@ -4095,16 +4095,16 @@ NIL (-1041 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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-842))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3321 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) +((|HasCategory| |#1| (QUOTE (-842))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (|HasCategory| |#1| (QUOTE (-429))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1042 |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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1043 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}"))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL -(-1044 UP -3576) +(-1044 UP -1730) ((|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 @@ -4151,18 +4151,18 @@ NIL (-1055 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."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018))) (-3321 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018))))) (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018))) (-3150 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -565) (QUOTE (-796)))) (-12 (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -288) (LIST (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1018))))) (|HasCategory| (-1054 |#1| |#2|) (LIST (QUOTE -565) (QUOTE (-796))))) (-1056 |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}."))) ((-4247 . T) (-4239 |has| |#2| (-6 (-4252 "*"))) (-4250 . T) (-4244 . T) (-4245 . T)) -((|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (-3321 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-341))) (-3321 (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-160)))) +((|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213))) (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-525)))) (-3150 (-12 (|HasCategory| |#2| (QUOTE (-213))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))))) (|HasCategory| |#2| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-286))) (|HasCategory| |#2| (QUOTE (-517))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-341))) (-3150 (|HasAttribute| |#2| (QUOTE (-4252 "*"))) (|HasCategory| |#2| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasCategory| |#2| (QUOTE (-213)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-160)))) (-1057 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1058) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-1059 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4175,19 +4175,19 @@ NIL (-1061 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-1062 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 (-1063 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})}."))) -((-2137 . T)) +((-4131 . T)) NIL (-1064 |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."))) ((-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-788))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-788))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-1065) ((|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 @@ -4211,19 +4211,19 @@ NIL (-1070 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."))) ((-4251 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-1071) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-1072) NIL ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135)))))) (|HasCategory| (-135) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| (-135) (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| (-135) (QUOTE (-1018))) (-12 (|HasCategory| (-135) (QUOTE (-1018))) (|HasCategory| (-135) (LIST (QUOTE -288) (QUOTE (-135))))) (|HasCategory| (-135) (LIST (QUOTE -565) (QUOTE (-796))))) (-1073 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#1|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (QUOTE (-1018))) (|HasCategory| (-1072) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (QUOTE (-1072))) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#1|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (QUOTE (-1018))) (|HasCategory| (-1072) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-1074 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 @@ -4250,9 +4250,9 @@ NIL NIL (-1080 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4252 "*") -3321 (-1213 (|has| |#1| (-341)) (|has| (-1087 |#1| |#2| |#3|) (-761))) (|has| |#1| (-160)) (-1213 (|has| |#1| (-341)) (|has| (-1087 |#1| |#2| |#3|) (-842)))) (-4243 -3321 (-1213 (|has| |#1| (-341)) (|has| (-1087 |#1| |#2| |#3|) (-761))) (|has| |#1| (-517)) (-1213 (|has| |#1| (-341)) (|has| (-1087 |#1| |#2| |#3|) (-842)))) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . 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T)) -((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-357))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -819) (QUOTE (-525)))) (|HasCategory| |#1| (LIST (QUOTE -819) (QUOTE (-525))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-357)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -566) (LIST (QUOTE -825) (QUOTE (-525)))))) (-12 (|HasCategory| (-1003) (LIST (QUOTE -566) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -587) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE 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(-842)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| |#1| (QUOTE (-213))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (-3150 (-12 (|HasCategory| $ (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (QUOTE (-136))))) (-1086 |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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-1087 |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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|)))) (|HasCategory| (-712) (QUOTE (-1030))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|)))) (|HasCategory| (-712) (QUOTE (-1030))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-1088) ((|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 @@ -4295,7 +4295,7 @@ NIL (-1091 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-6 -4248)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-902) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-429))) (-12 (|HasCategory| (-902) (QUOTE (-126))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasAttribute| |#1| (QUOTE -4248))) (-1092) ((|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 @@ -4327,7 +4327,7 @@ NIL (-1099 |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}"))) ((-4250 . T) (-4251 . T)) -((-12 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2019) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1221) (|devaluate| |#2|)))))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3321 (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -288) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1265) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1568) (|devaluate| |#2|)))))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1018)))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -566) (QUOTE (-501)))) (-12 (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (LIST (QUOTE -288) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-1018))) (-3150 (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#2| (LIST (QUOTE -565) (QUOTE (-796)))) (|HasCategory| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (LIST (QUOTE -565) (QUOTE (-796))))) (-1100 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 @@ -4338,7 +4338,7 @@ NIL NIL (-1102 |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})}."))) -((-4251 . T) (-2137 . T)) +((-4251 . T) (-4131 . T)) NIL (-1103 |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."))) @@ -4379,7 +4379,7 @@ NIL (-1112 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4251 . T) (-4250 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1018))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-1113 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4388,7 +4388,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1115 R -3576) +(-1115 R -1730) ((|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 @@ -4396,7 +4396,7 @@ 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 -(-1117 R -3576) +(-1117 R -1730) ((|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 -566) (LIST (QUOTE -825) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -819) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -566) (LIST (QUOTE -825) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -819) (|devaluate| |#1|))))) @@ -4406,12 +4406,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-346)))) (-1119 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-1120 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4245 . T) (-4244 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#1| (QUOTE (-136))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-341)))) (-1121 |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 @@ -4424,13 +4424,13 @@ 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 (-1018))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) -(-1124 -3576) +(-1124 -1730) ((|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 (-1125) ((|constructor| (NIL "The fundamental Type."))) -((-2137 . T)) +((-4131 . T)) NIL (-1126 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}.}"))) @@ -4462,16 +4462,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-341)))) (-1133 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) 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factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|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."))) (((-4252 "*") |has| |#2| (-160)) (-4243 |has| |#2| (-517)) (-4246 |has| |#2| (-341)) (-4248 |has| |#2| (-6 -4248)) (-4245 . T) (-4244 . T) (-4247 . 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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 @@ -4523,7 +4523,7 @@ NIL (-1148 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 -833) (QUOTE (-1089)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1030))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3022) (LIST (|devaluate| |#2|) (QUOTE (-1089)))))) +((|HasCategory| |#2| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1030))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2686) (LIST (|devaluate| |#2|) (QUOTE (-1089)))))) (-1149 |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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) @@ -4551,22 +4551,22 @@ NIL (-1155 |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)}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) +((|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-1156 |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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4248 |has| |#1| (-341)) (-4242 |has| |#1| (-341)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3321 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (|HasCategory| |#1| (QUOTE (-160))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525))) (|devaluate| |#1|)))) (|HasCategory| (-385 (-525)) (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-3150 (|HasCategory| |#1| (QUOTE (-341))) (|HasCategory| |#1| (QUOTE (-517)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -385) (QUOTE (-525)))))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-1157 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))}."))) (((-4252 "*") |has| (-1156 |#2| |#3| |#4|) (-160)) (-4243 |has| (-1156 |#2| |#3| |#4|) (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-429))) (-3321 (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-517)))) +((|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-138))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-160))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (QUOTE (-525)))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-341))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-429))) (-3150 (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (LIST (QUOTE -966) (LIST (QUOTE -385) (QUOTE (-525)))))) (|HasCategory| (-1156 |#2| |#3| |#4|) (QUOTE (-517)))) (-1158 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4251))) (-1159 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2137 . T)) +((-4131 . T)) NIL (-1160 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4575,7 +4575,7 @@ NIL (-1161 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4141) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2452) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#2| (QUOTE (-341)))) (-1162 |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."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) @@ -4583,18 +4583,18 @@ NIL (-1163 |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}."))) (((-4252 "*") |has| |#1| (-160)) (-4243 |has| |#1| (-517)) (-4244 . T) (-4245 . T) (-4247 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3321 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|)))) (|HasCategory| (-712) (QUOTE (-1030))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasSignature| |#1| (LIST (QUOTE -3022) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasCategory| |#1| (QUOTE (-341))) (-3321 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -4141) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1507) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasCategory| |#1| (QUOTE (-517))) (-3150 (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-160))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-138))) (-12 (|HasCategory| |#1| (LIST (QUOTE -833) (QUOTE (-1089)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-712)) (|devaluate| |#1|)))) (|HasCategory| (-712) (QUOTE (-1030))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasSignature| |#1| (LIST (QUOTE -2686) (LIST (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-712))))) (|HasCategory| |#1| (QUOTE (-341))) (-3150 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-525)))) (|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -385) (QUOTE (-525))))) (|HasSignature| |#1| (LIST (QUOTE -2452) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (LIST (QUOTE -1444) (LIST (LIST (QUOTE -591) (QUOTE (-1089))) (|devaluate| |#1|))))))) (-1164 |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 -(-1165 -3576 UP L UTS) +(-1165 -1730 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-517)))) (-1166) ((|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."))) -((-2137 . T)) +((-4131 . T)) NIL (-1167 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4606,7 +4606,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-668))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1169 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4251 . T) (-4250 . T) (-2137 . T)) +((-4251 . T) (-4250 . T) (-4131 . T)) NIL (-1170 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4615,7 +4615,7 @@ NIL (-1171 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4251 . T) (-4250 . T)) -((-3321 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3321 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3321 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) +((-3150 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|))))) (-3150 (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (|HasCategory| |#1| (LIST (QUOTE -566) (QUOTE (-501)))) (-3150 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018)))) (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| (-525) (QUOTE (-788))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-668))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-975)))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -288) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -565) (QUOTE (-796))))) (-1172) ((|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 @@ -4648,7 +4648,7 @@ 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 -(-1180 K R UP -3576) +(-1180 K R UP -1730) ((|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 @@ -4676,11 +4676,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4243 |has| |#2| (-6 -4243)) (-4245 . T) (-4244 . T) (-4247 . T)) NIL -(-1187 S -3576) +(-1187 S -1730) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-346))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-138)))) -(-1188 -3576) +(-1188 -1730) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4242 . T) (-4248 . T) (-4243 . T) ((-4252 "*") . T) (-4244 . T) (-4245 . T) (-4247 . T)) NIL @@ -4736,4 +4736,4 @@ NIL NIL NIL NIL -((-3 NIL 2237757 2237762 2237767 2237772) (-2 NIL 2237737 2237742 2237747 2237752) (-1 NIL 2237717 2237722 2237727 2237732) (0 NIL 2237697 2237702 2237707 2237712) (-1197 "ZMOD.spad" 2237506 2237519 2237635 2237692) (-1196 "ZLINDEP.spad" 2236550 2236561 2237496 2237501) (-1195 "ZDSOLVE.spad" 2226399 2226421 2236540 2236545) (-1194 "YSTREAM.spad" 2225892 2225903 2226389 2226394) (-1193 "XRPOLY.spad" 2225112 2225132 2225748 2225817) (-1192 "XPR.spad" 2222841 2222854 2224830 2224929) (-1191 "XPOLY.spad" 2222396 2222407 2222697 2222766) (-1190 "XPOLYC.spad" 2221713 2221729 2222322 2222391) (-1189 "XPBWPOLY.spad" 2220150 2220170 2221493 2221562) (-1188 "XF.spad" 2218611 2218626 2220052 2220145) (-1187 "XF.spad" 2217052 2217069 2218495 2218500) (-1186 "XFALG.spad" 2214076 2214092 2216978 2217047) (-1185 "XEXPPKG.spad" 2213327 2213353 2214066 2214071) (-1184 "XDPOLY.spad" 2212941 2212957 2213183 2213252) (-1183 "XALG.spad" 2212539 2212550 2212897 2212936) (-1182 "WUTSET.spad" 2208378 2208395 2212185 2212212) (-1181 "WP.spad" 2207392 2207436 2208236 2208303) (-1180 "WFFINTBS.spad" 2204955 2204977 2207382 2207387) (-1179 "WEIER.spad" 2203169 2203180 2204945 2204950) (-1178 "VSPACE.spad" 2202842 2202853 2203137 2203164) (-1177 "VSPACE.spad" 2202535 2202548 2202832 2202837) (-1176 "VOID.spad" 2202125 2202134 2202525 2202530) (-1175 "VIEW.spad" 2199747 2199756 2202115 2202120) (-1174 "VIEWDEF.spad" 2194944 2194953 2199737 2199742) (-1173 "VIEW3D.spad" 2178779 2178788 2194934 2194939) (-1172 "VIEW2D.spad" 2166516 2166525 2178769 2178774) (-1171 "VECTOR.spad" 2165193 2165204 2165444 2165471) (-1170 "VECTOR2.spad" 2163820 2163833 2165183 2165188) (-1169 "VECTCAT.spad" 2161708 2161719 2163776 2163815) (-1168 "VECTCAT.spad" 2159417 2159430 2161487 2161492) (-1167 "VARIABLE.spad" 2159197 2159212 2159407 2159412) (-1166 "UTYPE.spad" 2158831 2158840 2159177 2159192) (-1165 "UTSODETL.spad" 2158124 2158148 2158787 2158792) (-1164 "UTSODE.spad" 2156312 2156332 2158114 2158119) (-1163 "UTS.spad" 2151101 2151129 2154779 2154876) (-1162 "UTSCAT.spad" 2148552 2148568 2150999 2151096) (-1161 "UTSCAT.spad" 2145647 2145665 2148096 2148101) (-1160 "UTS2.spad" 2145240 2145275 2145637 2145642) (-1159 "URAGG.spad" 2139862 2139873 2145220 2145235) (-1158 "URAGG.spad" 2134458 2134471 2139818 2139823) (-1157 "UPXSSING.spad" 2132104 2132130 2133542 2133675) (-1156 "UPXS.spad" 2129131 2129159 2130236 2130385) (-1155 "UPXSCONS.spad" 2126888 2126908 2127263 2127412) (-1154 "UPXSCCA.spad" 2125346 2125366 2126734 2126883) (-1153 "UPXSCCA.spad" 2123946 2123968 2125336 2125341) (-1152 "UPXSCAT.spad" 2122527 2122543 2123792 2123941) (-1151 "UPXS2.spad" 2122068 2122121 2122517 2122522) (-1150 "UPSQFREE.spad" 2120480 2120494 2122058 2122063) (-1149 "UPSCAT.spad" 2118073 2118097 2120378 2120475) (-1148 "UPSCAT.spad" 2115372 2115398 2117679 2117684) (-1147 "UPOLYC.spad" 2110350 2110361 2115214 2115367) (-1146 "UPOLYC.spad" 2105220 2105233 2110086 2110091) (-1145 "UPOLYC2.spad" 2104689 2104708 2105210 2105215) (-1144 "UP.spad" 2101734 2101749 2102242 2102395) (-1143 "UPMP.spad" 2100624 2100637 2101724 2101729) (-1142 "UPDIVP.spad" 2100187 2100201 2100614 2100619) (-1141 "UPDECOMP.spad" 2098424 2098438 2100177 2100182) (-1140 "UPCDEN.spad" 2097631 2097647 2098414 2098419) (-1139 "UP2.spad" 2096993 2097014 2097621 2097626) (-1138 "UNISEG.spad" 2096346 2096357 2096912 2096917) (-1137 "UNISEG2.spad" 2095839 2095852 2096302 2096307) (-1136 "UNIFACT.spad" 2094940 2094952 2095829 2095834) (-1135 "ULS.spad" 2085499 2085527 2086592 2087021) (-1134 "ULSCONS.spad" 2079542 2079562 2079914 2080063) (-1133 "ULSCCAT.spad" 2077139 2077159 2079362 2079537) (-1132 "ULSCCAT.spad" 2074870 2074892 2077095 2077100) (-1131 "ULSCAT.spad" 2073086 2073102 2074716 2074865) (-1130 "ULS2.spad" 2072598 2072651 2073076 2073081) (-1129 "UFD.spad" 2071663 2071672 2072524 2072593) (-1128 "UFD.spad" 2070790 2070801 2071653 2071658) (-1127 "UDVO.spad" 2069637 2069646 2070780 2070785) (-1126 "UDPO.spad" 2067064 2067075 2069593 2069598) (-1125 "TYPE.spad" 2066986 2066995 2067044 2067059) (-1124 "TWOFACT.spad" 2065636 2065651 2066976 2066981) (-1123 "TUPLE.spad" 2065022 2065033 2065535 2065540) (-1122 "TUBETOOL.spad" 2061859 2061868 2065012 2065017) (-1121 "TUBE.spad" 2060500 2060517 2061849 2061854) (-1120 "TS.spad" 2059089 2059105 2060065 2060162) (-1119 "TSETCAT.spad" 2046204 2046221 2059045 2059084) (-1118 "TSETCAT.spad" 2033317 2033336 2046160 2046165) (-1117 "TRMANIP.spad" 2027683 2027700 2033023 2033028) (-1116 "TRIMAT.spad" 2026642 2026667 2027673 2027678) (-1115 "TRIGMNIP.spad" 2025159 2025176 2026632 2026637) (-1114 "TRIGCAT.spad" 2024671 2024680 2025149 2025154) (-1113 "TRIGCAT.spad" 2024181 2024192 2024661 2024666) (-1112 "TREE.spad" 2022752 2022763 2023788 2023815) (-1111 "TRANFUN.spad" 2022583 2022592 2022742 2022747) (-1110 "TRANFUN.spad" 2022412 2022423 2022573 2022578) (-1109 "TOPSP.spad" 2022086 2022095 2022402 2022407) (-1108 "TOOLSIGN.spad" 2021749 2021760 2022076 2022081) (-1107 "TEXTFILE.spad" 2020306 2020315 2021739 2021744) (-1106 "TEX.spad" 2017323 2017332 2020296 2020301) (-1105 "TEX1.spad" 2016879 2016890 2017313 2017318) (-1104 "TEMUTL.spad" 2016434 2016443 2016869 2016874) (-1103 "TBCMPPK.spad" 2014527 2014550 2016424 2016429) (-1102 "TBAGG.spad" 2013551 2013574 2014495 2014522) (-1101 "TBAGG.spad" 2012595 2012620 2013541 2013546) (-1100 "TANEXP.spad" 2011971 2011982 2012585 2012590) (-1099 "TABLE.spad" 2010382 2010405 2010652 2010679) (-1098 "TABLEAU.spad" 2009863 2009874 2010372 2010377) (-1097 "TABLBUMP.spad" 2006646 2006657 2009853 2009858) (-1096 "SYSTEM.spad" 2005920 2005929 2006636 2006641) (-1095 "SYSSOLP.spad" 2003393 2003404 2005910 2005915) (-1094 "SYNTAX.spad" 1999585 1999594 2003383 2003388) (-1093 "SYMTAB.spad" 1997641 1997650 1999575 1999580) (-1092 "SYMS.spad" 1993626 1993635 1997631 1997636) (-1091 "SYMPOLY.spad" 1992636 1992647 1992718 1992845) (-1090 "SYMFUNC.spad" 1992111 1992122 1992626 1992631) (-1089 "SYMBOL.spad" 1989447 1989456 1992101 1992106) (-1088 "SWITCH.spad" 1986204 1986213 1989437 1989442) (-1087 "SUTS.spad" 1983103 1983131 1984671 1984768) (-1086 "SUPXS.spad" 1980117 1980145 1981235 1981384) (-1085 "SUP.spad" 1976889 1976900 1977670 1977823) (-1084 "SUPFRACF.spad" 1975994 1976012 1976879 1976884) (-1083 "SUP2.spad" 1975384 1975397 1975984 1975989) (-1082 "SUMRF.spad" 1974350 1974361 1975374 1975379) (-1081 "SUMFS.spad" 1973983 1974000 1974340 1974345) (-1080 "SULS.spad" 1964529 1964557 1965635 1966064) (-1079 "SUCH.spad" 1964209 1964224 1964519 1964524) (-1078 "SUBSPACE.spad" 1956216 1956231 1964199 1964204) (-1077 "SUBRESP.spad" 1955376 1955390 1956172 1956177) (-1076 "STTF.spad" 1951475 1951491 1955366 1955371) (-1075 "STTFNC.spad" 1947943 1947959 1951465 1951470) (-1074 "STTAYLOR.spad" 1940341 1940352 1947824 1947829) (-1073 "STRTBL.spad" 1938846 1938863 1938995 1939022) (-1072 "STRING.spad" 1938255 1938264 1938269 1938296) (-1071 "STRICAT.spad" 1938031 1938040 1938211 1938250) (-1070 "STREAM.spad" 1934799 1934810 1937556 1937571) (-1069 "STREAM3.spad" 1934344 1934359 1934789 1934794) (-1068 "STREAM2.spad" 1933412 1933425 1934334 1934339) (-1067 "STREAM1.spad" 1933116 1933127 1933402 1933407) (-1066 "STINPROD.spad" 1932022 1932038 1933106 1933111) (-1065 "STEP.spad" 1931223 1931232 1932012 1932017) (-1064 "STBL.spad" 1929749 1929777 1929916 1929931) (-1063 "STAGG.spad" 1928814 1928825 1929729 1929744) (-1062 "STAGG.spad" 1927887 1927900 1928804 1928809) (-1061 "STACK.spad" 1927238 1927249 1927494 1927521) (-1060 "SREGSET.spad" 1924942 1924959 1926884 1926911) (-1059 "SRDCMPK.spad" 1923487 1923507 1924932 1924937) (-1058 "SRAGG.spad" 1918572 1918581 1923443 1923482) (-1057 "SRAGG.spad" 1913689 1913700 1918562 1918567) (-1056 "SQMATRIX.spad" 1911315 1911333 1912223 1912310) (-1055 "SPLTREE.spad" 1905867 1905880 1910751 1910778) (-1054 "SPLNODE.spad" 1902455 1902468 1905857 1905862) (-1053 "SPFCAT.spad" 1901232 1901241 1902445 1902450) (-1052 "SPECOUT.spad" 1899782 1899791 1901222 1901227) (-1051 "spad-parser.spad" 1899247 1899256 1899772 1899777) (-1050 "SPACEC.spad" 1883260 1883271 1899237 1899242) (-1049 "SPACE3.spad" 1883036 1883047 1883250 1883255) (-1048 "SORTPAK.spad" 1882581 1882594 1882992 1882997) (-1047 "SOLVETRA.spad" 1880338 1880349 1882571 1882576) (-1046 "SOLVESER.spad" 1878858 1878869 1880328 1880333) (-1045 "SOLVERAD.spad" 1874868 1874879 1878848 1878853) (-1044 "SOLVEFOR.spad" 1873288 1873306 1874858 1874863) (-1043 "SNTSCAT.spad" 1872876 1872893 1873244 1873283) (-1042 "SMTS.spad" 1871136 1871162 1872441 1872538) (-1041 "SMP.spad" 1868578 1868598 1868968 1869095) (-1040 "SMITH.spad" 1867421 1867446 1868568 1868573) (-1039 "SMATCAT.spad" 1865519 1865549 1867353 1867416) (-1038 "SMATCAT.spad" 1863561 1863593 1865397 1865402) (-1037 "SKAGG.spad" 1862510 1862521 1863517 1863556) (-1036 "SINT.spad" 1860818 1860827 1862376 1862505) (-1035 "SIMPAN.spad" 1860546 1860555 1860808 1860813) (-1034 "SIGNRF.spad" 1859654 1859665 1860536 1860541) (-1033 "SIGNEF.spad" 1858923 1858940 1859644 1859649) (-1032 "SHP.spad" 1856841 1856856 1858879 1858884) (-1031 "SHDP.spad" 1848231 1848258 1848740 1848869) (-1030 "SGROUP.spad" 1847697 1847706 1848221 1848226) (-1029 "SGROUP.spad" 1847161 1847172 1847687 1847692) (-1028 "SGCF.spad" 1840042 1840051 1847151 1847156) (-1027 "SFRTCAT.spad" 1838958 1838975 1839998 1840037) (-1026 "SFRGCD.spad" 1838021 1838041 1838948 1838953) (-1025 "SFQCMPK.spad" 1832658 1832678 1838011 1838016) (-1024 "SFORT.spad" 1832093 1832107 1832648 1832653) (-1023 "SEXOF.spad" 1831936 1831976 1832083 1832088) (-1022 "SEX.spad" 1831828 1831837 1831926 1831931) (-1021 "SEXCAT.spad" 1828932 1828972 1831818 1831823) (-1020 "SET.spad" 1827232 1827243 1828353 1828392) (-1019 "SETMN.spad" 1825666 1825683 1827222 1827227) (-1018 "SETCAT.spad" 1825151 1825160 1825656 1825661) (-1017 "SETCAT.spad" 1824634 1824645 1825141 1825146) (-1016 "SETAGG.spad" 1821157 1821168 1824602 1824629) (-1015 "SETAGG.spad" 1817700 1817713 1821147 1821152) (-1014 "SEGXCAT.spad" 1816812 1816825 1817680 1817695) (-1013 "SEG.spad" 1816625 1816636 1816731 1816736) (-1012 "SEGCAT.spad" 1815444 1815455 1816605 1816620) (-1011 "SEGBIND.spad" 1814516 1814527 1815399 1815404) (-1010 "SEGBIND2.spad" 1814212 1814225 1814506 1814511) (-1009 "SEG2.spad" 1813637 1813650 1814168 1814173) (-1008 "SDVAR.spad" 1812913 1812924 1813627 1813632) (-1007 "SDPOL.spad" 1810306 1810317 1810597 1810724) (-1006 "SCPKG.spad" 1808385 1808396 1810296 1810301) (-1005 "SCOPE.spad" 1807530 1807539 1808375 1808380) (-1004 "SCACHE.spad" 1806212 1806223 1807520 1807525) (-1003 "SAOS.spad" 1806084 1806093 1806202 1806207) (-1002 "SAERFFC.spad" 1805797 1805817 1806074 1806079) (-1001 "SAE.spad" 1803975 1803991 1804586 1804721) (-1000 "SAEFACT.spad" 1803676 1803696 1803965 1803970) (-999 "RURPK.spad" 1801318 1801333 1803666 1803671) (-998 "RULESET.spad" 1800760 1800783 1801308 1801313) (-997 "RULE.spad" 1798965 1798988 1800750 1800755) (-996 "RULECOLD.spad" 1798818 1798830 1798955 1798960) (-995 "RSETGCD.spad" 1795197 1795216 1798808 1798813) (-994 "RSETCAT.spad" 1784970 1784986 1795153 1795192) (-993 "RSETCAT.spad" 1774775 1774793 1784960 1784965) (-992 "RSDCMPK.spad" 1773228 1773247 1774765 1774770) (-991 "RRCC.spad" 1771613 1771642 1773218 1773223) (-990 "RRCC.spad" 1769996 1770027 1771603 1771608) (-989 "RPOLCAT.spad" 1749357 1749371 1769864 1769991) (-988 "RPOLCAT.spad" 1728433 1728449 1748942 1748947) (-987 "ROUTINE.spad" 1724297 1724305 1727080 1727107) (-986 "ROMAN.spad" 1723530 1723538 1724163 1724292) (-985 "ROIRC.spad" 1722611 1722642 1723520 1723525) (-984 "RNS.spad" 1721515 1721523 1722513 1722606) (-983 "RNS.spad" 1720505 1720515 1721505 1721510) (-982 "RNG.spad" 1720241 1720249 1720495 1720500) (-981 "RMODULE.spad" 1719880 1719890 1720231 1720236) (-980 "RMCAT2.spad" 1719289 1719345 1719870 1719875) (-979 "RMATRIX.spad" 1717969 1717987 1718456 1718495) (-978 "RMATCAT.spad" 1713491 1713521 1717913 1717964) (-977 "RMATCAT.spad" 1708915 1708947 1713339 1713344) (-976 "RINTERP.spad" 1708804 1708823 1708905 1708910) (-975 "RING.spad" 1708162 1708170 1708784 1708799) (-974 "RING.spad" 1707528 1707538 1708152 1708157) (-973 "RIDIST.spad" 1706913 1706921 1707518 1707523) (-972 "RGCHAIN.spad" 1705493 1705508 1706398 1706425) (-971 "RF.spad" 1703108 1703118 1705483 1705488) (-970 "RFFACTOR.spad" 1702571 1702581 1703098 1703103) (-969 "RFFACT.spad" 1702307 1702318 1702561 1702566) (-968 "RFDIST.spad" 1701296 1701304 1702297 1702302) (-967 "RETSOL.spad" 1700714 1700726 1701286 1701291) (-966 "RETRACT.spad" 1700064 1700074 1700704 1700709) (-965 "RETRACT.spad" 1699412 1699424 1700054 1700059) (-964 "RESULT.spad" 1697473 1697481 1698059 1698086) (-963 "RESRING.spad" 1696821 1696867 1697411 1697468) (-962 "RESLATC.spad" 1696146 1696156 1696811 1696816) (-961 "REPSQ.spad" 1695876 1695886 1696136 1696141) (-960 "REP.spad" 1693429 1693437 1695866 1695871) (-959 "REPDB.spad" 1693135 1693145 1693419 1693424) (-958 "REP2.spad" 1682708 1682718 1692977 1692982) (-957 "REP1.spad" 1676699 1676709 1682658 1682663) (-956 "REGSET.spad" 1674497 1674513 1676345 1676372) (-955 "REF.spad" 1673827 1673837 1674452 1674457) (-954 "REDORDER.spad" 1673004 1673020 1673817 1673822) (-953 "RECLOS.spad" 1671794 1671813 1672497 1672590) (-952 "REALSOLV.spad" 1670927 1670935 1671784 1671789) (-951 "REAL.spad" 1670800 1670808 1670917 1670922) (-950 "REAL0Q.spad" 1668083 1668097 1670790 1670795) (-949 "REAL0.spad" 1664912 1664926 1668073 1668078) (-948 "RDIV.spad" 1664564 1664588 1664902 1664907) (-947 "RDIST.spad" 1664128 1664138 1664554 1664559) (-946 "RDETRS.spad" 1662925 1662942 1664118 1664123) (-945 "RDETR.spad" 1661033 1661050 1662915 1662920) (-944 "RDEEFS.spad" 1660107 1660123 1661023 1661028) (-943 "RDEEF.spad" 1659104 1659120 1660097 1660102) (-942 "RCFIELD.spad" 1656288 1656296 1659006 1659099) (-941 "RCFIELD.spad" 1653558 1653568 1656278 1656283) (-940 "RCAGG.spad" 1651461 1651471 1653538 1653553) (-939 "RCAGG.spad" 1649301 1649313 1651380 1651385) (-938 "RATRET.spad" 1648662 1648672 1649291 1649296) (-937 "RATFACT.spad" 1648355 1648366 1648652 1648657) (-936 "RANDSRC.spad" 1647675 1647683 1648345 1648350) (-935 "RADUTIL.spad" 1647430 1647438 1647665 1647670) (-934 "RADIX.spad" 1644223 1644236 1645900 1645993) (-933 "RADFF.spad" 1642640 1642676 1642758 1642914) (-932 "RADCAT.spad" 1642234 1642242 1642630 1642635) (-931 "RADCAT.spad" 1641826 1641836 1642224 1642229) (-930 "QUEUE.spad" 1641169 1641179 1641433 1641460) (-929 "QUAT.spad" 1639755 1639765 1640097 1640162) (-928 "QUATCT2.spad" 1639374 1639392 1639745 1639750) (-927 "QUATCAT.spad" 1637539 1637549 1639304 1639369) (-926 "QUATCAT.spad" 1635456 1635468 1637223 1637228) (-925 "QUAGG.spad" 1634270 1634280 1635412 1635451) (-924 "QFORM.spad" 1633733 1633747 1634260 1634265) (-923 "QFCAT.spad" 1632424 1632434 1633623 1633728) (-922 "QFCAT.spad" 1630721 1630733 1631922 1631927) (-921 "QFCAT2.spad" 1630412 1630428 1630711 1630716) (-920 "QEQUAT.spad" 1629969 1629977 1630402 1630407) (-919 "QCMPACK.spad" 1624716 1624735 1629959 1629964) (-918 "QALGSET.spad" 1620791 1620823 1624630 1624635) (-917 "QALGSET2.spad" 1618787 1618805 1620781 1620786) (-916 "PWFFINTB.spad" 1616097 1616118 1618777 1618782) (-915 "PUSHVAR.spad" 1615426 1615445 1616087 1616092) (-914 "PTRANFN.spad" 1611552 1611562 1615416 1615421) (-913 "PTPACK.spad" 1608640 1608650 1611542 1611547) (-912 "PTFUNC2.spad" 1608461 1608475 1608630 1608635) (-911 "PTCAT.spad" 1607543 1607553 1608417 1608456) (-910 "PSQFR.spad" 1606850 1606874 1607533 1607538) (-909 "PSEUDLIN.spad" 1605708 1605718 1606840 1606845) (-908 "PSETPK.spad" 1591141 1591157 1605586 1605591) (-907 "PSETCAT.spad" 1585049 1585072 1591109 1591136) (-906 "PSETCAT.spad" 1578943 1578968 1585005 1585010) (-905 "PSCURVE.spad" 1577926 1577934 1578933 1578938) (-904 "PSCAT.spad" 1576693 1576722 1577824 1577921) (-903 "PSCAT.spad" 1575550 1575581 1576683 1576688) (-902 "PRTITION.spad" 1574393 1574401 1575540 1575545) (-901 "PRS.spad" 1563955 1563972 1574349 1574354) (-900 "PRQAGG.spad" 1563374 1563384 1563911 1563950) (-899 "PROPLOG.spad" 1562777 1562785 1563364 1563369) (-898 "PROPFRML.spad" 1560642 1560653 1562713 1562718) (-897 "PROPERTY.spad" 1560136 1560144 1560632 1560637) (-896 "PRODUCT.spad" 1557816 1557828 1558102 1558157) (-895 "PR.spad" 1556205 1556217 1556910 1557037) (-894 "PRINT.spad" 1555957 1555965 1556195 1556200) (-893 "PRIMES.spad" 1554208 1554218 1555947 1555952) (-892 "PRIMELT.spad" 1552189 1552203 1554198 1554203) (-891 "PRIMCAT.spad" 1551812 1551820 1552179 1552184) (-890 "PRIMARR.spad" 1550817 1550827 1550995 1551022) (-889 "PRIMARR2.spad" 1549540 1549552 1550807 1550812) (-888 "PREASSOC.spad" 1548912 1548924 1549530 1549535) (-887 "PPCURVE.spad" 1548049 1548057 1548902 1548907) (-886 "POLYROOT.spad" 1546821 1546843 1548005 1548010) (-885 "POLY.spad" 1544121 1544131 1544638 1544765) (-884 "POLYLIFT.spad" 1543382 1543405 1544111 1544116) (-883 "POLYCATQ.spad" 1541484 1541506 1543372 1543377) (-882 "POLYCAT.spad" 1534890 1534911 1541352 1541479) (-881 "POLYCAT.spad" 1527598 1527621 1534062 1534067) (-880 "POLY2UP.spad" 1527046 1527060 1527588 1527593) (-879 "POLY2.spad" 1526641 1526653 1527036 1527041) (-878 "POLUTIL.spad" 1525582 1525611 1526597 1526602) (-877 "POLTOPOL.spad" 1524330 1524345 1525572 1525577) (-876 "POINT.spad" 1523171 1523181 1523258 1523285) (-875 "PNTHEORY.spad" 1519837 1519845 1523161 1523166) (-874 "PMTOOLS.spad" 1518594 1518608 1519827 1519832) (-873 "PMSYM.spad" 1518139 1518149 1518584 1518589) (-872 "PMQFCAT.spad" 1517726 1517740 1518129 1518134) (-871 "PMPRED.spad" 1517195 1517209 1517716 1517721) (-870 "PMPREDFS.spad" 1516639 1516661 1517185 1517190) (-869 "PMPLCAT.spad" 1515709 1515727 1516571 1516576) (-868 "PMLSAGG.spad" 1515290 1515304 1515699 1515704) (-867 "PMKERNEL.spad" 1514857 1514869 1515280 1515285) (-866 "PMINS.spad" 1514433 1514443 1514847 1514852) (-865 "PMFS.spad" 1514006 1514024 1514423 1514428) (-864 "PMDOWN.spad" 1513292 1513306 1513996 1514001) (-863 "PMASS.spad" 1512304 1512312 1513282 1513287) (-862 "PMASSFS.spad" 1511273 1511289 1512294 1512299) (-861 "PLOTTOOL.spad" 1511053 1511061 1511263 1511268) (-860 "PLOT.spad" 1505884 1505892 1511043 1511048) (-859 "PLOT3D.spad" 1502304 1502312 1505874 1505879) (-858 "PLOT1.spad" 1501445 1501455 1502294 1502299) (-857 "PLEQN.spad" 1488661 1488688 1501435 1501440) (-856 "PINTERP.spad" 1488277 1488296 1488651 1488656) (-855 "PINTERPA.spad" 1488059 1488075 1488267 1488272) (-854 "PI.spad" 1487666 1487674 1488033 1488054) (-853 "PID.spad" 1486622 1486630 1487592 1487661) (-852 "PICOERCE.spad" 1486279 1486289 1486612 1486617) (-851 "PGROEB.spad" 1484876 1484890 1486269 1486274) (-850 "PGE.spad" 1476129 1476137 1484866 1484871) (-849 "PGCD.spad" 1475011 1475028 1476119 1476124) (-848 "PFRPAC.spad" 1474154 1474164 1475001 1475006) (-847 "PFR.spad" 1470811 1470821 1474056 1474149) (-846 "PFOTOOLS.spad" 1470069 1470085 1470801 1470806) (-845 "PFOQ.spad" 1469439 1469457 1470059 1470064) (-844 "PFO.spad" 1468858 1468885 1469429 1469434) (-843 "PF.spad" 1468432 1468444 1468663 1468756) (-842 "PFECAT.spad" 1466098 1466106 1468358 1468427) (-841 "PFECAT.spad" 1463792 1463802 1466054 1466059) (-840 "PFBRU.spad" 1461662 1461674 1463782 1463787) (-839 "PFBR.spad" 1459200 1459223 1461652 1461657) (-838 "PERM.spad" 1454881 1454891 1459030 1459045) (-837 "PERMGRP.spad" 1449617 1449627 1454871 1454876) (-836 "PERMCAT.spad" 1448169 1448179 1449597 1449612) (-835 "PERMAN.spad" 1446701 1446715 1448159 1448164) (-834 "PENDTREE.spad" 1445974 1445984 1446330 1446335) (-833 "PDRING.spad" 1444465 1444475 1445954 1445969) (-832 "PDRING.spad" 1442964 1442976 1444455 1444460) (-831 "PDEPROB.spad" 1441921 1441929 1442954 1442959) (-830 "PDEPACK.spad" 1435923 1435931 1441911 1441916) (-829 "PDECOMP.spad" 1435385 1435402 1435913 1435918) (-828 "PDECAT.spad" 1433739 1433747 1435375 1435380) (-827 "PCOMP.spad" 1433590 1433603 1433729 1433734) (-826 "PBWLB.spad" 1432172 1432189 1433580 1433585) (-825 "PATTERN.spad" 1426603 1426613 1432162 1432167) (-824 "PATTERN2.spad" 1426339 1426351 1426593 1426598) (-823 "PATTERN1.spad" 1424641 1424657 1426329 1426334) (-822 "PATRES.spad" 1422188 1422200 1424631 1424636) (-821 "PATRES2.spad" 1421850 1421864 1422178 1422183) (-820 "PATMATCH.spad" 1420012 1420043 1421563 1421568) (-819 "PATMAB.spad" 1419437 1419447 1420002 1420007) (-818 "PATLRES.spad" 1418521 1418535 1419427 1419432) (-817 "PATAB.spad" 1418285 1418295 1418511 1418516) (-816 "PARTPERM.spad" 1415647 1415655 1418275 1418280) (-815 "PARSURF.spad" 1415075 1415103 1415637 1415642) (-814 "PARSU2.spad" 1414870 1414886 1415065 1415070) (-813 "script-parser.spad" 1414390 1414398 1414860 1414865) (-812 "PARSCURV.spad" 1413818 1413846 1414380 1414385) (-811 "PARSC2.spad" 1413607 1413623 1413808 1413813) (-810 "PARPCURV.spad" 1413065 1413093 1413597 1413602) (-809 "PARPC2.spad" 1412854 1412870 1413055 1413060) (-808 "PAN2EXPR.spad" 1412266 1412274 1412844 1412849) (-807 "PALETTE.spad" 1411236 1411244 1412256 1412261) (-806 "PAIR.spad" 1410219 1410232 1410824 1410829) (-805 "PADICRC.spad" 1407552 1407570 1408727 1408820) (-804 "PADICRAT.spad" 1405570 1405582 1405791 1405884) (-803 "PADIC.spad" 1405265 1405277 1405496 1405565) (-802 "PADICCT.spad" 1403806 1403818 1405191 1405260) (-801 "PADEPAC.spad" 1402485 1402504 1403796 1403801) (-800 "PADE.spad" 1401225 1401241 1402475 1402480) (-799 "OWP.spad" 1400209 1400239 1401083 1401150) (-798 "OVAR.spad" 1399990 1400013 1400199 1400204) (-797 "OUT.spad" 1399074 1399082 1399980 1399985) (-796 "OUTFORM.spad" 1388488 1388496 1399064 1399069) (-795 "OSI.spad" 1387963 1387971 1388478 1388483) (-794 "ORTHPOL.spad" 1386424 1386434 1387880 1387885) (-793 "OREUP.spad" 1385784 1385812 1386106 1386145) (-792 "ORESUP.spad" 1385085 1385109 1385466 1385505) (-791 "OREPCTO.spad" 1382904 1382916 1385005 1385010) (-790 "OREPCAT.spad" 1376961 1376971 1382860 1382899) (-789 "OREPCAT.spad" 1370908 1370920 1376809 1376814) (-788 "ORDSET.spad" 1370074 1370082 1370898 1370903) (-787 "ORDSET.spad" 1369238 1369248 1370064 1370069) (-786 "ORDRING.spad" 1368628 1368636 1369218 1369233) (-785 "ORDRING.spad" 1368026 1368036 1368618 1368623) (-784 "ORDMON.spad" 1367881 1367889 1368016 1368021) (-783 "ORDFUNS.spad" 1367007 1367023 1367871 1367876) (-782 "ORDFIN.spad" 1366941 1366949 1366997 1367002) (-781 "ORDCOMP.spad" 1365409 1365419 1366491 1366520) (-780 "ORDCOMP2.spad" 1364694 1364706 1365399 1365404) (-779 "OPTPROB.spad" 1363274 1363282 1364684 1364689) (-778 "OPTPACK.spad" 1355659 1355667 1363264 1363269) (-777 "OPTCAT.spad" 1353334 1353342 1355649 1355654) (-776 "OPQUERY.spad" 1352883 1352891 1353324 1353329) (-775 "OP.spad" 1352625 1352635 1352705 1352772) (-774 "ONECOMP.spad" 1351373 1351383 1352175 1352204) (-773 "ONECOMP2.spad" 1350791 1350803 1351363 1351368) (-772 "OMSERVER.spad" 1349793 1349801 1350781 1350786) (-771 "OMSAGG.spad" 1349569 1349579 1349737 1349788) (-770 "OMPKG.spad" 1348181 1348189 1349559 1349564) (-769 "OM.spad" 1347146 1347154 1348171 1348176) (-768 "OMLO.spad" 1346571 1346583 1347032 1347071) (-767 "OMEXPR.spad" 1346405 1346415 1346561 1346566) (-766 "OMERR.spad" 1345948 1345956 1346395 1346400) (-765 "OMERRK.spad" 1344982 1344990 1345938 1345943) (-764 "OMENC.spad" 1344326 1344334 1344972 1344977) (-763 "OMDEV.spad" 1338615 1338623 1344316 1344321) (-762 "OMCONN.spad" 1338024 1338032 1338605 1338610) (-761 "OINTDOM.spad" 1337787 1337795 1337950 1338019) (-760 "OFMONOID.spad" 1333974 1333984 1337777 1337782) (-759 "ODVAR.spad" 1333235 1333245 1333964 1333969) (-758 "ODR.spad" 1332683 1332709 1333047 1333196) (-757 "ODPOL.spad" 1330032 1330042 1330372 1330499) (-756 "ODP.spad" 1321558 1321578 1321931 1322060) (-755 "ODETOOLS.spad" 1320141 1320160 1321548 1321553) (-754 "ODESYS.spad" 1317791 1317808 1320131 1320136) (-753 "ODERTRIC.spad" 1313732 1313749 1317748 1317753) (-752 "ODERED.spad" 1313119 1313143 1313722 1313727) (-751 "ODERAT.spad" 1310670 1310687 1313109 1313114) (-750 "ODEPRRIC.spad" 1307561 1307583 1310660 1310665) (-749 "ODEPROB.spad" 1306760 1306768 1307551 1307556) (-748 "ODEPRIM.spad" 1304034 1304056 1306750 1306755) (-747 "ODEPAL.spad" 1303410 1303434 1304024 1304029) (-746 "ODEPACK.spad" 1290012 1290020 1303400 1303405) (-745 "ODEINT.spad" 1289443 1289459 1290002 1290007) (-744 "ODEIFTBL.spad" 1286838 1286846 1289433 1289438) (-743 "ODEEF.spad" 1282205 1282221 1286828 1286833) (-742 "ODECONST.spad" 1281724 1281742 1282195 1282200) (-741 "ODECAT.spad" 1280320 1280328 1281714 1281719) (-740 "OCT.spad" 1278467 1278477 1279183 1279222) (-739 "OCTCT2.spad" 1278111 1278132 1278457 1278462) (-738 "OC.spad" 1275885 1275895 1278067 1278106) (-737 "OC.spad" 1273385 1273397 1275569 1275574) (-736 "OCAMON.spad" 1273233 1273241 1273375 1273380) (-735 "OASGP.spad" 1273048 1273056 1273223 1273228) (-734 "OAMONS.spad" 1272568 1272576 1273038 1273043) (-733 "OAMON.spad" 1272429 1272437 1272558 1272563) (-732 "OAGROUP.spad" 1272291 1272299 1272419 1272424) (-731 "NUMTUBE.spad" 1271878 1271894 1272281 1272286) (-730 "NUMQUAD.spad" 1259740 1259748 1271868 1271873) (-729 "NUMODE.spad" 1250876 1250884 1259730 1259735) (-728 "NUMINT.spad" 1248434 1248442 1250866 1250871) (-727 "NUMFMT.spad" 1247274 1247282 1248424 1248429) (-726 "NUMERIC.spad" 1239347 1239357 1247080 1247085) (-725 "NTSCAT.spad" 1237837 1237853 1239303 1239342) (-724 "NTPOLFN.spad" 1237382 1237392 1237754 1237759) (-723 "NSUP.spad" 1230395 1230405 1234935 1235088) (-722 "NSUP2.spad" 1229787 1229799 1230385 1230390) (-721 "NSMP.spad" 1225986 1226005 1226294 1226421) (-720 "NREP.spad" 1224358 1224372 1225976 1225981) (-719 "NPCOEF.spad" 1223604 1223624 1224348 1224353) (-718 "NORMRETR.spad" 1223202 1223241 1223594 1223599) (-717 "NORMPK.spad" 1221104 1221123 1223192 1223197) (-716 "NORMMA.spad" 1220792 1220818 1221094 1221099) 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1125895) (-677 "MRING.spad" 1122704 1122716 1125441 1125508) (-676 "MRF2.spad" 1122272 1122286 1122694 1122699) (-675 "MRATFAC.spad" 1121818 1121835 1122262 1122267) (-674 "MPRFF.spad" 1119848 1119867 1121808 1121813) (-673 "MPOLY.spad" 1117286 1117301 1117645 1117772) (-672 "MPCPF.spad" 1116550 1116569 1117276 1117281) (-671 "MPC3.spad" 1116365 1116405 1116540 1116545) (-670 "MPC2.spad" 1116007 1116040 1116355 1116360) (-669 "MONOTOOL.spad" 1114342 1114359 1115997 1116002) (-668 "MONOID.spad" 1113516 1113524 1114332 1114337) (-667 "MONOID.spad" 1112688 1112698 1113506 1113511) (-666 "MONOGEN.spad" 1111434 1111447 1112548 1112683) (-665 "MONOGEN.spad" 1110202 1110217 1111318 1111323) (-664 "MONADWU.spad" 1108216 1108224 1110192 1110197) (-663 "MONADWU.spad" 1106228 1106238 1108206 1108211) (-662 "MONAD.spad" 1105372 1105380 1106218 1106223) (-661 "MONAD.spad" 1104514 1104524 1105362 1105367) (-660 "MOEBIUS.spad" 1103200 1103214 1104494 1104509) (-659 "MODULE.spad" 1103070 1103080 1103168 1103195) (-658 "MODULE.spad" 1102960 1102972 1103060 1103065) (-657 "MODRING.spad" 1102291 1102330 1102940 1102955) (-656 "MODOP.spad" 1100950 1100962 1102113 1102180) (-655 "MODMONOM.spad" 1100482 1100500 1100940 1100945) (-654 "MODMON.spad" 1097187 1097203 1097963 1098116) (-653 "MODFIELD.spad" 1096545 1096584 1097089 1097182) (-652 "MMLFORM.spad" 1095405 1095413 1096535 1096540) (-651 "MMAP.spad" 1095145 1095179 1095395 1095400) (-650 "MLO.spad" 1093572 1093582 1095101 1095140) (-649 "MLIFT.spad" 1092144 1092161 1093562 1093567) (-648 "MKUCFUNC.spad" 1091677 1091695 1092134 1092139) (-647 "MKRECORD.spad" 1091279 1091292 1091667 1091672) (-646 "MKFUNC.spad" 1090660 1090670 1091269 1091274) (-645 "MKFLCFN.spad" 1089616 1089626 1090650 1090655) (-644 "MKCHSET.spad" 1089392 1089402 1089606 1089611) (-643 "MKBCFUNC.spad" 1088877 1088895 1089382 1089387) (-642 "MINT.spad" 1088316 1088324 1088779 1088872) (-641 "MHROWRED.spad" 1086817 1086827 1088306 1088311) (-640 "MFLOAT.spad" 1085262 1085270 1086707 1086812) (-639 "MFINFACT.spad" 1084662 1084684 1085252 1085257) (-638 "MESH.spad" 1082394 1082402 1084652 1084657) (-637 "MDDFACT.spad" 1080587 1080597 1082384 1082389) (-636 "MDAGG.spad" 1079862 1079872 1080555 1080582) (-635 "MCMPLX.spad" 1075842 1075850 1076456 1076657) (-634 "MCDEN.spad" 1075050 1075062 1075832 1075837) (-633 "MCALCFN.spad" 1072152 1072178 1075040 1075045) (-632 "MATSTOR.spad" 1069428 1069438 1072142 1072147) (-631 "MATRIX.spad" 1068132 1068142 1068616 1068643) (-630 "MATLIN.spad" 1065458 1065482 1068016 1068021) (-629 "MATCAT.spad" 1057031 1057053 1065414 1065453) (-628 "MATCAT.spad" 1048488 1048512 1056873 1056878) (-627 "MATCAT2.spad" 1047756 1047804 1048478 1048483) (-626 "MAPPKG3.spad" 1046655 1046669 1047746 1047751) (-625 "MAPPKG2.spad" 1045989 1046001 1046645 1046650) (-624 "MAPPKG1.spad" 1044807 1044817 1045979 1045984) (-623 "MAPHACK3.spad" 1044615 1044629 1044797 1044802) (-622 "MAPHACK2.spad" 1044380 1044392 1044605 1044610) (-621 "MAPHACK1.spad" 1044010 1044020 1044370 1044375) (-620 "MAGMA.spad" 1041800 1041817 1044000 1044005) (-619 "M3D.spad" 1039498 1039508 1041180 1041185) (-618 "LZSTAGG.spad" 1036716 1036726 1039478 1039493) (-617 "LZSTAGG.spad" 1033942 1033954 1036706 1036711) (-616 "LWORD.spad" 1030647 1030664 1033932 1033937) (-615 "LSQM.spad" 1028875 1028889 1029273 1029324) (-614 "LSPP.spad" 1028408 1028425 1028865 1028870) (-613 "LSMP.spad" 1027248 1027276 1028398 1028403) (-612 "LSMP1.spad" 1025052 1025066 1027238 1027243) (-611 "LSAGG.spad" 1024709 1024719 1025008 1025047) (-610 "LSAGG.spad" 1024398 1024410 1024699 1024704) (-609 "LPOLY.spad" 1023352 1023371 1024254 1024323) (-608 "LPEFRAC.spad" 1022609 1022619 1023342 1023347) (-607 "LO.spad" 1022010 1022024 1022543 1022570) (-606 "LOGIC.spad" 1021612 1021620 1022000 1022005) (-605 "LOGIC.spad" 1021212 1021222 1021602 1021607) (-604 "LODOOPS.spad" 1020130 1020142 1021202 1021207) (-603 "LODO.spad" 1019516 1019532 1019812 1019851) (-602 "LODOF.spad" 1018560 1018577 1019473 1019478) (-601 "LODOCAT.spad" 1017218 1017228 1018516 1018555) (-600 "LODOCAT.spad" 1015874 1015886 1017174 1017179) (-599 "LODO2.spad" 1015149 1015161 1015556 1015595) (-598 "LODO1.spad" 1014551 1014561 1014831 1014870) (-597 "LODEEF.spad" 1013323 1013341 1014541 1014546) (-596 "LNAGG.spad" 1009115 1009125 1013303 1013318) (-595 "LNAGG.spad" 1004881 1004893 1009071 1009076) (-594 "LMOPS.spad" 1001617 1001634 1004871 1004876) (-593 "LMODULE.spad" 1001259 1001269 1001607 1001612) (-592 "LMDICT.spad" 1000542 1000552 1000810 1000837) (-591 "LIST.spad" 998260 998270 999689 999716) (-590 "LIST3.spad" 997551 997565 998250 998255) (-589 "LIST2.spad" 996191 996203 997541 997546) (-588 "LIST2MAP.spad" 993068 993080 996181 996186) (-587 "LINEXP.spad" 992500 992510 993048 993063) (-586 "LINDEP.spad" 991277 991289 992412 992417) (-585 "LIMITRF.spad" 989191 989201 991267 991272) (-584 "LIMITPS.spad" 988074 988087 989181 989186) (-583 "LIE.spad" 986088 986100 987364 987509) (-582 "LIECAT.spad" 985564 985574 986014 986083) (-581 "LIECAT.spad" 985068 985080 985520 985525) (-580 "LIB.spad" 983116 983124 983727 983742) (-579 "LGROBP.spad" 980469 980488 983106 983111) (-578 "LF.spad" 979388 979404 980459 980464) (-577 "LFCAT.spad" 978407 978415 979378 979383) (-576 "LEXTRIPK.spad" 973910 973925 978397 978402) (-575 "LEXP.spad" 971913 971940 973890 973905) (-574 "LEADCDET.spad" 970297 970314 971903 971908) (-573 "LAZM3PK.spad" 969001 969023 970287 970292) (-572 "LAUPOL.spad" 967692 967705 968596 968665) (-571 "LAPLACE.spad" 967265 967281 967682 967687) (-570 "LA.spad" 966705 966719 967187 967226) (-569 "LALG.spad" 966481 966491 966685 966700) (-568 "LALG.spad" 966265 966277 966471 966476) (-567 "KOVACIC.spad" 964978 964995 966255 966260) (-566 "KONVERT.spad" 964700 964710 964968 964973) (-565 "KOERCE.spad" 964437 964447 964690 964695) (-564 "KERNEL.spad" 962972 962982 964221 964226) (-563 "KERNEL2.spad" 962675 962687 962962 962967) (-562 "KDAGG.spad" 961766 961788 962643 962670) (-561 "KDAGG.spad" 960877 960901 961756 961761) (-560 "KAFILE.spad" 959840 959856 960075 960102) (-559 "JORDAN.spad" 957667 957679 959130 959275) (-558 "IXAGG.spad" 955780 955804 957647 957662) (-557 "IXAGG.spad" 953758 953784 955627 955632) (-556 "IVECTOR.spad" 952531 952546 952686 952713) (-555 "ITUPLE.spad" 951676 951686 952521 952526) (-554 "ITRIGMNP.spad" 950487 950506 951666 951671) (-553 "ITFUN3.spad" 949981 949995 950477 950482) (-552 "ITFUN2.spad" 949711 949723 949971 949976) (-551 "ITAYLOR.spad" 947503 947518 949547 949672) (-550 "ISUPS.spad" 939914 939929 946477 946574) (-549 "ISUMP.spad" 939411 939427 939904 939909) (-548 "ISTRING.spad" 938414 938427 938580 938607) (-547 "IRURPK.spad" 937127 937146 938404 938409) (-546 "IRSN.spad" 935087 935095 937117 937122) (-545 "IRRF2F.spad" 933562 933572 935043 935048) (-544 "IRREDFFX.spad" 933163 933174 933552 933557) (-543 "IROOT.spad" 931494 931504 933153 933158) (-542 "IR.spad" 929284 929298 931350 931377) (-541 "IR2.spad" 928304 928320 929274 929279) (-540 "IR2F.spad" 927504 927520 928294 928299) (-539 "IPRNTPK.spad" 927264 927272 927494 927499) (-538 "IPF.spad" 926829 926841 927069 927162) (-537 "IPADIC.spad" 926590 926616 926755 926824) (-536 "INVLAPLA.spad" 926235 926251 926580 926585) (-535 "INTTR.spad" 919481 919498 926225 926230) (-534 "INTTOOLS.spad" 917193 917209 919056 919061) (-533 "INTSLPE.spad" 916499 916507 917183 917188) (-532 "INTRVL.spad" 916065 916075 916413 916494) (-531 "INTRF.spad" 914429 914443 916055 916060) (-530 "INTRET.spad" 913861 913871 914419 914424) (-529 "INTRAT.spad" 912536 912553 913851 913856) (-528 "INTPM.spad" 910899 910915 912179 912184) (-527 "INTPAF.spad" 908667 908685 910831 910836) (-526 "INTPACK.spad" 898977 898985 908657 908662) (-525 "INT.spad" 898338 898346 898831 898972) (-524 "INTHERTR.spad" 897604 897621 898328 898333) (-523 "INTHERAL.spad" 897270 897294 897594 897599) (-522 "INTHEORY.spad" 893683 893691 897260 897265) (-521 "INTG0.spad" 887146 887164 893615 893620) (-520 "INTFTBL.spad" 881175 881183 887136 887141) (-519 "INTFACT.spad" 880234 880244 881165 881170) (-518 "INTEF.spad" 878549 878565 880224 880229) (-517 "INTDOM.spad" 877164 877172 878475 878544) (-516 "INTDOM.spad" 875841 875851 877154 877159) (-515 "INTCAT.spad" 874094 874104 875755 875836) (-514 "INTBIT.spad" 873597 873605 874084 874089) (-513 "INTALG.spad" 872779 872806 873587 873592) (-512 "INTAF.spad" 872271 872287 872769 872774) (-511 "INTABL.spad" 870789 870820 870952 870979) (-510 "INS.spad" 868185 868193 870691 870784) (-509 "INS.spad" 865667 865677 868175 868180) (-508 "INPSIGN.spad" 865101 865114 865657 865662) (-507 "INPRODPF.spad" 864167 864186 865091 865096) (-506 "INPRODFF.spad" 863225 863249 864157 864162) (-505 "INNMFACT.spad" 862196 862213 863215 863220) (-504 "INMODGCD.spad" 861680 861710 862186 862191) (-503 "INFSP.spad" 859965 859987 861670 861675) (-502 "INFPROD0.spad" 859015 859034 859955 859960) (-501 "INFORM.spad" 856283 856291 859005 859010) (-500 "INFORM1.spad" 855908 855918 856273 856278) (-499 "INFINITY.spad" 855460 855468 855898 855903) (-498 "INEP.spad" 853992 854014 855450 855455) (-497 "INDE.spad" 853898 853915 853982 853987) (-496 "INCRMAPS.spad" 853319 853329 853888 853893) (-495 "INBFF.spad" 849089 849100 853309 853314) (-494 "IMATRIX.spad" 848034 848060 848546 848573) (-493 "IMATQF.spad" 847128 847172 847990 847995) (-492 "IMATLIN.spad" 845733 845757 847084 847089) (-491 "ILIST.spad" 844389 844404 844916 844943) (-490 "IIARRAY2.spad" 843777 843815 843996 844023) (-489 "IFF.spad" 843187 843203 843458 843551) (-488 "IFARRAY.spad" 840674 840689 842370 842397) (-487 "IFAMON.spad" 840536 840553 840630 840635) (-486 "IEVALAB.spad" 839925 839937 840526 840531) (-485 "IEVALAB.spad" 839312 839326 839915 839920) (-484 "IDPO.spad" 839110 839122 839302 839307) (-483 "IDPOAMS.spad" 838866 838878 839100 839105) (-482 "IDPOAM.spad" 838586 838598 838856 838861) (-481 "IDPC.spad" 837520 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(-460 "HELLFDIV.spad" 806139 806163 806539 806544) (-459 "HEAP.spad" 805531 805541 805746 805773) (-458 "HDP.spad" 797053 797069 797430 797559) (-457 "HDMP.spad" 794232 794247 794850 794977) (-456 "HB.spad" 792469 792477 794222 794227) (-455 "HASHTBL.spad" 790939 790970 791150 791177) (-454 "HACKPI.spad" 790422 790430 790841 790934) (-453 "GTSET.spad" 789361 789377 790068 790095) (-452 "GSTBL.spad" 787880 787915 788054 788069) (-451 "GSERIES.spad" 785047 785074 786012 786161) (-450 "GROUP.spad" 784221 784229 785027 785042) (-449 "GROUP.spad" 783403 783413 784211 784216) (-448 "GROEBSOL.spad" 781891 781912 783393 783398) (-447 "GRMOD.spad" 780462 780474 781881 781886) (-446 "GRMOD.spad" 779031 779045 780452 780457) (-445 "GRIMAGE.spad" 771636 771644 779021 779026) (-444 "GRDEF.spad" 770015 770023 771626 771631) (-443 "GRAY.spad" 768474 768482 770005 770010) (-442 "GRALG.spad" 767521 767533 768464 768469) (-441 "GRALG.spad" 766566 766580 767511 767516) (-440 "GPOLSET.spad" 766020 766043 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"BPADICRT.spad" 130472 130484 130727 130820) (-112 "BPADIC.spad" 130136 130148 130398 130467) (-111 "BOUNDZRO.spad" 129792 129809 130126 130131) (-110 "BOP.spad" 125256 125264 129782 129787) (-109 "BOP1.spad" 122642 122652 125212 125217) (-108 "BOOLEAN.spad" 121895 121903 122632 122637) (-107 "BMODULE.spad" 121607 121619 121863 121890) (-106 "BITS.spad" 121026 121034 121243 121270) (-105 "BINFILE.spad" 120369 120377 121016 121021) (-104 "BINDING.spad" 119788 119796 120359 120364) (-103 "BINARY.spad" 117681 117689 118258 118351) (-102 "BGAGG.spad" 116866 116876 117649 117676) (-101 "BGAGG.spad" 116071 116083 116856 116861) (-100 "BFUNCT.spad" 115635 115643 116051 116066) (-99 "BEZOUT.spad" 114770 114796 115585 115590) (-98 "BBTREE.spad" 111590 111599 114377 114404) (-97 "BASTYPE.spad" 111263 111270 111580 111585) (-96 "BASTYPE.spad" 110934 110943 111253 111258) (-95 "BALFACT.spad" 110374 110386 110924 110929) (-94 "AUTOMOR.spad" 109821 109830 110354 110369) (-93 "ATTREG.spad" 106540 106547 109573 109816) (-92 "ATTRBUT.spad" 102563 102570 106520 106535) (-91 "ATRIG.spad" 102033 102040 102553 102558) (-90 "ATRIG.spad" 101501 101510 102023 102028) (-89 "ASTACK.spad" 100834 100843 101108 101135) (-88 "ASSOCEQ.spad" 99634 99645 100790 100795) (-87 "ASP9.spad" 98715 98728 99624 99629) (-86 "ASP8.spad" 97758 97771 98705 98710) (-85 "ASP80.spad" 97080 97093 97748 97753) (-84 "ASP7.spad" 96240 96253 97070 97075) (-83 "ASP78.spad" 95691 95704 96230 96235) (-82 "ASP77.spad" 95060 95073 95681 95686) (-81 "ASP74.spad" 94152 94165 95050 95055) (-80 "ASP73.spad" 93423 93436 94142 94147) (-79 "ASP6.spad" 92055 92068 93413 93418) (-78 "ASP55.spad" 90564 90577 92045 92050) (-77 "ASP50.spad" 88381 88394 90554 90559) (-76 "ASP4.spad" 87676 87689 88371 88376) (-75 "ASP49.spad" 86675 86688 87666 87671) (-74 "ASP42.spad" 85082 85121 86665 86670) (-73 "ASP41.spad" 83661 83700 85072 85077) (-72 "ASP35.spad" 82649 82662 83651 83656) (-71 "ASP34.spad" 81950 81963 82639 82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2237747 2237752 2237757 2237762) (-2 NIL 2237727 2237732 2237737 2237742) (-1 NIL 2237707 2237712 2237717 2237722) (0 NIL 2237687 2237692 2237697 2237702) (-1197 "ZMOD.spad" 2237496 2237509 2237625 2237682) (-1196 "ZLINDEP.spad" 2236540 2236551 2237486 2237491) (-1195 "ZDSOLVE.spad" 2226389 2226411 2236530 2236535) (-1194 "YSTREAM.spad" 2225882 2225893 2226379 2226384) (-1193 "XRPOLY.spad" 2225102 2225122 2225738 2225807) (-1192 "XPR.spad" 2222831 2222844 2224820 2224919) (-1191 "XPOLY.spad" 2222386 2222397 2222687 2222756) (-1190 "XPOLYC.spad" 2221703 2221719 2222312 2222381) (-1189 "XPBWPOLY.spad" 2220140 2220160 2221483 2221552) (-1188 "XF.spad" 2218601 2218616 2220042 2220135) (-1187 "XF.spad" 2217042 2217059 2218485 2218490) (-1186 "XFALG.spad" 2214066 2214082 2216968 2217037) (-1185 "XEXPPKG.spad" 2213317 2213343 2214056 2214061) (-1184 "XDPOLY.spad" 2212931 2212947 2213173 2213242) (-1183 "XALG.spad" 2212529 2212540 2212887 2212926) (-1182 "WUTSET.spad" 2208368 2208385 2212175 2212202) (-1181 "WP.spad" 2207382 2207426 2208226 2208293) (-1180 "WFFINTBS.spad" 2204945 2204967 2207372 2207377) (-1179 "WEIER.spad" 2203159 2203170 2204935 2204940) (-1178 "VSPACE.spad" 2202832 2202843 2203127 2203154) (-1177 "VSPACE.spad" 2202525 2202538 2202822 2202827) (-1176 "VOID.spad" 2202115 2202124 2202515 2202520) (-1175 "VIEW.spad" 2199737 2199746 2202105 2202110) (-1174 "VIEWDEF.spad" 2194934 2194943 2199727 2199732) (-1173 "VIEW3D.spad" 2178769 2178778 2194924 2194929) (-1172 "VIEW2D.spad" 2166506 2166515 2178759 2178764) (-1171 "VECTOR.spad" 2165183 2165194 2165434 2165461) (-1170 "VECTOR2.spad" 2163810 2163823 2165173 2165178) (-1169 "VECTCAT.spad" 2161698 2161709 2163766 2163805) (-1168 "VECTCAT.spad" 2159407 2159420 2161477 2161482) (-1167 "VARIABLE.spad" 2159187 2159202 2159397 2159402) (-1166 "UTYPE.spad" 2158821 2158830 2159167 2159182) (-1165 "UTSODETL.spad" 2158114 2158138 2158777 2158782) (-1164 "UTSODE.spad" 2156302 2156322 2158104 2158109) (-1163 "UTS.spad" 2151091 2151119 2154769 2154866) (-1162 "UTSCAT.spad" 2148542 2148558 2150989 2151086) (-1161 "UTSCAT.spad" 2145637 2145655 2148086 2148091) (-1160 "UTS2.spad" 2145230 2145265 2145627 2145632) (-1159 "URAGG.spad" 2139852 2139863 2145210 2145225) (-1158 "URAGG.spad" 2134448 2134461 2139808 2139813) (-1157 "UPXSSING.spad" 2132094 2132120 2133532 2133665) (-1156 "UPXS.spad" 2129121 2129149 2130226 2130375) (-1155 "UPXSCONS.spad" 2126878 2126898 2127253 2127402) (-1154 "UPXSCCA.spad" 2125336 2125356 2126724 2126873) (-1153 "UPXSCCA.spad" 2123936 2123958 2125326 2125331) (-1152 "UPXSCAT.spad" 2122517 2122533 2123782 2123931) (-1151 "UPXS2.spad" 2122058 2122111 2122507 2122512) (-1150 "UPSQFREE.spad" 2120470 2120484 2122048 2122053) (-1149 "UPSCAT.spad" 2118063 2118087 2120368 2120465) (-1148 "UPSCAT.spad" 2115362 2115388 2117669 2117674) (-1147 "UPOLYC.spad" 2110340 2110351 2115204 2115357) (-1146 "UPOLYC.spad" 2105210 2105223 2110076 2110081) (-1145 "UPOLYC2.spad" 2104679 2104698 2105200 2105205) (-1144 "UP.spad" 2101724 2101739 2102232 2102385) (-1143 "UPMP.spad" 2100614 2100627 2101714 2101719) (-1142 "UPDIVP.spad" 2100177 2100191 2100604 2100609) (-1141 "UPDECOMP.spad" 2098414 2098428 2100167 2100172) (-1140 "UPCDEN.spad" 2097621 2097637 2098404 2098409) (-1139 "UP2.spad" 2096983 2097004 2097611 2097616) (-1138 "UNISEG.spad" 2096336 2096347 2096902 2096907) (-1137 "UNISEG2.spad" 2095829 2095842 2096292 2096297) (-1136 "UNIFACT.spad" 2094930 2094942 2095819 2095824) (-1135 "ULS.spad" 2085489 2085517 2086582 2087011) (-1134 "ULSCONS.spad" 2079532 2079552 2079904 2080053) (-1133 "ULSCCAT.spad" 2077129 2077149 2079352 2079527) (-1132 "ULSCCAT.spad" 2074860 2074882 2077085 2077090) (-1131 "ULSCAT.spad" 2073076 2073092 2074706 2074855) (-1130 "ULS2.spad" 2072588 2072641 2073066 2073071) (-1129 "UFD.spad" 2071653 2071662 2072514 2072583) (-1128 "UFD.spad" 2070780 2070791 2071643 2071648) (-1127 "UDVO.spad" 2069627 2069636 2070770 2070775) (-1126 "UDPO.spad" 2067054 2067065 2069583 2069588) (-1125 "TYPE.spad" 2066976 2066985 2067034 2067049) (-1124 "TWOFACT.spad" 2065626 2065641 2066966 2066971) (-1123 "TUPLE.spad" 2065012 2065023 2065525 2065530) (-1122 "TUBETOOL.spad" 2061849 2061858 2065002 2065007) (-1121 "TUBE.spad" 2060490 2060507 2061839 2061844) (-1120 "TS.spad" 2059079 2059095 2060055 2060152) (-1119 "TSETCAT.spad" 2046194 2046211 2059035 2059074) (-1118 "TSETCAT.spad" 2033307 2033326 2046150 2046155) (-1117 "TRMANIP.spad" 2027673 2027690 2033013 2033018) (-1116 "TRIMAT.spad" 2026632 2026657 2027663 2027668) (-1115 "TRIGMNIP.spad" 2025149 2025166 2026622 2026627) (-1114 "TRIGCAT.spad" 2024661 2024670 2025139 2025144) (-1113 "TRIGCAT.spad" 2024171 2024182 2024651 2024656) (-1112 "TREE.spad" 2022742 2022753 2023778 2023805) (-1111 "TRANFUN.spad" 2022573 2022582 2022732 2022737) (-1110 "TRANFUN.spad" 2022402 2022413 2022563 2022568) (-1109 "TOPSP.spad" 2022076 2022085 2022392 2022397) (-1108 "TOOLSIGN.spad" 2021739 2021750 2022066 2022071) (-1107 "TEXTFILE.spad" 2020296 2020305 2021729 2021734) (-1106 "TEX.spad" 2017313 2017322 2020286 2020291) (-1105 "TEX1.spad" 2016869 2016880 2017303 2017308) (-1104 "TEMUTL.spad" 2016424 2016433 2016859 2016864) (-1103 "TBCMPPK.spad" 2014517 2014540 2016414 2016419) (-1102 "TBAGG.spad" 2013541 2013564 2014485 2014512) (-1101 "TBAGG.spad" 2012585 2012610 2013531 2013536) (-1100 "TANEXP.spad" 2011961 2011972 2012575 2012580) (-1099 "TABLE.spad" 2010372 2010395 2010642 2010669) (-1098 "TABLEAU.spad" 2009853 2009864 2010362 2010367) (-1097 "TABLBUMP.spad" 2006636 2006647 2009843 2009848) (-1096 "SYSTEM.spad" 2005910 2005919 2006626 2006631) (-1095 "SYSSOLP.spad" 2003383 2003394 2005900 2005905) (-1094 "SYNTAX.spad" 1999575 1999584 2003373 2003378) (-1093 "SYMTAB.spad" 1997631 1997640 1999565 1999570) (-1092 "SYMS.spad" 1993616 1993625 1997621 1997626) (-1091 "SYMPOLY.spad" 1992626 1992637 1992708 1992835) (-1090 "SYMFUNC.spad" 1992101 1992112 1992616 1992621) (-1089 "SYMBOL.spad" 1989437 1989446 1992091 1992096) (-1088 "SWITCH.spad" 1986194 1986203 1989427 1989432) (-1087 "SUTS.spad" 1983093 1983121 1984661 1984758) (-1086 "SUPXS.spad" 1980107 1980135 1981225 1981374) (-1085 "SUP.spad" 1976879 1976890 1977660 1977813) (-1084 "SUPFRACF.spad" 1975984 1976002 1976869 1976874) (-1083 "SUP2.spad" 1975374 1975387 1975974 1975979) (-1082 "SUMRF.spad" 1974340 1974351 1975364 1975369) (-1081 "SUMFS.spad" 1973973 1973990 1974330 1974335) (-1080 "SULS.spad" 1964519 1964547 1965625 1966054) (-1079 "SUCH.spad" 1964199 1964214 1964509 1964514) (-1078 "SUBSPACE.spad" 1956206 1956221 1964189 1964194) (-1077 "SUBRESP.spad" 1955366 1955380 1956162 1956167) (-1076 "STTF.spad" 1951465 1951481 1955356 1955361) (-1075 "STTFNC.spad" 1947933 1947949 1951455 1951460) (-1074 "STTAYLOR.spad" 1940331 1940342 1947814 1947819) (-1073 "STRTBL.spad" 1938836 1938853 1938985 1939012) (-1072 "STRING.spad" 1938245 1938254 1938259 1938286) (-1071 "STRICAT.spad" 1938021 1938030 1938201 1938240) (-1070 "STREAM.spad" 1934789 1934800 1937546 1937561) (-1069 "STREAM3.spad" 1934334 1934349 1934779 1934784) (-1068 "STREAM2.spad" 1933402 1933415 1934324 1934329) (-1067 "STREAM1.spad" 1933106 1933117 1933392 1933397) (-1066 "STINPROD.spad" 1932012 1932028 1933096 1933101) (-1065 "STEP.spad" 1931213 1931222 1932002 1932007) (-1064 "STBL.spad" 1929739 1929767 1929906 1929921) (-1063 "STAGG.spad" 1928804 1928815 1929719 1929734) (-1062 "STAGG.spad" 1927877 1927890 1928794 1928799) (-1061 "STACK.spad" 1927228 1927239 1927484 1927511) (-1060 "SREGSET.spad" 1924932 1924949 1926874 1926901) (-1059 "SRDCMPK.spad" 1923477 1923497 1924922 1924927) (-1058 "SRAGG.spad" 1918562 1918571 1923433 1923472) (-1057 "SRAGG.spad" 1913679 1913690 1918552 1918557) (-1056 "SQMATRIX.spad" 1911305 1911323 1912213 1912300) (-1055 "SPLTREE.spad" 1905857 1905870 1910741 1910768) (-1054 "SPLNODE.spad" 1902445 1902458 1905847 1905852) (-1053 "SPFCAT.spad" 1901222 1901231 1902435 1902440) (-1052 "SPECOUT.spad" 1899772 1899781 1901212 1901217) (-1051 "spad-parser.spad" 1899237 1899246 1899762 1899767) (-1050 "SPACEC.spad" 1883250 1883261 1899227 1899232) (-1049 "SPACE3.spad" 1883026 1883037 1883240 1883245) (-1048 "SORTPAK.spad" 1882571 1882584 1882982 1882987) (-1047 "SOLVETRA.spad" 1880328 1880339 1882561 1882566) (-1046 "SOLVESER.spad" 1878848 1878859 1880318 1880323) (-1045 "SOLVERAD.spad" 1874858 1874869 1878838 1878843) (-1044 "SOLVEFOR.spad" 1873278 1873296 1874848 1874853) (-1043 "SNTSCAT.spad" 1872866 1872883 1873234 1873273) (-1042 "SMTS.spad" 1871126 1871152 1872431 1872528) (-1041 "SMP.spad" 1868568 1868588 1868958 1869085) (-1040 "SMITH.spad" 1867411 1867436 1868558 1868563) (-1039 "SMATCAT.spad" 1865509 1865539 1867343 1867406) (-1038 "SMATCAT.spad" 1863551 1863583 1865387 1865392) (-1037 "SKAGG.spad" 1862500 1862511 1863507 1863546) (-1036 "SINT.spad" 1860808 1860817 1862366 1862495) (-1035 "SIMPAN.spad" 1860536 1860545 1860798 1860803) (-1034 "SIGNRF.spad" 1859644 1859655 1860526 1860531) (-1033 "SIGNEF.spad" 1858913 1858930 1859634 1859639) (-1032 "SHP.spad" 1856831 1856846 1858869 1858874) (-1031 "SHDP.spad" 1848221 1848248 1848730 1848859) (-1030 "SGROUP.spad" 1847687 1847696 1848211 1848216) (-1029 "SGROUP.spad" 1847151 1847162 1847677 1847682) (-1028 "SGCF.spad" 1840032 1840041 1847141 1847146) (-1027 "SFRTCAT.spad" 1838948 1838965 1839988 1840027) (-1026 "SFRGCD.spad" 1838011 1838031 1838938 1838943) (-1025 "SFQCMPK.spad" 1832648 1832668 1838001 1838006) (-1024 "SFORT.spad" 1832083 1832097 1832638 1832643) (-1023 "SEXOF.spad" 1831926 1831966 1832073 1832078) (-1022 "SEX.spad" 1831818 1831827 1831916 1831921) (-1021 "SEXCAT.spad" 1828922 1828962 1831808 1831813) (-1020 "SET.spad" 1827222 1827233 1828343 1828382) (-1019 "SETMN.spad" 1825656 1825673 1827212 1827217) (-1018 "SETCAT.spad" 1825141 1825150 1825646 1825651) (-1017 "SETCAT.spad" 1824624 1824635 1825131 1825136) (-1016 "SETAGG.spad" 1821147 1821158 1824592 1824619) (-1015 "SETAGG.spad" 1817690 1817703 1821137 1821142) (-1014 "SEGXCAT.spad" 1816802 1816815 1817670 1817685) (-1013 "SEG.spad" 1816615 1816626 1816721 1816726) (-1012 "SEGCAT.spad" 1815434 1815445 1816595 1816610) (-1011 "SEGBIND.spad" 1814506 1814517 1815389 1815394) (-1010 "SEGBIND2.spad" 1814202 1814215 1814496 1814501) (-1009 "SEG2.spad" 1813627 1813640 1814158 1814163) (-1008 "SDVAR.spad" 1812903 1812914 1813617 1813622) (-1007 "SDPOL.spad" 1810296 1810307 1810587 1810714) (-1006 "SCPKG.spad" 1808375 1808386 1810286 1810291) (-1005 "SCOPE.spad" 1807520 1807529 1808365 1808370) (-1004 "SCACHE.spad" 1806202 1806213 1807510 1807515) (-1003 "SAOS.spad" 1806074 1806083 1806192 1806197) (-1002 "SAERFFC.spad" 1805787 1805807 1806064 1806069) (-1001 "SAE.spad" 1803965 1803981 1804576 1804711) (-1000 "SAEFACT.spad" 1803666 1803686 1803955 1803960) (-999 "RURPK.spad" 1801308 1801323 1803656 1803661) (-998 "RULESET.spad" 1800750 1800773 1801298 1801303) (-997 "RULE.spad" 1798955 1798978 1800740 1800745) (-996 "RULECOLD.spad" 1798808 1798820 1798945 1798950) (-995 "RSETGCD.spad" 1795187 1795206 1798798 1798803) (-994 "RSETCAT.spad" 1784960 1784976 1795143 1795182) (-993 "RSETCAT.spad" 1774765 1774783 1784950 1784955) (-992 "RSDCMPK.spad" 1773218 1773237 1774755 1774760) (-991 "RRCC.spad" 1771603 1771632 1773208 1773213) (-990 "RRCC.spad" 1769986 1770017 1771593 1771598) (-989 "RPOLCAT.spad" 1749347 1749361 1769854 1769981) (-988 "RPOLCAT.spad" 1728423 1728439 1748932 1748937) (-987 "ROUTINE.spad" 1724287 1724295 1727070 1727097) (-986 "ROMAN.spad" 1723520 1723528 1724153 1724282) (-985 "ROIRC.spad" 1722601 1722632 1723510 1723515) (-984 "RNS.spad" 1721505 1721513 1722503 1722596) (-983 "RNS.spad" 1720495 1720505 1721495 1721500) (-982 "RNG.spad" 1720231 1720239 1720485 1720490) (-981 "RMODULE.spad" 1719870 1719880 1720221 1720226) (-980 "RMCAT2.spad" 1719279 1719335 1719860 1719865) (-979 "RMATRIX.spad" 1717959 1717977 1718446 1718485) (-978 "RMATCAT.spad" 1713481 1713511 1717903 1717954) (-977 "RMATCAT.spad" 1708905 1708937 1713329 1713334) (-976 "RINTERP.spad" 1708794 1708813 1708895 1708900) (-975 "RING.spad" 1708152 1708160 1708774 1708789) (-974 "RING.spad" 1707518 1707528 1708142 1708147) (-973 "RIDIST.spad" 1706903 1706911 1707508 1707513) (-972 "RGCHAIN.spad" 1705483 1705498 1706388 1706415) (-971 "RF.spad" 1703098 1703108 1705473 1705478) (-970 "RFFACTOR.spad" 1702561 1702571 1703088 1703093) (-969 "RFFACT.spad" 1702297 1702308 1702551 1702556) (-968 "RFDIST.spad" 1701286 1701294 1702287 1702292) (-967 "RETSOL.spad" 1700704 1700716 1701276 1701281) (-966 "RETRACT.spad" 1700054 1700064 1700694 1700699) (-965 "RETRACT.spad" 1699402 1699414 1700044 1700049) (-964 "RESULT.spad" 1697463 1697471 1698049 1698076) (-963 "RESRING.spad" 1696811 1696857 1697401 1697458) (-962 "RESLATC.spad" 1696136 1696146 1696801 1696806) (-961 "REPSQ.spad" 1695866 1695876 1696126 1696131) (-960 "REP.spad" 1693419 1693427 1695856 1695861) (-959 "REPDB.spad" 1693125 1693135 1693409 1693414) (-958 "REP2.spad" 1682698 1682708 1692967 1692972) (-957 "REP1.spad" 1676689 1676699 1682648 1682653) (-956 "REGSET.spad" 1674487 1674503 1676335 1676362) (-955 "REF.spad" 1673817 1673827 1674442 1674447) (-954 "REDORDER.spad" 1672994 1673010 1673807 1673812) (-953 "RECLOS.spad" 1671784 1671803 1672487 1672580) (-952 "REALSOLV.spad" 1670917 1670925 1671774 1671779) (-951 "REAL.spad" 1670790 1670798 1670907 1670912) (-950 "REAL0Q.spad" 1668073 1668087 1670780 1670785) (-949 "REAL0.spad" 1664902 1664916 1668063 1668068) (-948 "RDIV.spad" 1664554 1664578 1664892 1664897) (-947 "RDIST.spad" 1664118 1664128 1664544 1664549) (-946 "RDETRS.spad" 1662915 1662932 1664108 1664113) (-945 "RDETR.spad" 1661023 1661040 1662905 1662910) (-944 "RDEEFS.spad" 1660097 1660113 1661013 1661018) (-943 "RDEEF.spad" 1659094 1659110 1660087 1660092) (-942 "RCFIELD.spad" 1656278 1656286 1658996 1659089) (-941 "RCFIELD.spad" 1653548 1653558 1656268 1656273) 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1631917) (-921 "QFCAT2.spad" 1630402 1630418 1630701 1630706) (-920 "QEQUAT.spad" 1629959 1629967 1630392 1630397) (-919 "QCMPACK.spad" 1624706 1624725 1629949 1629954) (-918 "QALGSET.spad" 1620781 1620813 1624620 1624625) (-917 "QALGSET2.spad" 1618777 1618795 1620771 1620776) (-916 "PWFFINTB.spad" 1616087 1616108 1618767 1618772) (-915 "PUSHVAR.spad" 1615416 1615435 1616077 1616082) (-914 "PTRANFN.spad" 1611542 1611552 1615406 1615411) (-913 "PTPACK.spad" 1608630 1608640 1611532 1611537) (-912 "PTFUNC2.spad" 1608451 1608465 1608620 1608625) (-911 "PTCAT.spad" 1607533 1607543 1608407 1608446) (-910 "PSQFR.spad" 1606840 1606864 1607523 1607528) (-909 "PSEUDLIN.spad" 1605698 1605708 1606830 1606835) (-908 "PSETPK.spad" 1591131 1591147 1605576 1605581) (-907 "PSETCAT.spad" 1585039 1585062 1591099 1591126) (-906 "PSETCAT.spad" 1578933 1578958 1584995 1585000) (-905 "PSCURVE.spad" 1577916 1577924 1578923 1578928) (-904 "PSCAT.spad" 1576683 1576712 1577814 1577911) (-903 "PSCAT.spad" 1575540 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1474139) (-846 "PFOTOOLS.spad" 1470059 1470075 1470791 1470796) (-845 "PFOQ.spad" 1469429 1469447 1470049 1470054) (-844 "PFO.spad" 1468848 1468875 1469419 1469424) (-843 "PF.spad" 1468422 1468434 1468653 1468746) (-842 "PFECAT.spad" 1466088 1466096 1468348 1468417) (-841 "PFECAT.spad" 1463782 1463792 1466044 1466049) (-840 "PFBRU.spad" 1461652 1461664 1463772 1463777) (-839 "PFBR.spad" 1459190 1459213 1461642 1461647) (-838 "PERM.spad" 1454871 1454881 1459020 1459035) (-837 "PERMGRP.spad" 1449607 1449617 1454861 1454866) (-836 "PERMCAT.spad" 1448159 1448169 1449587 1449602) (-835 "PERMAN.spad" 1446691 1446705 1448149 1448154) (-834 "PENDTREE.spad" 1445964 1445974 1446320 1446325) (-833 "PDRING.spad" 1444455 1444465 1445944 1445959) (-832 "PDRING.spad" 1442954 1442966 1444445 1444450) (-831 "PDEPROB.spad" 1441911 1441919 1442944 1442949) (-830 "PDEPACK.spad" 1435913 1435921 1441901 1441906) (-829 "PDECOMP.spad" 1435375 1435392 1435903 1435908) (-828 "PDECAT.spad" 1433729 1433737 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329109 329114) (-234 "DRAWCFUN.spad" 317828 317836 328646 328651) (-233 "DQAGG.spad" 315984 315994 317784 317823) (-232 "DPOLCAT.spad" 311325 311341 315852 315979) (-231 "DPOLCAT.spad" 306752 306770 311281 311286) (-230 "DPMO.spad" 300739 300755 300877 301173) (-229 "DPMM.spad" 294739 294757 294864 295160) (-228 "DOMAIN.spad" 294010 294018 294729 294734) (-227 "DMP.spad" 291235 291250 291807 291934) (-226 "DLP.spad" 290583 290593 291225 291230) (-225 "DLIST.spad" 288995 289005 289766 289793) (-224 "DLAGG.spad" 287396 287406 288975 288990) (-223 "DIVRING.spad" 286843 286851 287340 287391) (-222 "DIVRING.spad" 286334 286344 286833 286838) (-221 "DISPLAY.spad" 284514 284522 286324 286329) (-220 "DIRPROD.spad" 275773 275789 276413 276542) (-219 "DIRPROD2.spad" 274581 274599 275763 275768) (-218 "DIRPCAT.spad" 273513 273529 274435 274576) (-217 "DIRPCAT.spad" 272185 272203 273109 273114) (-216 "DIOSP.spad" 271010 271018 272175 272180) (-215 "DIOPS.spad" 269982 269992 270978 271005) (-214 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"D03FAFA.spad" 238012 238020 238174 238179) (-193 "D03EEFA.spad" 237832 237840 238002 238007) (-192 "D03AGNT.spad" 236912 236920 237822 237827) (-191 "D02EJFA.spad" 236374 236382 236902 236907) (-190 "D02CJFA.spad" 235852 235860 236364 236369) (-189 "D02BHFA.spad" 235342 235350 235842 235847) (-188 "D02BBFA.spad" 234832 234840 235332 235337) (-187 "D02AGNT.spad" 229636 229644 234822 234827) (-186 "D01WGTS.spad" 227955 227963 229626 229631) (-185 "D01TRNS.spad" 227932 227940 227945 227950) (-184 "D01GBFA.spad" 227454 227462 227922 227927) (-183 "D01FCFA.spad" 226976 226984 227444 227449) (-182 "D01ASFA.spad" 226444 226452 226966 226971) (-181 "D01AQFA.spad" 225890 225898 226434 226439) (-180 "D01APFA.spad" 225314 225322 225880 225885) (-179 "D01ANFA.spad" 224808 224816 225304 225309) (-178 "D01AMFA.spad" 224318 224326 224798 224803) (-177 "D01ALFA.spad" 223858 223866 224308 224313) (-176 "D01AKFA.spad" 223384 223392 223848 223853) (-175 "D01AJFA.spad" 222907 222915 223374 223379) (-174 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"COMPCAT.spad" 184260 184270 185926 186199) (-153 "COMPCAT.spad" 182023 182035 183691 183696) (-152 "COMMUPC.spad" 181769 181787 182013 182018) (-151 "COMMONOP.spad" 181302 181310 181759 181764) (-150 "COMM.spad" 181111 181119 181292 181297) (-149 "COMBOPC.spad" 180016 180024 181101 181106) (-148 "COMBINAT.spad" 178761 178771 180006 180011) (-147 "COMBF.spad" 176129 176145 178751 178756) (-146 "COLOR.spad" 174966 174974 176119 176124) (-145 "CMPLXRT.spad" 174675 174692 174956 174961) (-144 "CLIP.spad" 170767 170775 174665 174670) (-143 "CLIF.spad" 169406 169422 170723 170762) (-142 "CLAGG.spad" 165881 165891 169386 169401) (-141 "CLAGG.spad" 162237 162249 165744 165749) (-140 "CINTSLPE.spad" 161562 161575 162227 162232) (-139 "CHVAR.spad" 159640 159662 161552 161557) (-138 "CHARZ.spad" 159555 159563 159620 159635) (-137 "CHARPOL.spad" 159063 159073 159545 159550) (-136 "CHARNZ.spad" 158816 158824 159043 159058) (-135 "CHAR.spad" 156684 156692 158806 158811) (-134 "CFCAT.spad" 156000 156008 156674 156679) (-133 "CDEN.spad" 155158 155172 155990 155995) (-132 "CCLASS.spad" 153307 153315 154569 154608) (-131 "CATEGORY.spad" 153086 153094 153297 153302) (-130 "CARTEN.spad" 148189 148213 153076 153081) (-129 "CARTEN2.spad" 147575 147602 148179 148184) (-128 "CARD.spad" 144864 144872 147549 147570) (-127 "CACHSET.spad" 144486 144494 144854 144859) (-126 "CABMON.spad" 144039 144047 144476 144481) (-125 "BYTE.spad" 143751 143759 144029 144034) (-124 "BYTEARY.spad" 142826 142834 142920 142947) (-123 "BTREE.spad" 141895 141905 142433 142460) (-122 "BTOURN.spad" 140898 140908 141502 141529) (-121 "BTCAT.spad" 140274 140284 140854 140893) (-120 "BTCAT.spad" 139682 139694 140264 140269) (-119 "BTAGG.spad" 138698 138706 139638 139677) (-118 "BTAGG.spad" 137746 137756 138688 138693) (-117 "BSTREE.spad" 136481 136491 137353 137380) (-116 "BRILL.spad" 134676 134687 136471 136476) (-115 "BRAGG.spad" 133590 133600 134656 134671) (-114 "BRAGG.spad" 132478 132490 133546 133551) (-113 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106547 109573 109816) (-92 "ATTRBUT.spad" 102563 102570 106520 106535) (-91 "ATRIG.spad" 102033 102040 102553 102558) (-90 "ATRIG.spad" 101501 101510 102023 102028) (-89 "ASTACK.spad" 100834 100843 101108 101135) (-88 "ASSOCEQ.spad" 99634 99645 100790 100795) (-87 "ASP9.spad" 98715 98728 99624 99629) (-86 "ASP8.spad" 97758 97771 98705 98710) (-85 "ASP80.spad" 97080 97093 97748 97753) (-84 "ASP7.spad" 96240 96253 97070 97075) (-83 "ASP78.spad" 95691 95704 96230 96235) (-82 "ASP77.spad" 95060 95073 95681 95686) (-81 "ASP74.spad" 94152 94165 95050 95055) (-80 "ASP73.spad" 93423 93436 94142 94147) (-79 "ASP6.spad" 92055 92068 93413 93418) (-78 "ASP55.spad" 90564 90577 92045 92050) (-77 "ASP50.spad" 88381 88394 90554 90559) (-76 "ASP4.spad" 87676 87689 88371 88376) (-75 "ASP49.spad" 86675 86688 87666 87671) (-74 "ASP42.spad" 85082 85121 86665 86670) (-73 "ASP41.spad" 83661 83700 85072 85077) (-72 "ASP35.spad" 82649 82662 83651 83656) (-71 "ASP34.spad" 81950 81963 82639 82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 6c515db3..6b7fd020 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(142764 . 3417777702) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(142764 . 3419169932) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (((|#2| |#2|) . T)) ((((-525)) . T)) -((($ $) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) +((($ $) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) ((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) -((($) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) +((($) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) ((|#2|) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525))))) (|has| |#1| (-842)) ((((-796)) . T)) ((((-796)) . T)) @@ -23,28 +23,28 @@ ((((-205)) . T) (((-796)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1|) . T)) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-786))) -((($ $) . 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T)) @@ -54,10 +54,10 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-517)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-796)) . T)) ((((-796)) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) ((((-796)) . 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T)) -(((|#3| |#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($ $) |has| |#3| (-160))) -(((|#4| |#4|) -3321 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-975))) (($ $) |has| |#4| (-160))) +(((|#3| |#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($ $) |has| |#3| (-160))) +(((|#4| |#4|) -3150 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-975))) (($ $) |has| |#4| (-160))) (((|#1|) . T)) (((|#2|) . T)) ((((-501)) |has| |#2| (-566 (-501))) (((-825 (-357))) |has| |#2| (-566 (-825 (-357)))) (((-825 (-525))) |has| |#2| (-566 (-825 (-525))))) @@ -231,21 +231,21 @@ ((((-796)) . T)) ((((-501)) |has| |#1| (-566 (-501))) (((-825 (-357))) |has| |#1| (-566 (-825 (-357)))) (((-825 (-525))) |has| |#1| (-566 (-825 (-525))))) ((((-796)) . 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T) (((-205)) . T) (((-357)) . T) (((-825 (-357))) . T)) ((((-796)) . T)) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) (((|#1|) |has| |#1| (-160))) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-796)) . T)) @@ -256,15 +256,15 @@ (|has| |#1| (-788)) (|has| |#1| (-1018)) (((|#1|) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) ((((-125)) . 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T)) (((|#1| (-902)) . T)) (((#0=(-803 |#1|) $) |has| #0# (-265 #0# #0#))) @@ -273,7 +273,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1065)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) (|has| (-1157 |#1| |#2| |#3| |#4|) (-136)) (|has| (-1157 |#1| |#2| |#3| |#4|) (-138)) (|has| |#1| (-136)) @@ -290,20 +290,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-975))) ((((-796)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (((|#1|) . 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T)) @@ -550,12 +550,12 @@ (((|#1| (-712) (-1003)) . T)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| (-497 (-1008 (-1089))) (-1008 (-1089))) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#1|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) (|has| |#2| (-734)) -(-3321 (|has| |#2| (-734)) (|has| |#2| (-786))) +(-3150 (|has| |#2| (-734)) (|has| |#2| (-786))) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) @@ -588,63 +588,63 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) (((|#2|) . 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T)) ((((-525) (-125)) . T)) ((((-796)) . T)) @@ -660,22 +660,22 @@ (|has| |#1| (-1018)) (((|#2|) . T)) ((((-501)) |has| |#2| (-566 (-501))) (((-825 (-357))) |has| |#2| (-566 (-825 (-357)))) (((-825 (-525))) |has| |#2| (-566 (-825 (-525))))) -(((|#4|) -3321 (|has| |#4| (-160)) (|has| |#4| (-341)))) -(((|#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#4|) -3150 (|has| |#4| (-160)) (|has| |#4| (-341)))) +(((|#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)))) ((((-796)) . T)) (((|#1|) . T)) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-842))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-842))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-842))) ((($ $) . T) ((#0=(-1089) $) |has| |#1| (-213)) ((#0# |#1|) |has| |#1| (-213)) ((#1=(-759 (-1089)) |#1|) . T) ((#1# $) . 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T)) (|has| (-385 |#2|) (-138)) (|has| (-385 |#2|) (-136)) @@ -688,22 +688,22 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-796)) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-366) (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-366) (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#2| (-1065)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((|#1|) . T)) ((((-366) (-1072)) . T)) (|has| |#1| (-517)) ((((-112 |#1|)) . T)) ((((-125)) . T)) ((((-525) |#1|) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#2|) . T)) ((((-796)) . T)) ((((-760 |#1|)) . T)) @@ -716,7 +716,7 @@ (((|#1|) |has| |#1| (-160))) ((((-796)) . T)) ((((-501)) |has| |#1| (-566 (-501)))) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) (((|#2|) |has| |#2| (-288 |#2|))) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -726,7 +726,7 @@ (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((($) . T) (((-525)) . T) (((-385 (-525))) . T)) (|has| |#2| (-346)) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) @@ -737,9 +737,9 @@ ((((-1087 |#1| |#2| |#3|) $) -12 (|has| (-1087 |#1| |#2| |#3|) (-265 (-1087 |#1| |#2| |#3|) (-1087 |#1| |#2| |#3|))) (|has| |#1| (-341))) (($ $) . T)) ((((-796)) . T)) ((((-796)) . T)) -((($) . T) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) ((($ $) . T)) ((($ $) . T)) ((((-796)) . T)) @@ -749,12 +749,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-385 (-525))) . 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T) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +((($) . T) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) (|has| |#1| (-769)) ((((-385 (-525))) |has| |#1| (-966 (-385 (-525)))) (((-525)) |has| |#1| (-966 (-525))) ((|#1|) . T)) (|has| |#1| (-1018)) @@ -819,8 +819,8 @@ (((|#3|) |has| |#3| (-1018))) (|has| |#3| (-346)) (((|#1|) . T) (((-796)) . T)) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((((-796)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) . T)) @@ -830,30 +830,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (((-525)) . T)) -((($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3321 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-160)) (|has| |#1| (-517))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) ((((-135)) . T)) (((|#1|) . T)) ((((-135)) . T)) -((($) -3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975)))) +((($) -3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975)))) ((((-135)) . T)) (((|#1| |#2| |#3|) . T)) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) (|has| $ (-138)) (|has| $ (-138)) (|has| |#1| (-1018)) ((((-796)) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-975)) (|has| |#1| (-1030))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-975)) (|has| |#1| (-1030))) ((($ $) |has| |#1| (-265 $ $)) ((|#1| $) |has| |#1| (-265 |#1| |#1|))) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) ((((-1089)) . T)) (|has| |#1| (-517)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) @@ -864,7 +864,7 @@ (|has| |#1| (-138)) (|has| |#1| (-136)) (|has| |#4| (-786)) -(((|#2| (-220 (-4045 |#1|) (-712)) (-798 |#1|)) . T)) +(((|#2| (-220 (-2028 |#1|) (-712)) (-798 |#1|)) . T)) (|has| |#3| (-786)) (((|#1| (-497 |#3|) |#3|) . T)) (|has| |#1| (-138)) @@ -878,21 +878,21 @@ (|has| |#1| (-136)) ((((-385 (-525))) |has| |#2| (-341)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-327)) (|has| |#1| (-346))) ((((-1056 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-160)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-213)) (|has| |#2| (-975))) -(((|#2|) . T) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -(-3321 (|has| |#3| (-734)) (|has| |#3| (-786))) -(-3321 (|has| |#3| (-734)) (|has| |#3| (-786))) +(((|#2|) . T) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +(-3150 (|has| |#3| (-734)) (|has| |#3| (-786))) +(-3150 (|has| |#3| (-734)) (|has| |#3| (-786))) ((((-796)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-640)) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) (|has| |#1| (-517)) (((|#1|) . T)) (((|#1|) . T)) @@ -914,10 +914,10 @@ (((|#1| (-385 (-525))) . T)) (((|#3|) . T) (((-564 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((#0=(-1087 |#1| |#2| |#3|) #0#) -12 (|has| (-1087 |#1| |#2| |#3|) (-288 (-1087 |#1| |#2| |#3|))) (|has| |#1| (-341))) (((-1089) #0#) -12 (|has| (-1087 |#1| |#2| |#3|) (-486 (-1089) (-1087 |#1| |#2| |#3|))) (|has| |#1| (-341)))) @@ -925,8 +925,8 @@ ((((-796)) . T)) ((((-796)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) (((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) |has| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (-288 (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) (((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) |has| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (-288 (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))))) ((((-796)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -937,10 +937,10 @@ ((($ $) . T) ((#0=(-798 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-769)) (|has| |#1| (-1018)) -(((|#2| |#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($ $) |has| |#2| (-160))) -(((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)))) -((((-525) (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($) |has| |#2| (-160))) +(((|#2| |#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($ $) |has| |#2| (-160))) +(((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)))) +((((-525) (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($) |has| |#2| (-160))) ((((-712)) . T)) ((((-525)) . T)) (|has| |#1| (-517)) @@ -953,29 +953,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-138)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-517))) ((((-825 (-525))) . T) (((-825 (-357))) . T) (((-501)) . T) (((-1089)) . T)) ((((-796)) . T)) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) ((($) . T)) ((((-796)) . 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T)) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (-12 (|has| |#3| (-213)) (|has| |#3| (-975))) (|has| |#2| (-1065)) -(((#0=(-51)) . T) (((-2 (|:| -2019 (-1089)) (|:| -1221 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1265 (-1089)) (|:| -1568 #0#))) . T)) (((|#1| |#2|) . T)) -(-3321 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) +(-3150 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) (((|#1| (-525) (-1003)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1| (-385 (-525)) (-1003)) . T)) -((($) -3321 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3150 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (((-385 (-525))) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -983,37 +983,37 @@ (-12 (|has| |#1| (-346)) (|has| |#2| (-346))) ((((-796)) . T)) ((((-1089) |#1|) |has| |#1| (-486 (-1089) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (((|#1|) . 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T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) ((($) . T)) ((((-796)) . T)) (((|#1|) . T)) ((((-803 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) ((((-796)) . T)) -(((|#3| |#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($ $) |has| |#3| (-160))) +(((|#3| |#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($ $) |has| |#3| (-160))) (|has| |#1| (-951)) ((((-796)) . T)) -(((|#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($) |has| |#3| (-160))) +(((|#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975))) (($) |has| |#3| (-160))) ((((-525) (-108)) . T)) (((|#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-346)) @@ -1021,31 +1021,31 @@ (|has| |#1| (-346)) ((((-1089) $) |has| |#1| (-486 (-1089) $)) (($ $) |has| |#1| (-288 $)) ((|#1| |#1|) |has| |#1| (-288 |#1|)) (((-1089) |#1|) |has| |#1| (-486 (-1089) |#1|))) ((((-1089)) |has| |#1| (-833 (-1089)))) -(-3321 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) +(-3150 (-12 (|has| |#1| (-213)) (|has| |#1| (-341))) (|has| |#1| (-327))) ((((-366) (-1036)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-366) |#1|) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1018)) ((((-796)) . T)) ((((-796)) . T)) ((((-843 |#1|)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-803 |#1|)) |has| #0# (-288 #0#))) (((|#1| |#2|) . T)) -(-3321 (|has| |#2| (-734)) (|has| |#2| (-786))) -(-3321 (|has| |#2| (-734)) (|has| |#2| (-786))) +(-3150 (|has| |#2| (-734)) (|has| |#2| (-786))) +(-3150 (|has| |#2| (-734)) (|has| |#2| (-786))) (-12 (|has| |#1| (-734)) (|has| |#2| (-734))) (((|#1|) . T)) (-12 (|has| |#1| (-734)) (|has| |#2| (-734))) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (|has| |#1| (-1111)) (((#0=(-525) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) ((((-385 (-525))) . T) (($) . T)) @@ -1056,8 +1056,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (|has| |#1| (-341)) ((((-525)) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) . T) ((#0=(-385 (-525)) #0#) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((($ $) . T) ((#0=(-385 (-525)) #0#) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1| |#1|) . T)) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) ((((-796)) . T)) ((((-796)) . T)) @@ -1072,14 +1072,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) -((($) . T) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-517))) -(((#0=(-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) #0#) |has| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (-288 (-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))))) +((($) . T) (((-385 (-525))) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-517))) +(((#0=(-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) #0#) |has| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (-288 (-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))))) ((($) . T)) (|has| |#2| (-788)) ((($) . T)) (((|#2|) |has| |#2| (-1018))) -((((-796)) -3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-565 (-796))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((-1171 |#2|)) . T)) +((((-796)) -3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-565 (-796))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((-1171 |#2|)) . T)) (|has| |#1| (-788)) (|has| |#1| (-788)) ((((-1072) (-51)) . T)) @@ -1087,10 +1087,10 @@ ((((-796)) . T)) ((((-525)) |has| #0=(-385 |#2|) (-587 (-525))) ((#0#) . T)) ((((-525) (-135)) . T)) -((((-525) (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T) ((|#1| |#2|) . T)) ((((-385 (-525))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-796)) . T)) ((((-843 |#1|)) . T)) (|has| |#1| (-341)) @@ -1115,31 +1115,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-160))) -((((-525) (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T) ((|#1| |#2|) . T)) +((((-525) (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-160))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842)))) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842)))) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) (((|#1|) . T)) ((((-501)) |has| |#1| (-566 (-501))) (((-825 (-357))) |has| |#1| (-566 (-825 (-357)))) (((-825 (-525))) |has| |#1| (-566 (-825 (-525))))) ((((-796)) . T)) -(((|#2|) . T) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (|has| |#2| (-786)) (-12 (|has| |#2| (-213)) (|has| |#2| (-975))) (|has| |#1| (-517)) (|has| |#1| (-1065)) ((((-1072) |#1|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) -(((#0=(-385 (-525)) #0#) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(((#0=(-385 (-525)) #0#) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-385 (-525))) |has| |#1| (-966 (-525))) (((-525)) |has| |#1| (-966 (-525))) (((-1089)) |has| |#1| (-966 (-1089))) ((|#1|) . T)) ((((-525) |#2|) . T)) ((((-385 (-525))) |has| |#1| (-966 (-385 (-525)))) (((-525)) |has| |#1| (-966 (-525))) ((|#1|) . T)) ((((-525)) |has| |#1| (-819 (-525))) (((-357)) |has| |#1| (-819 (-357)))) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1|) . T)) ((((-591 |#4|)) . T) (((-796)) . T)) ((((-501)) |has| |#4| (-566 (-501)))) @@ -1152,17 +1152,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1089)) |has| (-385 |#2|) (-833 (-1089)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-796)) -3321 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-565 (-796))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) (((-1171 |#3|)) . T)) +((((-796)) -3150 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-565 (-796))) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) (((-1171 |#3|)) . T)) ((((-525) |#2|) . T)) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) -(((|#2| |#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($ $) |has| |#2| (-160))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(((|#2| |#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($ $) |has| |#2| (-160))) ((((-796)) . T)) ((((-796)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T) ((|#2|) . T)) ((((-796)) . T)) ((((-796)) . T)) ((((-1072) (-1089) (-525) (-205) (-796)) . T)) @@ -1197,8 +1197,8 @@ (|has| |#1| (-37 (-385 (-525)))) ((((-796)) . T)) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) -(((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($) |has| |#2| (-160))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +(((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-975))) (($) |has| |#2| (-160))) (|has| $ (-138)) ((((-385 |#2|)) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-966 (-385 (-525)))) (((-525)) |has| #0# (-966 (-525))) ((#0#) . T)) @@ -1209,11 +1209,11 @@ (((|#3|) |has| |#3| (-160))) (|has| |#1| (-138)) (|has| |#1| (-136)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) @@ -1244,7 +1244,7 @@ ((((-929 |#1|)) . T) ((|#1|) . T)) ((((-796)) . T)) ((((-796)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-385 (-525))) . T) (((-385 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1085 |#1|)) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) @@ -1252,9 +1252,9 @@ (|has| |#1| (-788)) (((|#2|) . T)) ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) ((((-525) |#2|) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#2|) . T)) ((((-525) |#3|) . T)) (((|#2|) . T)) @@ -1269,7 +1269,7 @@ (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1018)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-341)) (((|#2|) . T) (((-525)) |has| |#2| (-966 (-525))) (((-385 (-525))) |has| |#2| (-966 (-385 (-525))))) @@ -1299,19 +1299,19 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1| |#2|) . T)) ((((-525) (-135)) . T)) -(((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) -((($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +(((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) +((($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#1| (-788)) (((|#2| (-712) (-1003)) . T)) (((|#1| |#2|) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-517))) (|has| |#1| (-732)) (((|#1|) |has| |#1| (-160))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3321 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) -(-3321 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) +(-3150 (|has| |#1| (-138)) (-12 (|has| |#1| (-341)) (|has| |#2| (-138)))) +(-3150 (|has| |#1| (-136)) (-12 (|has| |#1| (-341)) (|has| |#2| (-136)))) (((|#4|) . T)) (|has| |#1| (-136)) ((((-1072) |#1|) . T)) @@ -1324,10 +1324,10 @@ (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#3|) . T)) ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) (((|#1|) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018))) (((-890 |#1|)) . T)) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018))) (((-890 |#1|)) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) @@ -1340,8 +1340,8 @@ ((($) . T)) ((((-366) (-1072)) . T)) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-796)) -3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-565 (-796))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((-1171 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2019 (-1072)) (|:| -1221 #0#))) . T)) +((((-796)) -3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-565 (-796))) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((-1171 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1265 (-1072)) (|:| -1568 #0#))) . T)) (((|#1|) . T)) ((((-796)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) @@ -1349,7 +1349,7 @@ (|has| |#2| (-136)) (|has| |#2| (-138)) (|has| |#1| (-450)) -(-3321 (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) +(-3150 (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) (|has| |#1| (-341)) ((((-796)) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -1358,8 +1358,8 @@ (|has| |#1| (-786)) (|has| |#1| (-786)) ((((-796)) . T)) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1163 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1089)) |has| |#1| (-833 (-1089)))) @@ -1367,7 +1367,7 @@ ((((-796)) . T)) ((((-796)) . T)) (|has| |#1| (-1018)) -(((|#2| (-458 (-4045 |#1|) (-712)) (-798 |#1|)) . T)) +(((|#2| (-458 (-2028 |#1|) (-712)) (-798 |#1|)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1| (-497 (-1089)) (-1089)) . T)) (((|#1|) . T)) @@ -1387,16 +1387,16 @@ (|has| |#1| (-138)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) ((((-1087 |#1| |#2| |#3|)) |has| |#1| (-341))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-1089) (-51)) . T)) ((($ $) . T)) (((|#1| (-525)) . T)) ((((-843 |#1|)) . T)) -(((|#1|) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975))) (($) -3321 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)))) +(((|#1|) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975))) (($) -3150 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)))) (((|#1|) . T) (((-525)) |has| |#1| (-966 (-525))) (((-385 (-525))) |has| |#1| (-966 (-385 (-525))))) (|has| |#1| (-788)) (|has| |#1| (-788)) @@ -1411,13 +1411,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) (((|#1|) |has| |#1| (-160))) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) -(((|#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#2| (-788)) (|has| |#1| (-788)) -(-3321 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-842))) +(-3150 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-842))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-525) |#2|) . T)) -(((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)))) (|has| |#1| (-327)) (((|#3| |#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1018)))) ((($) . T) (((-385 (-525))) . T)) @@ -1425,7 +1425,7 @@ (|has| |#1| (-761)) (|has| |#1| (-761)) (((|#1|) . T)) -(-3321 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-786)) (|has| |#1| (-786)) (|has| |#1| (-786)) @@ -1434,13 +1434,13 @@ ((((-525)) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-1089)) |has| |#1| (-833 (-1089))) (((-1003)) . T)) (((|#1|) . T)) (|has| |#1| (-786)) -(((#0=(-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) #0#) |has| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (-288 (-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))))) +(((#0=(-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) #0#) |has| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (-288 (-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (|has| |#1| (-1018)) (((|#1|) . T)) @@ -1459,7 +1459,7 @@ (((|#1|) . T)) ((((-135)) . T)) (((|#2|) |has| |#2| (-160))) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((|#1|) . T)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1481,32 +1481,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) ((#0=(-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) #0#) |has| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (-288 (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))))) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-842))) +(((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) ((#0=(-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) #0#) |has| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (-288 (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-842))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)))) +(((|#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)))) (|has| |#1| (-788)) (|has| |#1| (-517)) ((((-538 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3321 (-12 (|has| |#1| (-341)) (|has| |#2| (-761))) (-12 (|has| |#1| (-341)) (|has| |#2| (-788)))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (-12 (|has| |#1| (-341)) (|has| |#2| (-761))) (-12 (|has| |#1| (-341)) (|has| |#2| (-788)))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-843 |#1|)) . T)) (((|#1| (-469 |#1| |#3|) (-469 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-712)) . T)) ((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) |has| |#1| (-160)) (($) |has| |#1| (-517))) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1087 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) -(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517)))) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-1087 |#1| |#2| |#3|)) |has| |#1| (-341)) ((|#1|) |has| |#1| (-160))) +(((|#1|) |has| |#1| (-160)) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517)))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) ((((-616 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1514,17 +1514,17 @@ ((((-796)) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) ((((-796)) . T)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) ((((-796)) . T)) ((((-796)) . T)) ((((-796)) . T)) (((|#2|) . T)) -(-3321 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((((-385 (-525))) |has| |#1| (-966 (-385 (-525)))) (((-525)) |has| |#1| (-966 (-525))) ((|#1|) . T)) (|has| |#1| (-1111)) (|has| |#1| (-1111)) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (|has| |#1| (-1111)) (|has| |#1| (-1111)) (((|#3| |#3|) . T)) @@ -1537,43 +1537,43 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((((-1072) (-51)) . T)) (|has| |#1| (-1018)) -(-3321 (|has| |#2| (-761)) (|has| |#2| (-788))) +(-3150 (|has| |#2| (-761)) (|has| |#2| (-788))) (((|#1|) . T)) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . 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T)) (((|#1|) . T)) ((((-525)) . T)) ((((-108)) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-37 (-385 (-525)))) (((|#1| (-525)) . T)) ((($) . T)) @@ -1595,7 +1595,7 @@ (((|#1| (-1135 |#1| |#2| |#3|)) . T)) (((|#1| (-712)) . T)) (((|#1|) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-796)) . T)) (|has| |#1| (-1018)) ((((-1072) |#1|) . T)) @@ -1615,18 +1615,18 @@ (((|#1|) . T)) ((((-525)) . T)) ((((-796)) . T)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-796)) . T)) (((|#3|) . T)) -(-3321 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) +(-3150 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) ((((-796)) . T)) ((((-1156 |#2| |#3| |#4|)) . T) (((-1157 |#1| |#2| |#3| |#4|)) . T)) ((((-796)) . T)) -((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-966 (-525)))) (((-564 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-966 (-525))) (((-385 (-525))) -3321 (-12 (|has| |#1| (-517)) (|has| |#1| (-966 (-525)))) (|has| |#1| (-966 (-385 (-525))))) (((-385 (-885 |#1|))) |has| |#1| (-517)) (((-885 |#1|)) |has| |#1| (-975)) (((-1089)) . T)) +((((-47)) -12 (|has| |#1| (-517)) (|has| |#1| (-966 (-525)))) (((-564 $)) . T) ((|#1|) . T) (((-525)) |has| |#1| (-966 (-525))) (((-385 (-525))) -3150 (-12 (|has| |#1| (-517)) (|has| |#1| (-966 (-525)))) (|has| |#1| (-966 (-385 (-525))))) (((-385 (-885 |#1|))) |has| |#1| (-517)) (((-885 |#1|)) |has| |#1| (-975)) (((-1089)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-712)) . T)) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-288 |#1|))) ((((-1157 |#1| |#2| |#3| |#4|)) . T)) ((((-525)) |has| |#1| (-819 (-525))) (((-357)) |has| |#1| (-819 (-357)))) @@ -1634,14 +1634,14 @@ (|has| |#1| (-517)) (((|#1|) . T)) ((((-796)) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (((|#1|) |has| |#1| (-160))) ((($) |has| |#1| (-517)) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1018))) -(((|#2|) -3321 (|has| |#2| (-160)) (|has| |#2| (-341)))) +(((|#2|) -3150 (|has| |#2| (-160)) (|has| |#2| (-341)))) ((((-1156 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-761)) @@ -1651,8 +1651,8 @@ (|has| |#1| (-786)) (|has| |#1| (-786)) (((|#1| (-525) (-1003)) . T)) -(-3321 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +(-3150 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1| (-385 (-525)) (-1003)) . T)) (((|#1| (-712) (-1003)) . T)) (|has| |#1| (-788)) @@ -1668,28 +1668,28 @@ (((|#1|) . T)) (|has| |#1| (-1018)) ((((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-587 (-525)))) ((|#2|) |has| |#1| (-341))) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((|#2|) |has| |#2| (-160))) (((|#1|) |has| |#1| (-160))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) ((((-796)) . T)) (|has| |#3| (-786)) ((((-796)) . T)) ((((-1156 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-796)) . T)) -(((|#1| |#1|) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975)))) +(((|#1| |#1|) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975)))) (((|#1|) . T)) ((((-525)) . T)) ((((-525)) . T)) -(((|#1|) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975)))) +(((|#1|) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-975)))) (((|#2|) |has| |#2| (-341))) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-788)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) |has| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (-288 (-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-842))) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) |has| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (-288 (-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-842))) (((|#2|) . T) (((-525)) |has| |#2| (-587 (-525)))) ((((-796)) . T)) ((((-796)) . T)) @@ -1724,18 +1724,18 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (((|#1|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-796)) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| (-385 |#2|) (-213)) (|has| |#1| (-842)) (((|#2|) |has| |#2| (-975))) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (|has| |#1| (-341)) (((|#1|) |has| |#1| (-160))) (((|#1| |#1|) . T)) @@ -1760,7 +1760,7 @@ (((|#1| (-385 (-525)) (-1003)) . T)) (((|#1| (-712) (-1003)) . T)) (((#0=(-385 |#2|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-525)) -3321 (|has| (-385 (-525)) (-966 (-525))) (|has| |#1| (-966 (-525)))) (((-385 (-525))) . T)) +(((|#1|) . T) (((-525)) -3150 (|has| (-385 (-525)) (-966 (-525))) (|has| |#1| (-966 (-525)))) (((-385 (-525))) . T)) (((|#1| (-556 |#1| |#3|) (-556 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -1779,24 +1779,24 @@ ((((-640)) . T)) (((|#2|) |has| |#2| (-160))) (|has| |#2| (-786)) -((((-108)) |has| |#1| (-1018)) (((-796)) -3321 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018)))) +((((-108)) |has| |#1| (-1018)) (((-796)) -3150 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))) . T)) ((((-796)) . T)) ((((-525) |#1|) . T)) ((((-640)) . T) (((-385 (-525))) . T) (((-525)) . T)) (((|#1| |#1|) |has| |#1| (-160))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) ((((-357)) . T)) ((((-640)) . T)) ((((-385 (-525))) . #0=(|has| |#2| (-341))) (($) . #0#)) (((|#1|) |has| |#1| (-160))) ((((-385 (-885 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#2|) . T)) (|has| |#2| (-788)) (((|#3|) |has| |#3| (-975))) @@ -1806,14 +1806,14 @@ (|has| |#1| (-788)) ((((-1089)) |has| |#2| (-833 (-1089)))) ((((-796)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-450)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-346)) (|has| |#1| (-341)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-975)) (|has| |#1| (-1030))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-450)) (|has| |#1| (-517)) (|has| |#1| (-975)) (|has| |#1| (-1030))) (|has| |#1| (-37 (-385 (-525)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1834,11 +1834,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-788)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)))) ((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1856,11 +1856,11 @@ ((((-501)) |has| |#1| (-566 (-501))) (((-825 (-525))) |has| |#1| (-566 (-825 (-525)))) (((-825 (-357))) |has| |#1| (-566 (-825 (-357)))) (((-357)) . #0=(|has| |#1| (-951))) (((-205)) . #0#)) (((|#1|) |has| |#1| (-341))) ((((-796)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((($ $) . T) (((-564 $) $) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) ((($) . T) (((-1157 |#1| |#2| |#3| |#4|)) . T) (((-385 (-525))) . T)) -((($) -3321 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) +((($) -3150 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-341)) (|has| |#1| (-341)) @@ -1871,11 +1871,11 @@ ((((-357)) . T)) (((|#3|) -12 (|has| |#3| (-288 |#3|)) (|has| |#3| (-1018)))) ((((-796)) . T)) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-842))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-842))) (((|#1|) . T)) (|has| |#1| (-788)) (|has| |#1| (-788)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (|has| |#1| (-1018)) @@ -1884,13 +1884,13 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((((-525)) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((#0=(-1156 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525)))) (($) . T)) ((((-525)) . T)) (|has| |#1| (-341)) -(-3321 (-12 (|has| (-1163 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3321 (-12 (|has| (-1163 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3150 (-12 (|has| (-1163 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3150 (-12 (|has| (-1163 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-341)) (|has| |#1| (-136)) (|has| |#1| (-138)) @@ -1907,18 +1907,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-525)) |has| |#1| (-587 (-525)))) (((|#3|) |has| |#3| (-160))) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) ((((-525)) . T)) (((|#1| $) |has| |#1| (-265 |#1| |#1|))) ((((-385 (-525))) . T) (($) . T) (((-385 |#1|)) . T) ((|#1|) . T)) ((((-796)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3321 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3150 (|has| |#1| (-269)) (|has| |#1| (-341))) ((#0=(-385 (-525)) #0#) |has| |#1| (-341))) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) ((($) . T)) ((((-525) |#1|) . T)) ((((-1089)) |has| (-385 |#2|) (-833 (-1089)))) -(((|#1|) . T) (($) -3321 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) +(((|#1|) . T) (($) -3150 (|has| |#1| (-269)) (|has| |#1| (-341))) (((-385 (-525))) |has| |#1| (-341))) ((((-501)) |has| |#2| (-566 (-501)))) ((((-631 |#2|)) . T) (((-796)) . T)) (((|#1|) . T)) @@ -1926,8 +1926,8 @@ (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) ((((-803 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) -(-3321 (|has| |#4| (-734)) (|has| |#4| (-786))) -(-3321 (|has| |#3| (-734)) (|has| |#3| (-786))) +(-3150 (|has| |#4| (-734)) (|has| |#4| (-786))) +(-3150 (|has| |#3| (-734)) (|has| |#3| (-786))) ((((-796)) . T)) ((((-796)) . T)) (((|#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) @@ -1943,17 +1943,17 @@ ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) ((((-385 (-525))) . T) (($) . T)) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-1129))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-1129))) ((($) . T)) ((((-385 (-525))) |has| #0=(-385 |#2|) (-966 (-385 (-525)))) (((-525)) |has| #0# (-966 (-525))) ((#0#) . T)) (((|#2|) . T) (((-525)) |has| |#2| (-587 (-525)))) (((|#1| (-712)) . T)) (|has| |#1| (-788)) (((|#1|) . T) (((-525)) |has| |#1| (-587 (-525)))) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (((-385 (-525))) -3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) ((((-525)) . T)) (|has| |#1| (-37 (-385 (-525)))) -((((-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))) |has| (-2 (|:| -2019 (-1072)) (|:| -1221 (-51))) (-288 (-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))))) +((((-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))) |has| (-2 (|:| -1265 (-1072)) (|:| -1568 (-51))) (-288 (-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))))) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (|has| |#1| (-786)) (|has| |#1| (-37 (-385 (-525)))) @@ -1978,24 +1978,24 @@ (((|#1| |#2|) . T)) ((((-135)) . T)) ((((-721 |#1| (-798 |#2|))) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (|has| |#1| (-1111)) (((|#1|) . T)) -(-3321 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) +(-3150 (|has| |#3| (-25)) (|has| |#3| (-126)) (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-346)) (|has| |#3| (-734)) (|has| |#3| (-786)) (|has| |#3| (-975)) (|has| |#3| (-1018))) ((((-1089) |#1|) |has| |#1| (-486 (-1089) |#1|))) (((|#2|) . T)) -((($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-843 |#1|)) . T)) ((($) . T)) ((((-385 (-885 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) ((((-501)) |has| |#4| (-566 (-501)))) ((((-796)) . T) (((-591 |#4|)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-786)) -(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) (((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) |has| (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|)) (-288 (-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))))) +(((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018))) (((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) |has| (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|)) (-288 (-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))))) (|has| |#1| (-1018)) (|has| |#1| (-341)) (|has| |#1| (-788)) @@ -2003,16 +2003,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) . T)) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) |has| |#1| (-160))) (|has| |#1| (-136)) (|has| |#1| (-138)) -(-3321 (-12 (|has| (-1087 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) -(-3321 (-12 (|has| (-1087 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) +(-3150 (-12 (|has| (-1087 |#1| |#2| |#3|) (-138)) (|has| |#1| (-341))) (|has| |#1| (-138))) +(-3150 (-12 (|has| (-1087 |#1| |#2| |#3|) (-136)) (|has| |#1| (-341))) (|has| |#1| (-136))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-138)) (|has| |#1| (-136)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) (|has| |#1| (-786)) (((|#1| |#2|) . T)) @@ -2035,9 +2035,9 @@ ((((-796)) . T)) ((((-796)) . T)) ((((-501)) |has| |#1| (-566 (-501)))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-1089) |#1|) |has| |#1| (-486 (-1089) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) -(((|#1|) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)))) +(((|#1|) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)))) ((((-294 |#1|)) . T)) (((|#2|) |has| |#2| (-341))) (((|#2|) . T)) @@ -2058,14 +2058,14 @@ (|has| |#1| (-136)) (|has| |#1| (-138)) ((($ $) . T)) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018))) (|has| |#1| (-517)) (((|#2|) . T)) ((((-525)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) ((((-538 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2090,12 +2090,12 @@ (((|#1| |#2|) . T)) ((((-1089) |#1|) . T)) (((|#4|) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) ((((-1089) (-51)) . T)) ((((-1156 |#2| |#3| |#4|) (-297 |#2| |#3| |#4|)) . T)) ((((-385 (-525))) |has| |#1| (-966 (-385 (-525)))) (((-525)) |has| |#1| (-966 (-525))) ((|#1|) . T)) ((((-796)) . T)) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-346)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975)) (|has| |#2| (-1018))) (((#0=(-1157 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-160)) ((#0=(-385 (-525)) #0#) |has| |#1| (-517)) (($ $) |has| |#1| (-517))) (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) @@ -2114,14 +2114,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (((|#2| |#3|) . T)) -(-3321 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#2| (-341)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) (((|#1| (-497 |#2|)) . T)) (((|#1| (-712)) . T)) (((|#1| (-497 (-1008 (-1089)))) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (|has| |#2| (-842)) -(-3321 (|has| |#2| (-734)) (|has| |#2| (-786))) +(-3150 (|has| |#2| (-734)) (|has| |#2| (-786))) ((((-796)) . T)) ((($ $) . T) ((#0=(-1156 |#2| |#3| |#4|) #0#) . T) ((#1=(-385 (-525)) #1#) |has| #0# (-37 (-385 (-525))))) ((((-843 |#1|)) . T)) @@ -2130,13 +2130,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-341)) -(-3321 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327)) (|has| |#1| (-517))) (|has| |#1| (-341)) ((($) . T) ((#0=(-1156 |#2| |#3| |#4|)) . T) (((-385 (-525))) |has| #0# (-37 (-385 (-525))))) (((|#1| |#2|) . T)) ((((-1087 |#1| |#2| |#3|)) |has| |#1| (-341))) -(-3321 (-12 (|has| |#1| (-286)) (|has| |#1| (-842))) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3321 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) +(-3150 (-12 (|has| |#1| (-286)) (|has| |#1| (-842))) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-833 (-1089))) (|has| |#1| (-975))) ((((-525)) |has| |#1| (-587 (-525))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-796)) . T)) @@ -2168,27 +2168,27 @@ (((|#1|) |has| |#1| (-160))) ((((-796)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) -(((|#2|) -3321 (|has| |#2| (-6 (-4252 "*"))) (|has| |#2| (-160)))) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(((|#2|) -3150 (|has| |#2| (-6 (-4252 "*"))) (|has| |#2| (-160)))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (|has| |#2| (-788)) (|has| |#2| (-842)) (|has| |#1| (-842)) (((|#2|) |has| |#2| (-160))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-796)) . T)) ((((-796)) . T)) ((((-501)) . T) (((-525)) . T) (((-825 (-525))) . T) (((-357)) . T) (((-205)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))) . T)) (((|#1|) . T)) ((((-796)) . T)) (((|#1| |#2|) . T)) (((|#1| (-385 (-525))) . T)) (((|#1|) . T)) -(-3321 (|has| |#1| (-269)) (|has| |#1| (-341))) +(-3150 (|has| |#1| (-269)) (|has| |#1| (-341))) ((((-135)) . T)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) (|has| |#1| (-786)) @@ -2203,7 +2203,7 @@ ((((-385 (-525))) . T) (($) . T)) ((((-796)) . T)) ((((-796)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-796)) . T)) ((((-796)) . T)) @@ -2214,7 +2214,7 @@ (((|#1|) . T)) ((((-591 (-135))) . T) (((-1072)) . T)) ((((-796)) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) ((((-1089) |#1|) |has| |#1| (-486 (-1089) |#1|)) ((|#1| |#1|) |has| |#1| (-288 |#1|))) (|has| |#1| (-788)) ((((-796)) . T)) @@ -2226,16 +2226,16 @@ ((((-796)) . T) (((-591 |#4|)) . T)) (((|#2|) . T)) ((((-843 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3321 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) -(-3321 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) +(-3150 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) +(-3150 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) ((((-1089) (-51)) . T)) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-786)) (|has| |#2| (-975))) (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#2|) . T)) @@ -2250,12 +2250,12 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (|has| |#1| (-761)) (((#0=(-843 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((((-385 |#2|)) . T)) (|has| |#1| (-786)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) . T) ((#1=(-525) #1#) . T) (($ $) . T)) ((((-843 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) (((|#2|) |has| |#2| (-975)) (((-525)) -12 (|has| |#2| (-587 (-525))) (|has| |#2| (-975)))) @@ -2265,25 +2265,25 @@ (|has| |#1| (-136)) (((|#2|) . T)) ((((-796)) . T)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2019 (-1089)) (|:| -1221 #0#))) . T)) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -1265 (-1089)) (|:| -1568 #0#))) . T)) (|has| |#1| (-327)) ((((-525)) . T)) ((((-796)) . T)) (((#0=(-1157 |#1| |#2| |#3| |#4|) $) |has| #0# (-265 #0# #0#))) (|has| |#1| (-341)) (((#0=(-1003) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (((#0=(-385 (-525)) #0#) . T) ((#1=(-640) #1#) . T) (($ $) . T)) ((((-294 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) |has| |#1| (-341))) (|has| |#1| (-1018)) (((|#1|) . T)) -(((|#1|) -3321 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) -(((|#1|) -3321 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3150 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) +(((|#1|) -3150 (|has| |#2| (-345 |#1|)) (|has| |#2| (-395 |#1|)))) (((|#2|) . T)) ((((-385 (-525))) . T) (((-640)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2302,7 +2302,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-525)) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#2|) . T) (((-525)) |has| |#2| (-587 (-525)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2339,7 +2339,7 @@ (|has| |#2| (-951)) ((($) . T)) (|has| |#1| (-842)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2347,24 +2347,24 @@ ((($) . T)) (|has| |#1| (-341)) ((((-843 |#1|)) . T)) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) -(-3321 (|has| |#1| (-346)) (|has| |#1| (-788))) +(-3150 (|has| |#1| (-346)) (|has| |#1| (-788))) (((|#1|) . T)) ((((-796)) . T)) ((((-1089)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-833 (-1089))))) ((((-385 |#2|) |#3|) . T)) ((($) . T) (((-385 (-525))) . T)) ((((-712) |#1|) . T)) -(((|#2| (-220 (-4045 |#1|) (-712))) . T)) +(((|#2| (-220 (-2028 |#1|) (-712))) . T)) (((|#1| (-497 |#3|)) . T)) ((((-385 (-525))) . T)) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((((-796)) . T)) -(((#0=(-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) #0#) |has| (-2 (|:| -2019 (-1089)) (|:| -1221 (-51))) (-288 (-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))))) +(((#0=(-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) #0#) |has| (-2 (|:| -1265 (-1089)) (|:| -1568 (-51))) (-288 (-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))))) (|has| |#1| (-842)) (|has| |#2| (-341)) -(-3321 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-796)) . T)) (((|#1|) . T)) @@ -2381,11 +2381,11 @@ (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-37 (-385 (-525)))) (-12 (|has| |#1| (-510)) (|has| |#1| (-769))) ((((-796)) . T)) -((((-1089)) -3321 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-833 (-1089)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-833 (-1089)))))) +((((-1089)) -3150 (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-833 (-1089)))) (-12 (|has| |#1| (-341)) (|has| |#2| (-833 (-1089)))))) (|has| |#1| (-341)) ((((-1089)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-833 (-1089))))) (|has| |#1| (-341)) @@ -2395,7 +2395,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-341))) (((|#2|) |has| |#1| (-341))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) @@ -2418,31 +2418,31 @@ (((|#2|) |has| |#1| (-341))) ((((-357)) -12 (|has| |#1| (-341)) (|has| |#2| (-819 (-357)))) (((-525)) -12 (|has| |#1| (-341)) (|has| |#2| (-819 (-525))))) (|has| |#1| (-341)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) (|has| |#1| (-341)) (|has| |#1| (-517)) (((|#4| |#4|) -12 (|has| |#4| (-288 |#4|)) (|has| |#4| (-1018)))) (((|#3|) . T)) (((|#1|) . T)) -(-3321 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) (((|#2|) . T)) (((|#2|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (|has| |#1| (-37 (-385 (-525)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-1072) |#1|) . T)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-346))) (|has| |#1| (-138)) ((((-538 |#1|)) . T)) ((($) . T)) @@ -2450,7 +2450,7 @@ (|has| |#1| (-517)) (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-37 (-385 (-525)))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-327))) (|has| |#1| (-138)) ((((-796)) . T)) ((($) . T)) @@ -2475,7 +2475,7 @@ (|has| |#1| (-732)) (|has| |#1| (-732)) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2496,7 +2496,7 @@ ((((-525)) . T)) ((((-796)) . T)) ((((-525)) . T)) -(-3321 (|has| |#2| (-734)) (|has| |#2| (-786))) +(-3150 (|has| |#2| (-734)) (|has| |#2| (-786))) ((((-157 (-357))) . T) (((-205)) . T) (((-357)) . T)) ((((-796)) . T)) ((((-796)) . T)) @@ -2508,9 +2508,9 @@ (((|#1|) . T) (($) . T) (((-385 (-525))) . T)) (|has| |#1| (-341)) (|has| |#1| (-341)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-450)) (|has| |#1| (-668)) (|has| |#1| (-833 (-1089))) (|has| |#1| (-975)) (|has| |#1| (-1030)) (|has| |#1| (-1018))) (|has| |#1| (-1065)) ((((-525) |#1|) . T)) (((|#1|) . T)) @@ -2528,8 +2528,8 @@ (((|#1|) . T)) (|has| |#1| (-517)) ((((-385 |#2|)) . T) (((-385 (-525))) . T) (($) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) ((((-357)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2538,7 +2538,7 @@ (|has| |#1| (-517)) (|has| |#1| (-1018)) ((((-721 |#1| (-798 |#2|))) |has| (-721 |#1| (-798 |#2|)) (-288 (-721 |#1| (-798 |#2|))))) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-842)) @@ -2548,12 +2548,12 @@ (|has| |#1| (-213)) (((|#1| (-497 (-1008 (-1089)))) . T)) (|has| |#2| (-341)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 (-51)))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) ((((-796)) . T)) ((((-796)) . T)) -(-3321 (|has| |#3| (-734)) (|has| |#3| (-786))) +(-3150 (|has| |#3| (-734)) (|has| |#3| (-786))) ((((-796)) . T)) ((((-796)) . T)) (((|#1|) . T)) @@ -2562,8 +2562,8 @@ ((((-525)) . T)) (((|#3|) . T)) ((((-796)) . T)) -(-3321 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3321 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) +(-3150 (|has| |#1| (-286)) (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-160)) (|has| |#1| (-517)) (|has| |#1| (-975))) (((#0=(-538 |#1|) #0#) . T) (($ $) . T) ((#1=(-385 (-525)) #1#) . T)) ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) (((|#1|) |has| |#1| (-160))) @@ -2576,7 +2576,7 @@ (((|#1|) . T)) ((((-796)) |has| |#1| (-565 (-796)))) ((((-273 |#3|)) . T)) -(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3321 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) +(((#0=(-385 (-525)) #0#) |has| |#2| (-37 (-385 (-525)))) ((|#2| |#2|) . T) (($ $) -3150 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) @@ -2584,20 +2584,20 @@ (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) (((|#1|) . T) (((-385 (-525))) . T) (($) . T)) -((($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1| |#1|) . T) ((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525))))) -((($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1| |#1|) . 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T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-842)) (|has| |#1| (-842)) -((($) -3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#1|) . T)) -((((-2 (|:| -2019 (-1072)) (|:| -1221 |#1|))) . T)) +((((-2 (|:| -1265 (-1072)) (|:| -1568 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2611,10 +2611,10 @@ (((|#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018)))) (((#0=(-385 (-525)) #0#) . T)) ((((-385 (-525))) . T)) -(-3321 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-25)) (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) (((|#1|) . T)) (((|#1|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((((-501)) . T)) ((((-796)) . T)) ((((-1089)) |has| |#2| (-833 (-1089))) (((-1003)) . T)) @@ -2628,12 +2628,12 @@ ((($ $) . T) ((#0=(-385 (-525)) #0#) . T)) ((((-1089)) |has| |#1| (-833 (-1089)))) ((((-843 |#1|)) . T) (((-385 (-525))) . T) (($) . T)) -((($) . T) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) -(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((($) . T) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#1|) . T)) +(((#0=(-385 (-525)) #0#) |has| |#1| (-37 (-385 (-525)))) ((|#1| |#1|) . T) (($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-517)))) ((($) . T) (((-385 (-525))) . T)) (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((|#2|) |has| |#2| (-975)) (((-525)) -12 (|has| |#2| (-587 (-525))) (|has| |#2| (-975)))) -((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3321 (|has| |#1| (-160)) (|has| |#1| (-517)))) +((((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T) (($) -3150 (|has| |#1| (-160)) (|has| |#1| (-517)))) (|has| |#1| (-517)) (((|#1|) |has| |#1| (-341))) ((((-525)) . T)) @@ -2652,8 +2652,8 @@ ((((-796)) . T)) (|has| |#2| (-761)) (|has| |#2| (-761)) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2|) |has| |#1| (-341)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1|) . T) (((-525)) |has| |#1| (-966 (-525))) (((-385 (-525))) |has| |#1| (-966 (-385 (-525))))) ((((-525)) |has| |#1| (-819 (-525))) (((-357)) |has| |#1| (-819 (-357)))) @@ -2679,12 +2679,12 @@ (((|#2| (-712)) . T)) ((((-1089)) . T)) ((((-803 |#1|)) . 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T)) +(((#0=(-385 (-525)) #0#) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1| |#1|) . T)) ((((-525) |#1|) . T)) ((((-294 |#1|)) . T)) (((#0=(-640) (-1085 #0#)) . T)) -((((-385 (-525))) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) +((((-385 (-525))) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) (($) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-786)) ((($ $) . T) ((#0=(-798 |#1|) $) . T) ((#0# |#2|) . T)) @@ -2909,12 +2909,12 @@ (((#0=(-1157 |#1| |#2| |#3| |#4|)) |has| #0# (-288 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2| |#2|) |has| |#1| (-341)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3321 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341)))) +((($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341))) ((|#2| |#2|) |has| |#1| (-341)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . T) (($ $) -3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-517))) ((#0=(-385 (-525)) #0#) -3150 (|has| |#1| (-37 (-385 (-525)))) (|has| |#1| (-341)))) (|has| |#2| (-213)) (|has| $ (-138)) ((((-796)) . T)) -((($) . T) (((-385 (-525))) -3321 (|has| |#1| (-341)) (|has| |#1| (-327))) ((|#1|) . T)) +((($) . 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T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) (((|#1|) . T)) (((|#1| (-497 (-759 (-1089)))) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#1|) . T)) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) (((|#1|) . T)) -(-3321 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) -(-3321 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-734)) (|has| |#2| (-734)))) +(-3150 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-734)) (|has| |#2| (-734)))) ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) ((($) . T) (((-803 |#1|)) . T) (((-385 (-525))) . T)) ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) @@ -2951,15 +2951,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-385 |#2|)) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-385 (-525)) #0#) . T) (($ $) . T)) ((((-525)) . T)) @@ -2988,32 +2988,32 @@ ((((-1163 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1089)) . T) (((-796)) . T)) (|has| |#1| (-341)) -((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) +((((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) |has| |#2| (-160)) (($) -3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-385 (-525))) |has| |#2| (-37 (-385 (-525)))) ((|#2|) . T)) -((($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((((-1022)) . T)) ((((-796)) . T)) -((($) -3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) ((($) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((|#1|) . T)) ((($) . T)) -((($) -3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) +((($) -3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((|#1|) |has| |#1| (-160)) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (|has| |#2| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-160))) ((((-640)) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#1|) |has| |#1| (-160))) (((|#1|) |has| |#1| (-160))) ((((-385 (-525))) . T) (($) . T)) (((|#1| (-525)) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-341)) (|has| |#1| (-341)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) -(-3321 (|has| |#1| (-160)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-160)) (|has| |#1| (-517))) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-712)) . T)) @@ -3028,16 +3028,16 @@ ((((-825 (-357))) . T) (((-825 (-525))) . T) (((-1089)) . T) (((-501)) . T)) (((|#1|) . T)) ((((-796)) . T)) -(-3321 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) -(-3321 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-734)) (|has| |#2| (-734)))) +(-3150 (|has| |#2| (-126)) (|has| |#2| (-160)) (|has| |#2| (-341)) (|has| |#2| (-734)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-126)) (|has| |#2| (-126))) (-12 (|has| |#1| (-734)) (|has| |#2| (-734)))) ((((-525)) . T)) ((((-525)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3321 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) +(-3150 (|has| |#2| (-160)) (|has| |#2| (-786)) (|has| |#2| (-975))) ((((-1089)) -12 (|has| |#2| (-833 (-1089))) (|has| |#2| (-975)))) -(-3321 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-668)) (|has| |#2| (-668)))) +(-3150 (-12 (|has| |#1| (-450)) (|has| |#2| (-450))) (-12 (|has| |#1| (-668)) (|has| |#2| (-668)))) (|has| |#1| (-136)) (|has| |#1| (-138)) (|has| |#1| (-341)) @@ -3061,7 +3061,7 @@ ((((-1072) (-1089) (-525) (-205) (-796)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3321 (|has| |#1| (-327)) (|has| |#1| (-346))) +(-3150 (|has| |#1| (-327)) (|has| |#1| (-346))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-796)) . T)) @@ -3069,7 +3069,7 @@ ((($) . T) ((|#1|) . T) (((-385 (-525))) |has| |#1| (-37 (-385 (-525))))) (((|#2|) |has| |#2| (-1018)) (((-525)) -12 (|has| |#2| (-966 (-525))) (|has| |#2| (-1018))) (((-385 (-525))) -12 (|has| |#2| (-966 (-385 (-525)))) (|has| |#2| (-1018)))) ((((-501)) |has| |#1| (-566 (-501)))) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-788)) (|has| |#1| (-1018)))) ((($) . T) (((-385 (-525))) . T)) (|has| |#1| (-842)) (|has| |#1| (-842)) @@ -3078,14 +3078,14 @@ ((((-796)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-160))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-517))) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-786))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-517))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-786))) (((|#2|) . T)) -(-3321 (|has| |#1| (-21)) (|has| |#1| (-786))) +(-3150 (|has| |#1| (-21)) (|has| |#1| (-786))) (((|#1|) |has| |#1| (-160))) (((|#1|) . T)) (((|#1|) . T)) -((((-796)) -3321 (-12 (|has| |#1| (-565 (-796))) (|has| |#2| (-565 (-796)))) (-12 (|has| |#1| (-1018)) (|has| |#2| (-1018))))) +((((-796)) -3150 (-12 (|has| |#1| (-565 (-796))) (|has| |#2| (-565 (-796)))) (-12 (|has| |#1| (-1018)) (|has| |#2| (-1018))))) ((((-385 |#2|) |#3|) . T)) ((((-385 (-525))) . T) (($) . T)) (|has| |#1| (-37 (-385 (-525)))) @@ -3097,17 +3097,17 @@ (((|#1|) . T) (((-385 (-525))) . T) (((-525)) . T) (($) . T)) (((#0=(-525) #0#) . T)) ((($) . T) (((-385 (-525))) . T)) -(-3321 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) -(-3321 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) +(-3150 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) +(-3150 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) (|has| |#4| (-734)) -(-3321 (|has| |#4| (-734)) (|has| |#4| (-786))) +(-3150 (|has| |#4| (-734)) (|has| |#4| (-786))) (|has| |#4| (-786)) (|has| |#3| (-734)) -(-3321 (|has| |#3| (-734)) (|has| |#3| (-786))) +(-3150 (|has| |#3| (-734)) (|has| |#3| (-786))) (|has| |#3| (-786)) ((((-525)) . T)) (((|#2|) . T)) -((((-1089)) -3321 (-12 (|has| (-1087 |#1| |#2| |#3|) (-833 (-1089))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-833 (-1089)))))) +((((-1089)) -3150 (-12 (|has| (-1087 |#1| |#2| |#3|) (-833 (-1089))) (|has| |#1| (-341))) (-12 (|has| |#1| (-15 * (|#1| (-525) |#1|))) (|has| |#1| (-833 (-1089)))))) ((((-1089)) -12 (|has| |#1| (-15 * (|#1| (-385 (-525)) |#1|))) (|has| |#1| (-833 (-1089))))) ((((-1089)) -12 (|has| |#1| (-15 * (|#1| (-712) |#1|))) (|has| |#1| (-833 (-1089))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3122,11 +3122,11 @@ ((((-1087 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1087 |#1| |#2| |#3|)) |has| |#1| (-341))) ((((-1054 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) ((($) . T)) (|has| |#1| (-951)) -(((|#2|) . T) (((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) ((((-796)) . T)) ((((-501)) |has| |#2| (-566 (-501))) (((-825 (-525))) |has| |#2| (-566 (-825 (-525)))) (((-825 (-357))) |has| |#2| (-566 (-825 (-357)))) (((-357)) . #0=(|has| |#2| (-951))) (((-205)) . #0#)) ((((-1089) (-51)) . T)) @@ -3138,15 +3138,15 @@ ((((-1087 |#1| |#2| |#3|)) . T)) ((((-1087 |#1| |#2| |#3|)) . T) (((-1080 |#1| |#2| |#3|)) . T)) ((((-796)) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) ((((-525) |#1|) . T)) ((((-1087 |#1| |#2| |#3|)) |has| |#1| (-341))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-341)) -(((|#3|) . T) ((|#2|) . T) (($) -3321 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) ((|#4|) -3321 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-975)))) -(((|#2|) . T) (($) -3321 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) ((|#3|) -3321 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975)))) +(((|#3|) . T) ((|#2|) . T) (($) -3150 (|has| |#4| (-160)) (|has| |#4| (-786)) (|has| |#4| (-975))) ((|#4|) -3150 (|has| |#4| (-160)) (|has| |#4| (-341)) (|has| |#4| (-975)))) +(((|#2|) . T) (($) -3150 (|has| |#3| (-160)) (|has| |#3| (-786)) (|has| |#3| (-975))) ((|#3|) -3150 (|has| |#3| (-160)) (|has| |#3| (-341)) (|has| |#3| (-975)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-341)) @@ -3158,37 +3158,37 @@ ((((-796)) . T)) ((((-796)) . T)) (((|#1|) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) ((((-525) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-341)) (|has| |#2| (-265 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-842))) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-429)) (|has| |#1| (-842))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) ((((-796)) . T)) ((((-796)) . T)) ((((-796)) . T)) (((|#1| (-497 |#2|)) . T)) -((((-2 (|:| -2019 (-1089)) (|:| -1221 (-51)))) . T)) +((((-2 (|:| -1265 (-1089)) (|:| -1568 (-51)))) . T)) (((|#1| (-525)) . T)) (((|#1| (-385 (-525))) . T)) (((|#1| (-712)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-385 (-525))) . T)) -(-3321 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) -(-3321 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) +(-3150 (|has| |#2| (-429)) (|has| |#2| (-517)) (|has| |#2| (-842))) +(-3150 (|has| |#1| (-429)) (|has| |#1| (-517)) (|has| |#1| (-842))) ((($) . T)) (((|#2| (-497 (-798 |#1|))) . T)) ((((-525) |#1|) . T)) (((|#2|) . T)) (((|#2| (-712)) . T)) -((((-796)) -3321 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) +((((-796)) -3150 (|has| |#1| (-565 (-796))) (|has| |#1| (-1018)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1072) |#1|) . T)) ((((-385 |#2|)) . T)) -((((-2 (|:| -2019 |#1|) (|:| -1221 |#2|))) . T)) +((((-2 (|:| -1265 |#1|) (|:| -1568 |#2|))) . T)) (|has| |#1| (-517)) (|has| |#1| (-517)) ((($) . T) ((|#2|) . T)) @@ -3196,12 +3196,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-265 |#2| |#2|))) (((|#1| (-591 |#1|)) |has| |#1| (-786))) -(-3321 (|has| |#1| (-213)) (|has| |#1| (-327))) -(-3321 (|has| |#1| (-341)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-213)) (|has| |#1| (-327))) +(-3150 (|has| |#1| (-341)) (|has| |#1| (-327))) (|has| |#1| (-1018)) (((|#1|) . T)) ((((-385 (-525))) . T) (($) . T)) -((((-929 |#1|)) . T) ((|#1|) . T) (((-525)) -3321 (|has| (-929 |#1|) (-966 (-525))) (|has| |#1| (-966 (-525)))) (((-385 (-525))) -3321 (|has| (-929 |#1|) (-966 (-385 (-525)))) (|has| |#1| (-966 (-385 (-525)))))) +((((-929 |#1|)) . T) ((|#1|) . T) (((-525)) -3150 (|has| (-929 |#1|) (-966 (-525))) (|has| |#1| (-966 (-525)))) (((-385 (-525))) -3150 (|has| (-929 |#1|) (-966 (-385 (-525)))) (|has| |#1| (-966 (-385 (-525)))))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) (((|#1| |#1|) -12 (|has| |#1| (-288 |#1|)) (|has| |#1| (-1018)))) @@ -3212,9 +3212,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1054 |#1| |#2|) #0#) |has| (-1054 |#1| |#2|) (-288 (-1054 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) #0#) |has| (-2 (|:| -2019 |#1|) (|:| -1221 |#2|)) (-288 (-2 (|:| -2019 |#1|) (|:| -1221 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((#0=(-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) #0#) |has| (-2 (|:| -1265 |#1|) (|:| -1568 |#2|)) (-288 (-2 (|:| -1265 |#1|) (|:| -1568 |#2|))))) (((#0=(-112 |#1|)) |has| #0# (-288 #0#))) -(-3321 (|has| |#1| (-788)) (|has| |#1| (-1018))) +(-3150 (|has| |#1| (-788)) (|has| |#1| (-1018))) ((($ $) . T)) ((($ $) . T) ((#0=(-798 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-213)) ((|#2| |#1|) |has| |#1| (-213)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index d18ff84e..489ad68d 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3417777695) +(30 . 3419169920) (4253 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,649 +460,647 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |semiDegreeSubResultantEuclidean| |leaf?| - |fixedPoint| |rationalPoints| |declare| |imagk| |numericIfCan| |or| - |removeSinSq| |top| |droot| |and| |continue| |OMlistSymbols| |e| - |RittWuCompare| |clip| |taylorRep| |f02agf| |entry| - |permutationRepresentation| |lift| |leadingBasisTerm| - |useEisensteinCriterion| |singularitiesOf| |reduce| |jacobian| - |addBadValue| |move| |setPosition| |SturmHabichtMultiple| - |semiLastSubResultantEuclidean| |numeric| |arguments| |padicFraction| - |tubeRadius| |radical| |extractClosed| |test| |alternating| - |tanintegrate| |numericalOptimization| |derivationCoordinates| - |function| |constant?| |id| |An| |s14abf| |laguerre| |retractIfCan| - |pastel| |real?| |jacobi| |bipolarCylindrical| |bumptab| |separant| - |cSech| |prefix| |table| |pair?| |mkcomm| |colorFunction| |iiacsc| - |mainSquareFreePart| |df2mf| |fortranComplex| |new| |OMgetEndAtp| - |exprHasWeightCosWXorSinWX| |loopPoints| |rootSimp| |LyndonWordsList| - |supDimElseRittWu?| |push!| |powerSum| |read!| |transpose| |property| - |certainlySubVariety?| |complexNumeric| |allRootsOf| - |quasiMonicPolynomials| |sts2stst| |argscript| |tubePoints| |redpps| - |bombieriNorm| |moduloP| |symmetric?| |squareFreePart| |iidsum| - |fracPart| |alternatingGroup| |saturate| |enqueue!| |extractIndex| - |kernels| |fortranDoubleComplex| |df2st| |decreasePrecision| - |evenlambert| |physicalLength| |indicialEquationAtInfinity| - |extractTop!| |slex| |alternative?| |leftRankPolynomial| |cot| - |coth2trigh| |removeSquaresIfCan| |univariate| |signAround| |B1solve| - |exponential| |degree| |eq| |zCoord| |wordsForStrongGenerators| - |complexNumericIfCan| |sec| |constantOpIfCan| |sn| |scalarTypeOf| - |c06ecf| |depth| |iter| |factorByRecursion| |midpoint| |besselI| - |cRationalPower| |adaptive?| |csc| |createIrreduciblePoly| - |symmetricPower| |infLex?| |iiasinh| |triangSolve| |optpair| |map| - |showTheFTable| |imagI| |reducedContinuedFraction| |setErrorBound| - |polynomialZeros| |asin| |c06fuf| |factor| - |internalSubQuasiComponent?| |overbar| |integralCoordinates| - |rational?| |setImagSteps| |orbits| |numberOfPrimitivePoly| |lcm| - |pol| |acos| |resetVariableOrder| |internalIntegrate| |sqrt| - |diagonals| |rombergo| |swapRows!| |pointPlot| |subCase?| |stFunc1| - |leftDiscriminant| |OMputFloat| |isAbsolutelyIrreducible?| |atan| - |invertibleElseSplit?| |real| |endSubProgram| |clearCache| |f01maf| - |relativeApprox| |printTypes| |getButtonValue| |lazyPremWithDefault| - |updateStatus!| |minimalPolynomial| |selectfirst| - |numberOfFractionalTerms| |acot| |imag| |cycleEntry| |vedf2vef| - |upperCase?| |unmakeSUP| |stirling2| |pade| |rootPoly| |printInfo| - |directProduct| |s17agf| |createNormalPoly| |argument| |gcd| |asec| - |kovacic| |ScanFloatIgnoreSpaces| |objectOf| |expenseOfEvaluationIF| - |mainKernel| |invertible?| |jordanAlgebra?| |convert| |exp| - |uniform01| |outputSpacing| |in?| |cycleRagits| |union| |acsc| SEGMENT - |iitanh| |scripted?| |localAbs| |any| |false| |bipolar| |totolex| - |s13acf| |sturmSequence| |localIntegralBasis| |iiatan| - |primlimitedint| |OMputApp| |trivialIdeal?| |sinh| |string| |xn| - |destruct| |Is| |lp| |charthRoot| |rdregime| |stoseInvertibleSet| - |genericRightTrace| |evenInfiniteProduct| |s15aef| |nullary| - |clipSurface| |selectODEIVPRoutines| |repeating| |roughBasicSet| - |algintegrate| |whileLoop| |numberOfComputedEntries| |zeroDimPrimary?| - |setStatus!| |decomposeFunc| |character?| |monicRightDivide| - |iCompose| |contractSolve| |iiacot| |e01daf| |factorList| - |toseInvertible?| |monomialIntegrate| |getOrder| |inspect| - |schwerpunkt| |branchPoint?| |c06fpf| |create3Space| |mapUnivariate| - |getlo| |splitLinear| |hermiteH| |selectOptimizationRoutines| - |changeWeightLevel| |setTopPredicate| |inGroundField?| |redPo| - |definingPolynomial| |Ci| |monomial| |s01eaf| |rootRadius| |error| - |distribute| |randomLC| |internalSubPolSet?| |fprindINFO| |log| - |compose| |d01anf| |recolor| |singRicDE| |multivariate| - |stoseInternalLastSubResultant| |curveColorPalette| |binaryTree| - |beauzamyBound| |assert| |limitedint| |e02bdf| |curryRight| |csch| - |stoseInvertible?reg| |scalarMatrix| |simpleBounds?| |clikeUniv| - |variables| |wholePart| |constDsolve| |inRadical?| |rationalIfCan| - |pmComplexintegrate| |subresultantVector| |exponential1| |asinh| - |imagE| |useSingleFactorBound?| |cyclic| |Aleph| |equiv| |middle| - |e02adf| |numberOfCycles| |acscIfCan| |makeSUP| |scan| |acosh| - |e02akf| |fixedDivisor| |s17ahf| |var1Steps| |antiAssociative?| - |completeHermite| |fglmIfCan| |systemCommand| |ideal| - |quasiAlgebraicSet| |unrankImproperPartitions1| |abs| - |leftFactorIfCan| |trueEqual| |keys| |implies?| |e01sef| |assign| |dn| - |trapezoidalo| |leftTraceMatrix| |commaSeparate| |expintegrate| - |csubst| |normInvertible?| |prod| |extendIfCan| |hcrf| |whatInfinity| - |cCos| |approxSqrt| |bandedHessian| |moebius| |denomRicDE| - |externalList| |atanh| |algebraicCoefficients?| |rationalPoint?| - |nthExpon| |buildSyntax| |stronglyReduce| |taylor| |next| |exptMod| - |normal| |root?| |imagj| |getDatabase| |stoseLastSubResultant| - |indiceSubResultant| |acoth| |getBadValues| |copy!| |laurent| - |setOrder| |graphState| |rquo| |oblateSpheroidal| |scopes| - |OMgetError| |bat| |viewPosDefault| |findBinding| |asech| |rightRank| - |structuralConstants| |localUnquote| |f02wef| |gethi| |puiseux| - |reduceBasisAtInfinity| |symbol| |evaluateInverse| |factorOfDegree| - |preprocess| |factorial| |asinhIfCan| |KrullNumber| |expIfCan| - |subSet| |createNormalElement| |cAcot| |setAttributeButtonStep| - |option?| |matrixConcat3D| |irreducibleRepresentation| |expandPower| - |entry?| |e02baf| |Beta| |palgLODE0| |relerror| |light| |leadingIndex| - |inv| |every?| |integer| |decrease| |factorPolynomial| |romberg| - |unexpand| |setLegalFortranSourceExtensions| |legendre| |terms| - |child?| |iicsc| |ground?| |primaryDecomp| |infieldint| |iiacosh| - |iiacoth| |minColIndex| |associatorDependence| |s19abf| |d01gbf| - |removeRoughlyRedundantFactorsInContents| |linkToFortran| - |tubePointsDefault| |ground| |physicalLength!| |resetBadValues| - |factorSFBRlcUnit| |ListOfTerms| |newLine| - |removeIrreducibleRedundantFactors| |eigenMatrix| |setVariableOrder| - |mindegTerm| |aromberg| |length| |complexLimit| - |unrankImproperPartitions0| |setClosed| |leadingMonomial| |rk4f| - |float?| |readLine!| |palgRDE0| |irreducible?| |f01rcf| |paren| - |argumentListOf| |algDsolve| |discriminantEuclidean| |scripts| - |univariatePolynomials| |writable?| |modularGcdPrimitive| |totalLex| - |startTableInvSet!| |leadingCoefficient| |concat!| |OMserve| - |ocf2ocdf| |center| |squareFreeFactors| |cons| |quote| - |clearTheSymbolTable| |cTanh| |blankSeparate| |iicsch| |bindings| - |transform| |seriesSolve| |makeSeries| |s13aaf| |primitiveMonomials| - |solveInField| |totalDifferential| |binomThmExpt| |inc| - |totalGroebner| |internalLastSubResultant| |leftDivide| - |rationalPower| |radPoly| |divisor| |primPartElseUnitCanonical| - |moebiusMu| |lyndon| |is?| |reductum| |quasiRegular| |euclideanSize| - |numberOfIrreduciblePoly| |log2| |unit?| |setPoly| |orbit| |tab| - |sech| |reverseLex| |string?| |shiftRoots| |leftMult| - |selectAndPolynomials| |pushdown| |rational| |elliptic?| |reset| - |solveLinear| |reduceLODE| |d01gaf| |purelyAlgebraic?| |tube| - |currentCategoryFrame| |triangularSystems| |alphabetic?| |submod| - |numer| |numberOfComponents| |enumerate| |univariatePolynomialsGcds| - |generic| |setColumn!| |credPol| |rst| |acothIfCan| - |halfExtendedSubResultantGcd2| |meatAxe| |weierstrass| |fortranDouble| - |normal?| |makeViewport2D| |vertConcat| |denom| |minRowIndex| - |selectMultiDimensionalRoutines| - |solveLinearPolynomialEquationByRecursion| |multiEuclidean| |notelem| - |lazyPseudoQuotient| |LazardQuotient| |head| |f02bjf| |pop!| - |sinh2csch| |reorder| |range| |listexp| |seed| |putGraph| |imagi| - |presub| |weights| |finiteBasis| |f04maf| |cyclicCopy| |prime| - |monomRDE| |leftExactQuotient| |setvalue!| |OMputSymbol| - |indicialEquations| |logIfCan| |pi| |fixedPointExquo| |viewPhiDefault| - |escape| |numberOfVariables| |balancedBinaryTree| |delete!| - |linearDependenceOverZ| |getMultiplicationTable| |column| |outputArgs| - |semiResultantEuclideannaif| |getCurve| |select!| |normalize| - |infinity| |zero?| |s21baf| |printStats!| |numberOfChildren| - |ScanRoman| |curveColor| |commutative?| |drawToScale| |palglimint0| - |normalized?| |coerceListOfPairs| |parent| |bracket| |rotatex| - |modularGcd| |tanh2coth| |closed?| |integral| |rootDirectory| - |singularAtInfinity?| |mkPrim| |primintegrate| - |unprotectedRemoveRedundantFactors| |csc2sin| |btwFact| - |idealiserMatrix| |computeBasis| |validExponential| |airyAi| |pack!| - |binaryFunction| |critMonD1| |npcoef| |double?| |musserTrials| |cAsin| - |e02dcf| |OMputObject| |leftRecip| |s17ajf| |orthonormalBasis| |nary?| - |primextendedint| |kernel| |mesh| |epilogue| |c02agf| - |fortranLinkerArgs| |seriesToOutputForm| |LyndonWordsList1| |maxint| - |exactQuotient!| |overset?| |OMgetType| |SturmHabicht| |prinshINFO| - |conical| |draw| |leftMinimalPolynomial| |laplace| |monic?| - |weakBiRank| |generalizedEigenvector| |multiEuclideanTree| |redPol| - |makeFloatFunction| |denomLODE| |OMencodingUnknown| |sin2csc| - |modifyPoint| |bag| |splitSquarefree| |color| |resultantEuclidean| - |testDim| |addPoint2| |reciprocalPolynomial| |torsion?| |OMgetEndBind| - |parametric?| |lazyGintegrate| |iFTable| |myDegree| - |drawComplexVectorField| |algebraic?| |wholeRagits| |OMputString| - |phiCoord| |result| |viewpoint| |inverseIntegralMatrix| - |integralMatrix| |genus| |sinIfCan| |f02axf| |zoom| |symbol?| - |derivative| |twist| |c06frf| |removeZeroes| |setfirst!| |poisson| - |central?| |genericRightDiscriminant| |identityMatrix| |nthRootIfCan| - |element?| |semiResultantEuclidean2| |unitsColorDefault| |bottom!| - |OMreadStr| |numberOfComposites| |tValues| |inverse| |setButtonValue| - |areEquivalent?| ~ |ParCond| |lagrange| |edf2efi| - |rewriteIdealWithHeadRemainder| |monomials| |space| - |linearAssociatedOrder| |cyclePartition| |insertRoot!| |stFuncN| - |wreath| |systemSizeIF| |generalTwoFactor| |trunc| |bit?| - |invertibleSet| |cot2tan| |figureUnits| |LyndonCoordinates| - |generalSqFr| |addmod| |cscIfCan| |numerators| |fill!| |s18dcf| - |llprop| |laurentIfCan| |selectSumOfSquaresRoutines| |nthFlag| - |sizeLess?| |OMputEndApp| |purelyTranscendental?| |iiacsch| - |rectangularMatrix| |constructorName| |cup| |mapExpon| |firstNumer| - |rightQuotient| |nonSingularModel| |ord| |generateIrredPoly| - |setAdaptive3D| |basisOfCentroid| |pointData| |trim| |roughBase?| - |squareFreePolynomial| |modifyPointData| |eigenvector| |leader| - |readable?| |components| |baseRDE| |coshIfCan| |cosh| |BumInSepFFE| - |type| |open| |makeSin| |lazyVariations| |leadingIdeal| |s17def| - |bezoutResultant| |basisOfNucleus| |setRealSteps| |charpol| - |Vectorise| |c06eaf| |tanh| |freeOf?| |postfix| |innerSolve1| |f04adf| - |dflist| |basisOfMiddleNucleus| |permutation| |quatern| |coth| - |basisOfLeftNucloid| |squareFreeLexTriangular| |makeTerm| - |reducedDiscriminant| |nextSublist| |expr| |showAll?| - |splitDenominator| |OMunhandledSymbol| |leadingExponent| |pointLists| - |exponent| |mvar| |isPlus| |patternMatch| |createZechTable| |f02aff| - |cap| |notOperand| |startTable!| |tan2trig| |scanOneDimSubspaces| - |key| |tableau| |generalPosition| |factorset| |low| |maxdeg| - |inconsistent?| |options| |firstUncouplingMatrix| |ksec| |finite?| - |coefChoose| |failed| |d01amf| |OMlistCDs| |linears| |findCycle| - |explicitlyEmpty?| |variable| |ptFunc| |nextsousResultant2| - |extendedResultant| |bat1| |cosSinInfo| |OMputBVar| - |particularSolution| |filename| |changeVar| |hash| |digit| - |subresultantSequence| |lyndonIfCan| |lineColorDefault| |OMputEndAtp| - |primPartElseUnitCanonical!| |linearAssociatedExp| |roughEqualIdeals?| - |pomopo!| |divideIfCan!| |constant| |simpsono| |getMeasure| - |maxPoints| |imagK| |not?| |count| |monicDecomposeIfCan| - |viewThetaDefault| LODO2FUN |iicot| |find| |OMReadError?| |nthr| - |airyBi| |patternVariable| |parse| |printCode| |e04ycf| |OMread| - |nsqfree| |ffactor| |backOldPos| |showAllElements| |bitCoef| - |midpoints| |squareMatrix| |nextItem| |subscript| |ode| |node| |exquo| - |flatten| |probablyZeroDim?| |unitVector| |numberOfImproperPartitions| - |hasoln| |createPrimitivePoly| |useSingleFactorBound| |c06gsf| - |presuper| |div| |say| |normalizeAtInfinity| |colorDef| |returnType!| - |isMult| |e02aef| |f07aef| |lowerCase!| |pr2dmp| |dot| |quo| - |SFunction| |OMgetFloat| |zeroSetSplit| |graphImage| |headReduced?| - |mapUp!| |conditionsForIdempotents| |d02bbf| |perfectNthRoot| - |fortranLiteral| |truncate| |basicSet| |f07adf| |pdct| |solid| |hex| - |OMgetEndApp| |characteristic| |rem| |d01bbf| |merge| - |pointSizeDefault| |testModulus| |positive?| |operation| |exp1| |nil| - |f04jgf| |expint| |selectIntegrationRoutines| |member?| - |OMgetVariable| |hostPlatform| |transcendent?| |lllp| |setrest!| - |perfectNthPower?| |node?| |hitherPlane| |mainCoefficients| - |subResultantGcdEuclidean| |constantToUnaryFunction| |c06ebf| - |infRittWu?| |fortranLiteralLine| |setStatus| |subtractIfCan| |cSin| - |pattern| |f04mbf| |sum| |rightDivide| |extensionDegree| - |euclideanGroebner| |autoReduced?| |outerProduct| |hermite| |zero| - |arrayStack| |newTypeLists| |imaginary| |leastPower| |leftQuotient| - |twoFactor| |cCosh| |approximate| |createLowComplexityTable| - |algebraicDecompose| |simplify| |specialTrigs| |thetaCoord| |complex| - |leftZero| |outputAsScript| |trigs| |c05nbf| |rightFactorCandidate| - |qinterval| |times!| |OMUnknownCD?| |And| |linGenPos| |squareFreePrim| - |operators| |primintfldpoly| |returnTypeOf| |cCot| |cyclicSubmodule| - |position!| |integralAtInfinity?| |Or| |monomial?| |interpolate| - |sylvesterSequence| |s21bbf| |subResultantChain| |normalForm| - |horizConcat| |e01sbf| |deleteProperty!| |critM| |taylorQuoByVar| - |Not| |charClass| |OMgetAttr| |hasPredicate?| |quotedOperators| - |revert| |leftRank| |rightExactQuotient| |normalDenom| - |characteristicSet| |ridHack1| |possiblyNewVariety?| |eulerE| |index| - |andOperands| |mr| |shiftRight| |listYoungTableaus| |squareTop| - |setPrologue!| |doublyTransitive?| |body| |formula| |compile| - |cyclic?| |determinant| |stopMusserTrials| |lyndon?| |char| |f02adf| - |coth2tanh| |mathieu12| |stirling1| |leadingCoefficientRicDE| |not| - |lieAdmissible?| |s17dlf| |removeRedundantFactorsInContents| - |torsionIfCan| |solveLinearPolynomialEquation| - |leftCharacteristicPolynomial| |mainVariable| |normal01| |froot| - |atoms| |clipBoolean| |selectPDERoutines| |SturmHabichtCoefficients| - |associatedSystem| |resultantnaif| |pair| |modularFactor| |conditionP| - |mapmult| |linearPart| |c06ekf| |completeHensel| |rur| |besselY| - |iiasin| |pseudoQuotient| |complexRoots| |fillPascalTriangle| - |PDESolve| |contains?| |showTheSymbolTable| |minimize| - |removeConstantTerm| |nrows| |polyRDE| |laplacian| |integers| |comp| - |float| |enterPointData| |separate| |width| |plotPolar| - |oneDimensionalArray| |isExpt| |innerint| |fortranInteger| - |atrapezoidal| |ncols| |setEmpty!| |mapdiv| |primeFrobenius| - |sqfrFactor| |fortranCarriageReturn| |PollardSmallFactor| |region| - |cyclicParents| |select| |OMputBind| |polygamma| |outputFloating| - |rootBound| |polar| |dictionary| |c05pbf| |insertMatch| |messagePrint| - |viewZoomDefault| |sdf2lst| |OMencodingSGML| |doubleComplex?| - |rightMult| |df2ef| |returns| |rischDE| |csch2sinh| - |showTheRoutinesTable| |write| |interReduce| |extractBottom!| |cfirst| - |summation| |critMTonD1| |save| |leftLcm| |moreAlgebraic?| |s18aff| - |s21bcf| |debug3D| |obj| |nextPrime| |latex| |branchIfCan| - |parametersOf| |normalDeriv| |solveid| |binary| |chainSubResultants| - |tab1| |screenResolution3D| |mapUnivariateIfCan| |cache| - |showClipRegion| |palgintegrate| |leftGcd| |message| |compound?| - |bezoutMatrix| |companionBlocks| |permutations| |LowTriBddDenomInv| - |stoseInvertibleSetreg| |graeffe| |neglist| |e02bef| |OMgetInteger| - |OMencodingBinary| |rootSplit| |hdmpToP| |integerBound| |numerator| - |radicalEigenvector| |makeRecord| |zeroDim?| |leftExtendedGcd| - |rubiksGroup| GE |basisOfLeftNucleus| |movedPoints| |setProperties| - |getCode| |digit?| |denominators| |insertionSort!| |input| |ignore?| - |palglimint| |supRittWu?| |mainDefiningPolynomial| GT |palgLODE| - |quickSort| |aQuadratic| |s18def| |associator| |OMconnectTCP| - |library| |e02ahf| |aspFilename| |high| |viewWriteDefault| LE |name| - |search| |monicModulo| |calcRanges| |elements| - |eisensteinIrreducible?| |gbasis| |clipWithRanges| |getMatch| - |rewriteIdealWithQuasiMonicGenerators| |removeSuperfluousCases| - |imagJ| LT |composite| |groebner?| |fortranTypeOf| |defineProperty| - |setMinPoints| |screenResolution| |odd?| |diophantineSystem| - |numberOfHues| |convergents| |nthFactor| Y |partialNumerators| |tanNa| - |exponents| |e01bgf| |drawStyle| |chiSquare1| |ode1| |measure| |li| - |push| |closedCurve| |fTable| |smith| |roughSubIdeal?| |mathieu24| - |ratPoly| |mathieu23| |set| |splitNodeOf!| - |semiSubResultantGcdEuclidean1| |createMultiplicationTable| - |nextPrimitiveNormalPoly| |t| |leftAlternative?| |rightDiscriminant| - |rCoord| |nlde| |localReal?| |zerosOf| |rowEch| |point?| |e02def| - |mirror| |graphStates| |viewport2D| |UnVectorise| |iisinh| - |plenaryPower| |f01qef| |OMputAttr| |factorGroebnerBasis| - |realEigenvalues| |powmod| UTS2UP |acschIfCan| |insert!| - |setMinPoints3D| |ef2edf| |finiteBound| |idealiser| |quoByVar| - |se2rfi| |sncndn| |max| |setnext!| |usingTable?| |s18acf| |nullity| - |wordInStrongGenerators| |key?| |pushuconst| |numericalIntegration| - |collectQuasiMonic| |complexZeros| RF2UTS |changeName| |accuracyIF| - |makeVariable| |countRealRootsMultiple| |domainOf| |associates?| - |s21bdf| |randnum| |trigs2explogs| |padicallyExpand| |iisqrt2| - |extendedIntegrate| |rightTrim| |iisec| |overlap| |cosh2sech| - |hyperelliptic| |critB| |infinite?| |quasiMonic?| |cartesian| - |indices| |cardinality| |leftTrim| |readLineIfCan!| |Si| |binomial| - |innerEigenvectors| |irreducibleFactor| |iifact| |rotatez| - |OMgetSymbol| |stoseInvertibleSetsqfreg| |tanhIfCan| |s17aff| - |nthFractionalTerm| |gcdPolynomial| |ScanFloatIgnoreSpacesIfCan| - |sumOfKthPowerDivisors| |var1StepsDefault| |rationalApproximation| - |numberOfDivisors| |transcendentalDecompose| |augment| |OMgetAtp| - |setprevious!| |getPickedPoints| |mdeg| |generalLambert| |cSinh| - |tanQ| |checkRur| |bernoulliB| |show| |sh| |bandedJacobian| - |monomRDEsys| |removeRoughlyRedundantFactorsInPol| |monom| - |mkIntegral| |rightRankPolynomial| - |dimensionOfIrreducibleRepresentation| |members| |pToDmp| - |extendedint| |LyndonBasis| |mainForm| |linearlyDependentOverZ?| - |sin?| |rightRemainder| |coefficient| |appendPoint| |round| |OMwrite| - |asechIfCan| |coerceP| |hypergeometric0F1| |kmax| |matrixDimensions| - |trace| |OMgetApp| |number?| |upDateBranches| |setleaves!| - |brillhartIrreducible?| |elRow2!| |delta| |directSum| |lllip| - |trace2PowMod| |nor| |rdHack1| |closeComponent| |psolve| - |resetAttributeButtons| |lfinfieldint| |common| |primitivePart!| - |partialDenominators| |createNormalPrimitivePoly| |lieAlgebra?| - |precision| |rewriteSetByReducingWithParticularGenerators| |sup| - |makeEq| |stopTableGcd!| |cTan| |lazyPrem| |reverse!| |leaves| - |retractable?| ** |generalInfiniteProduct| |digits| - |oddInfiniteProduct| |biRank| |showSummary| |deepExpand| |someBasis| - |cycleSplit!| |reify| |contract| |symmetricSquare| |fractRadix| - |sumOfSquares| |raisePolynomial| |createPrimitiveElement| |reverse| - |euclideanNormalForm| |resize| |front| |minGbasis| |maxrank| |over| - |minimumDegree| |representationType| |getMultiplicationMatrix| - |lastSubResultant| |mainPrimitivePart| |BasicMethod| |iExquo| - |maxColIndex| |cLog| |addPointLast| |nullSpace| |divisorCascade| - |stiffnessAndStabilityOfODEIF| |conjugates| |exactQuotient| EQ - |setlast!| |updatD| |f04asf| |diff| |stack| |nonLinearPart| - |gcdcofactprim| |d01alf| |mpsode| |showAttributes| |e04dgf| - |reducedForm| |e04gcf| |objects| |stripCommentsAndBlanks| - |partialQuotients| |rewriteSetWithReduction| |processTemplate| |prem| - |leftUnit| |withPredicates| |belong?| |floor| |iibinom| |cylindrical| - |subQuasiComponent?| |integer?| |distFact| |content| |explimitedint| - F2FG |ptree| |base| |anfactor| |cAcosh| |OMputVariable| |stFunc2| - |elem?| |cos2sec| |power!| |compiledFunction| |decimal| - |viewDeltaYDefault| |qqq| |s17akf| |controlPanel| |iicosh| |limitPlus| - |jacobiIdentity?| |internalAugment| |lambda| |OMgetBVar| |flagFactor| - |gradient| |polarCoordinates| |minPoly| |coerceS| |tensorProduct| - |computeCycleEntry| |elementary| |perspective| |morphism| |mathieu22| - |nilFactor| |OMopenString| |component| |choosemon| |antiCommutator| - |slash| |bright| |coleman| |lastSubResultantElseSplit| - |stoseIntegralLastSubResultant| |rangeIsFinite| |chineseRemainder| - |removeRedundantFactors| |multMonom| |equation| |sub| |quasiComponent| - |corrPoly| |dimensionsOf| |ratDsolve| |rspace| |Nul| - |topFortranOutputStack| |hasHi| |rroot| |e02gaf| |multiple| |mesh?| - |headReduce| |negative?| |rootsOf| |OMputInteger| |dequeue| - |removeZero| |tablePow| |lazyPseudoRemainder| |rightScalarTimes!| - |diagonal?| |power| |opeval| |basisOfRightNucloid| |prime?| - |applyQuote| |normalizedAssociate| |simpson| |cyclicEqual?| |connect| - |expenseOfEvaluation| |stopTable!| |vspace| |rowEchelon| |null?| - |primes| |medialSet| |baseRDEsys| |trapezoidal| |hexDigit?| |iisqrt3| - |OMmakeConn| |realRoots| |regime| |ramified?| |setPredicates| - |zeroDimensional?| |variable?| |acoshIfCan| - |tryFunctionalDecomposition?| |tanh2trigh| |norm| |rightAlternative?| - |cosIfCan| |monomialIntPoly| |setRow!| |equivOperands| |delete| - |d02cjf| |mainContent| |idealSimplify| |doubleResultant| |tan2cot| - |ruleset| |extend| |toroidal| |basisOfLeftAnnihilator| |split| - |OMsend| |coord| |exprHasLogarithmicWeights| |index?| |swap| - |complexElementary| |initial| |qfactor| |traceMatrix| |hdmpToDmp| - |skewSFunction| |s17adf| |invertIfCan| |sinhcosh| - |parabolicCylindrical| |s19acf| |ldf2lst| |resultant| - |strongGenerators| |minordet| |numberOfFactors| |OMreceive| - |selectNonFiniteRoutines| |lquo| |subscriptedVariables| |untab| - |lowerCase| |readIfCan!| |lazyResidueClass| |OMbindTCP| - |setScreenResolution| |suchThat| |previous| |d01aqf| |GospersMethod| - |lfextendedint| |one?| |schema| |antiCommutative?| |squareFree| - |setTex!| |isOp| |asecIfCan| |composites| |startPolynomial| - |distdfact| |transcendenceDegree| |commonDenominator| |pToHdmp| - |makeCos| |algint| |totalfract| |gderiv| |level| |laurentRep| |lexico| - |internalDecompose| |sayLength| |factorsOfCyclicGroupSize| |f01qcf| - |properties| |bitLength| |prindINFO| |inverseLaplace| |Lazard2| |hue| - |cycleElt| |setScreenResolution3D| |stoseInvertible?| |iiperm| - |dfRange| |ravel| |flexibleArray| |unitNormalize| |e04fdf| - |leadingSupport| |increment| |radicalSolve| |translate| - |factorsOfDegree| |s20acf| |UP2ifCan| |e01saf| |cycles| |reshape| - |recoverAfterFail| |crest| |bezoutDiscriminant| |bivariateSLPEBR| - |polyPart| |expandTrigProducts| |e01bff| |uniform| |surface| - |alphabetic| |showIntensityFunctions| |e02dff| |invmod| |close!| - |makeResult| |lastSubResultantEuclidean| |polygon?| |prevPrime| |mix| - |true| |f04atf| |listConjugateBases| |minPoints3D| |mainMonomial| - |log10| |perfectSquare?| |logical?| |showTheIFTable| |eulerPhi| - |drawCurves| |OMgetObject| |quadraticForm| |logGamma| - |constantCoefficientRicDE| |sumSquares| |isQuotient| |aCubic| |more?| - |generalizedContinuumHypothesisAssumed?| |numFunEvals3D| - |swapColumns!| |addMatchRestricted| |toseLastSubResultant| - |factorSquareFreePolynomial| |addiag| |xCoord| |makeViewport3D| - |gcdcofact| |merge!| |iicoth| |setAdaptive| |bumptab1| - |genericLeftTraceForm| |listOfMonoms| |outputForm| |identity| - |ldf2vmf| |singleFactorBound| |update| |list| |reduceByQuasiMonic| - |headRemainder| |lowerCase?| |solveRetract| |radicalOfLeftTraceForm| - |associative?| |consnewpol| |zeroVector| |e04ucf| |bsolve| |car| - |subResultantGcd| |duplicates| |resultantReduitEuclidean| |writeLine!| - |debug| |extractProperty| |iipow| |dim| |setMaxPoints| |discreteLog| - |Hausdorff| |sequences| |repSq| |cdr| |removeRedundantFactorsInPols| - |genericLeftDiscriminant| |refine| |getVariableOrder| |matrixGcd| - |quotient| |pile| |height| |denominator| |setLabelValue| - |setDifference| |f02fjf| |basisOfCommutingElements| |e02agf| |largest| - |brace| |startTableGcd!| |iprint| |discriminant| |multiset| - |removeCoshSq| |commutativeEquality| |setIntersection| |lighting| - |RemainderList| |primlimintfrac| |UpTriBddDenomInv| |frobenius| - |expandLog| |unparse| |elColumn2!| |box| |radicalSimplify| |pushdterm| - |setUnion| |selectOrPolynomials| |getConstant| |meshFun2Var| |sec2cos| - |directory| |selectPolynomials| |unit| |optional?| |listBranches| - |oddintegers| |radicalEigenvectors| |position| |apply| - |showArrayValues| |sumOfDivisors| ~= |inR?| |collect| |nullary?| - |polygon| |roman| |rootPower| |intensity| |lookup| |pointColor| - |leftNorm| |OMputError| |radicalRoots| |degreeSubResultant| |coerce| - |coerceL| |value| |hconcat| |integralBasisAtInfinity| |nextSubsetGray| - |empty?| |comparison| |complement| |useEisensteinCriterion?| |size| - |noLinearFactor?| |genericLeftTrace| |completeSmith| |construct| - |rk4qc| |ddFact| |f04faf| |linearAssociatedLog| |shrinkable| - |quadratic?| |qroot| |iiasec| |comment| |positiveRemainder| |script| - |rightFactorIfCan| |viewDeltaXDefault| |subNode?| |sturmVariationsOf| - |d03edf| |integral?| |getStream| |knownInfBasis| |prinpolINFO| - |rightRecip| |e04naf| |dark| |ratpart| |cAtan| - |indiceSubResultantEuclidean| |pleskenSplit| |ricDsolve| |sparsityIF| - |first| |groebSolve| |cotIfCan| |root| |karatsubaDivide| |lexGroebner| - |yCoord| |showScalarValues| |moduleSum| |failed?| |makeCrit| - |reduction| |rest| |square?| |quoted?| |tex| |minset| |bringDown| - |showRegion| |closedCurve?| |mapCoef| |d02gaf| |substitute| - |karatsubaOnce| |bfEntry| |lSpaceBasis| |d01ajf| |fractionPart| - |f02xef| |crushedSet| |standardBasisOfCyclicSubmodule| |difference| - |removeDuplicates| |realElementary| |degreeSubResultantEuclidean| - |HenselLift| |meshPar1Var| |erf| |linSolve| |stop| |pseudoRemainder| - |d02raf| |changeBase| |rule| |mindeg| |multiplyExponents| - |inverseIntegralMatrixAtInfinity| |halfExtendedSubResultantGcd1| - |polyred| |scale| |uncouplingMatrices| |ipow| |fortranCompilerName| - |zeroDimPrime?| |arg1| |leftUnits| |iidprod| |pole?| |df2fi| - |symmetricTensors| |ref| |fullPartialFraction| |arg2| - |radicalEigenvalues| |stronglyReduced?| |dilog| |cyclotomic| |back| - |collectUpper| |reduced?| |symbolTable| |lifting1| |lintgcd| - |perfectSqrt| |s20adf| |f02bbf| |enterInCache| |lprop| |sin| - |divideIfCan| |red| |separateDegrees| |symbolIfCan| |second| - |OMsupportsCD?| |conditions| |setleft!| |explogs2trigs| |henselFact| - |compactFraction| |cos| |pushFortranOutputStack| - |rightCharacteristicPolynomial| |shiftLeft| |rightUnits| |third| - |c06gcf| |match| |elt| |paraboloidal| |exprex| |OMgetEndObject| - |quartic| |tan| |popFortranOutputStack| |normFactors| - |exponentialOrder| |and?| |mergeFactors| - |solveLinearPolynomialEquationByFractions| |oddlambert| - |axesColorDefault| |outputAsFortran| |tanAn| |module| |acosIfCan| - |rootNormalize| |lfextlimint| |addPoint| |continuedFraction| |setelt| - |cyclotomicDecomposition| |po| |nonQsign| |exists?| |innerSolve| - |c06gbf| |setEpilogue!| |varselect| |omError| |initiallyReduced?| - |weight| |e02ddf| |copy| |cot2trig| |predicate| - |integralMatrixAtInfinity| |sorted?| |removeSinhSq| |pdf2df| |queue| - |plusInfinity| |primitivePart| |empty| |equality| |term?| |curryLeft| - |minusInfinity| |subset?| |subTriSet?| |autoCoerce| |qelt| - |expextendedint| |operator| |f01rdf| |increase| - |stoseInvertible?sqfreg| |coHeight| |edf2df| |digamma| - |shanksDiscLogAlgorithm| |iiGamma| |conjugate| |xRange| |adaptive| - |e01bef| |substring?| |gcdprim| |cAcsch| |chebyshevT| |yRange| - |separateFactors| |printingInfo?| |lhs| |rootKerSimp| - |increasePrecision| |monicLeftDivide| |zRange| |OMParseError?| - |currentScope| |rhs| |suffix?| |cAcoth| |map!| |parameters| |ode2| - |rotate| |laguerreL| |linearDependence| |qsetelt!| |zeroSquareMatrix| - |getRef| |prefix?| |critBonD| |geometric| |vector| |f02awf| - |LagrangeInterpolation| |multiplyCoefficients| |pow| |differentiate| - |rationalFunction| |viewSizeDefault| |exprToGenUPS| |interval| - |palgRDE| |nextPartition| |univcase| |mainMonomials| |external?| - |HermiteIntegrate| |acsch| |d01akf| |f01qdf| |initials| - |coercePreimagesImages| |shallowCopy| |axes| |infix?| |outputMeasure| - |goto| |palginfieldint| |mapSolve| |constantRight| |simplifyExp| - |mask| |kroneckerDelta| |prepareDecompose| |superHeight| - |symmetricGroup| |swap!| |f02aef| |problemPoints| |janko2| |setValue!| - |definingInequation| |s17dgf| |deepestTail| |iflist2Result| - |reducedSystem| |complexIntegrate| |OMopenFile| |basisOfRightNucleus| - |anticoord| |limitedIntegrate| |algebraicSort| NOT |lazy?| |traverse| - |rightGcd| |ParCondList| |iomode| |youngGroup| |measure2Result| - |OMreadFile| OR |OMputEndError| |curve| |currentSubProgram| - 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|laurent| |putColorInfo| |acoshIfCan| + |optAttributes| |bringDown| |assign| |segment| UTS2UP |top| + |repeating?| |puiseux| |tryFunctionalDecomposition?| + |pointColorDefault| |bfKeys| |dn| |predicates| |acschIfCan| |continue| + |showRegion| |rarrow| |tanh2trigh| |iroot| |trapezoidalo| |insert!| + |closedCurve?| |recip| |inv| |semiSubResultantGcdEuclidean2| |norm| + |mapCoef| |clearTheFTable| |setMinPoints3D| |leftTraceMatrix| |cSec| + |ground?| |rightAlternative?| |rewriteIdealWithRemainder| |label| + |basisOfCenter| |ef2edf| |rightLcm| |d02gaf| |commaSeparate| |ground| + |shufflein| |cosIfCan| |finiteBound| |block| |exQuo| |expintegrate| + |karatsubaOnce| |leadingMonomial| |monomialIntPoly| |principalIdeal| + |idealiser| |f02aaf| |bfEntry| |represents| |expr| + |leadingCoefficient| |setRow!| |completeEchelonBasis| |lSpaceBasis| + |semiResultantReduitEuclidean| |quoByVar| |setFieldInfo| |csubst| + |primitiveMonomials| |infix?| |equivOperands| |children| |entry| + |d01ajf| |d01apf| 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|quasiMonicPolynomials| |semiDiscriminantEuclidean| + |split| |meshPar1Var| |s18adf| |numericalIntegration| |factorFraction| + |selectODEIVPRoutines| |sts2stst| |integralDerivationMatrix| |OMsend| + |nextPrimitivePoly| |goodnessOfFit| |collectQuasiMonic| |linSolve| + |repeating| |argscript| |setClipValue| |coord| |complexZeros| |f04arf| + |complete| |roughBasicSet| |pseudoRemainder| |tubePoints| + |exprHasLogarithmicWeights| |algebraicVariables| |algintegrate| + |coordinates| RF2UTS |d02raf| |linear?| |index?| |order| + |clipParametric| |changeName| |whileLoop| |update| |changeBase| + |create| |redpps| |swap| |wholeRadix| |accuracyIF| + |generalizedInverse| |constantKernel| |numberOfComputedEntries| + |clearCache| |mindeg| |bombieriNorm| |intPatternMatch| + |complexElementary| |makeVariable| |zeroDimPrimary?| |s17aef| + |multiplyExponents| UP2UTS |setOrder| |moduloP| |qfactor| |badNum| + |doubleRank| |inverseIntegralMatrixAtInfinity| + |countRealRootsMultiple| |userOrdered?| |center| |setStatus!| + |graphState| |symmetric?| |traceMatrix| |isPower| |domainOf| + |halfExtendedSubResultantGcd1| |prologue| |toseInvertibleSet| + |decomposeFunc| |rquo| |squareFreePart| |hdmpToDmp| |iteratedInitials| + |character?| |associates?| |divideExponents| |polyred| |deref| + |ellipticCylindrical| |skewSFunction| F |genericRightTraceForm| + |s21bdf| |nil?| |position| |scale| |oblateSpheroidal| |iidsum| + |s17adf| |atom?| |uncouplingMatrices| |safeFloor| |randnum| + |monicRightDivide| |removeRoughlyRedundantFactorsInPols| |scopes| + |invertIfCan| |definingEquations| |ipow| |trigs2explogs| + |impliesOperands| |zCoord| |iCompose| |outlineRender| |OMgetError| + |f01brf| |sinhcosh| |fortranCompilerName| |padicallyExpand| + |subPolSet?| |wordsForStrongGenerators| |contractSolve| |viewport3D| + |bat| |parabolicCylindrical| |zag| |iisqrt2| |iiacot| + |createGenericMatrix| |complexNumericIfCan| |zeroDimPrime?| |plot| + |viewPosDefault| |s19acf| |OMcloseConn| |constantOpIfCan| + |algSplitSimple| |extendedIntegrate| |pquo| |leftUnits| |e01daf| + |setProperty!| |ldf2lst| |sn| |iidprod| |doubleDisc| |findBinding| + |absolutelyIrreducible?| |resultant| |setProperties| |OMputEndAttr| + |cot2tan| |scalarTypeOf| |factorList| |cAsinh| |pole?| D + |strongGenerators| |resultantEuclideannaif| |getCode| |figureUnits| + |zeroMatrix| |c06ecf| |df2fi| |cross| |SturmHabichtSequence| + |minordet| |denominators| |LyndonCoordinates| |rk4a| + |factorByRecursion| |normDeriv2| |symmetricTensors| |null| |vconcat| + |insertionSort!| |generalSqFr| |midpoint| |adjoint| |ref| |case| + |jacobiIdentity?| |gramschmidt| LE |ignore?| |addmod| |maxIndex| + |besselI| |fullPartialFraction| |symFunc| |Zero| |blue| + |internalAugment| LT |palglimint| |s17dhf| |cRationalPower| |d01fcf| + |radicalEigenvalues| |One| |OMgetBVar| |characteristicSerie| + |cscIfCan| |supRittWu?| |cubic| |adaptive?| |getProperty| |flagFactor| + |rootProduct| |numerators| |createIrreduciblePoly| |unit| + |mainDefiningPolynomial| |dec| |complexEigenvectors| |gradient| + |graphCurves| |palgLODE| |fill!| |rename!| |optional?| |lazyPquo| + |replace| |polarCoordinates| |rightOne| |rightMinimalPolynomial| + |quickSort| |point| |symmetricPower| |s18dcf| |listBranches| + |extractSplittingLeaf| |print| |minPoly| |lexTriangular| |recur| + |rotate!| |aQuadratic| |llprop| |oddintegers| |infLex?| |elt| + |leviCivitaSymbol| |coerceS| |unravel| |iiasinh| |s18def| + |OMconnOutDevice| |plusInfinity| |radicalEigenvectors| |homogeneous?| + |tensorProduct| |alphanumeric| |palgint0| |associator| |series| + |laurentIfCan| |minusInfinity| |showArrayValues| |triangSolve| + |computeCycleEntry| |permanent| |sumOfDivisors| |cAcos| |OMconnectTCP| + |pushucoef| |optpair| |elementary| |factors| |e02ahf| |OMclose| + |singular?| |inR?| |argumentList!| |perspective| |showTheFTable| + |aspFilename| |contours| |collect| |realSolve| + |isAbsolutelyIrreducible?| |morphism| |product| |min| |high| |besselK| + |nullary?| |radix| |lp| |invertibleElseSplit?| |ran| |mathieu22| + |binding| |viewWriteDefault| |qPot| |polygon| |endSubProgram| + |nilFactor| |diag| |type| |OMencodingXML| |monicModulo| |atanIfCan| + |roman| |f01maf| |elliptic| |OMopenString| |calcRanges| + |selectSumOfSquaresRoutines| |purelyAlgebraicLeadingMonomial?| + |rootPower| |toseSquareFreePart| |component| |relativeApprox| + |function| |bubbleSort!| |nthFlag| |tubePointsDefault| + |deepestInitial| |elements| |mergeDifference| |intensity| |declare| + |choosemon| |super| |sizeLess?| |physicalLength!| + |eisensteinIrreducible?| |diagonalMatrix| |intermediateResultsIF| + |lookup| |antiCommutator| |lazyIntegrate| |pointColor| + |fortranLogical| |resetBadValues| |gbasis| |OMputEndApp| |totalDegree| + |numberOfChildren| |eval| |makeSketch| |slash| |clipWithRanges| + |leftNorm| |factorSFBRlcUnit| |antisymmetric?| |purelyTranscendental?| + |ScanRoman| |sinhIfCan| |highCommonTerms| |coleman| |modTree| + |iiacsch| |ListOfTerms| |getMatch| |triangular?| |curveColor| + |OMputError| |rightRank| |leftRegularRepresentation| + |lastSubResultantElseSplit| |newLine| |commutative?| + |rightTraceMatrix| |rewriteIdealWithQuasiMonicGenerators| |rischDEsys| + |rectangularMatrix| |precision| |radicalRoots| |structuralConstants| + |universe| |stoseIntegralLastSubResultant| |cup| |drawToScale| + |removeIrreducibleRedundantFactors| |halfExtendedResultant1| + |removeSuperfluousCases| |expressIdealMember| |degreeSubResultant| + |localUnquote| |rangeIsFinite| |constantLeft| |eq?| |palglimint0| + |mapExpon| |eigenMatrix| |imagJ| |#| |coerceL| |clearTable!| |f02wef| + |chineseRemainder| |computePowers| |f04axf| |firstNumer| + |setVariableOrder| |composite| |hconcat| |sech2cosh| |normalized?| + |gethi| |imagI| |removeRedundantFactors| |sincos| + |integralBasisAtInfinity| |groebner?| |mindegTerm| + |variationOfParameters| |rightQuotient| |coerceListOfPairs| |delay| + |reduceBasisAtInfinity| |reducedContinuedFraction| |multMonom| + |sample| |nonSingularModel| |nextSubsetGray| |dim| |insert| |aromberg| + |deriv| |fortranTypeOf| |expt| |parent| |leaves| |stack| + |evaluateInverse| |setErrorBound| |getProperties| |sub| |ord| + |repeatUntilLoop| |complexLimit| |defineProperty| |bracket| |routines| + |empty?| |factorOfDegree| |polynomialZeros| |simplifyPower| |lcm| + |quasiComponent| |comparison| |generateIrredPoly| |arg1| + |unrankImproperPartitions0| |setMaxPoints3D| |setMinPoints| |rotatex| + |wrregime| |finite?| |preprocess| |c06fuf| |outputGeneral| |corrPoly| + |primitive?| |arg2| |symbolTable| |squareMatrix| |setAdaptive3D| + |screenResolution| |diagonalProduct| |complement| |modularGcd| + |coefChoose| |factorial| |internalSubQuasiComponent?| |logpart| + |dimensionsOf| |basisOfCentroid| |constructorName| + |useEisensteinCriterion?| |groebnerIdeal| |setClosed| |nextItem| + |odd?| |bernoulli| |tanh2coth| |d01amf| |asinhIfCan| |ratDsolve| + |overbar| |symbol| |gcd| |aLinear| |pushFortranOutputStack| + |subscript| |OMputEndBVar| |conditions| |rk4f| |diophantineSystem| + |pointData| |basisOfRightAnnihilator| |noLinearFactor?| |false| + |OMlistCDs| |integralCoordinates| |KrullNumber| |rspace| + |integralLastSubResultant| |union| |laguerre| |numberOfHues| + |popFortranOutputStack| |genericLeftTrace| |ode| |match| |float?| + |evaluate| |trim| |removeCosSq| |closed?| |Nul| |linears| |groebner| + |expIfCan| |rational?| |integer| |keys| |pastel| |multinomial| + |convergents| |outputAsFortran| |complexExpand| |readLine!| + |probablyZeroDim?| |roughBase?| |integral| |completeSmith| |findCycle| + |setImagSteps| |topFortranOutputStack| |characteristicPolynomial| + |real?| |setright!| |palgRDE0| |d02kef| |nthFactor| + |squareFreePolynomial| |rk4qc| |rootDirectory| |explicitlyEmpty?| + |subSet| |green| |orbits| |jacobi| |hasHi| |dom| |partialNumerators| + |singularAtInfinity?| |unitVector| |vector| |rank| |distance| + |modifyPointData| |ddFact| |indicialEquation| |associatedEquations| + |ptFunc| |createNormalElement| |implies| |numberOfPrimitivePoly| |eq| + |bipolarCylindrical| |rroot| |irreducible?| |eigenvector| |forLoop| + |differentiate| |typeLists| |tanNa| |mkPrim| |f04faf| + |nextsousResultant2| |cAcot| |xor| |pol| |iter| |rowEchelonLocal| + |e02gaf| |exponents| |readable?| |pmintegrate| |linearAssociatedLog| + |hessian| |body| |extendedResultant| |setAttributeButtonStep| + |mightHaveRoots| |resetVariableOrder| |mesh?| |bumptab| |initial| + |top!| |nthCoef| |e01bgf| |components| |shrinkable| |primintegrate| + |bat1| |any| |option?| |separant| |internalIntegrate| |algebraicOf| + |headReduce| |mapMatrixIfCan| |baseRDE| |drawStyle| |quadratic?| + |setref| |cosSinInfo| |reindex| |diagonals| |cSech| |negative?| + |useNagFunctions| |append| |coshIfCan| |chiSquare1| + |createPrimitiveNormalPoly| |qroot| |OMputBVar| |title| + |matrixConcat3D| |rootsOf| |rombergo| |incrementKthElement| |pair?| + |setOfMinN| |lists| |BumInSepFFE| |ode1| |iiasec| |nodes| |mkcomm| + |constant| |setelt!| |OMputInteger| |makeSin| |e02daf| |measure| + |positiveRemainder| |multiple?| |particularSolution| |comment| + |swapRows!| |exp| |dequeue| |lex| |push| |pascalTriangle| + |getSyntaxFormsFromFile| |lazyVariations| + |unprotectedRemoveRedundantFactors| |rightFactorIfCan| |e| |changeVar| + |colorFunction| |pointPlot| |yCoordinates| |removeZero| |leadingIdeal| + |supersub| |closedCurve| |besselJ| |csc2sin| |viewDeltaXDefault| + |digit| |erf| |subCase?| |tablePow| + |zeroSetSplitIntoTriangularSystems| |wholePart| |btwFact| |fTable| + |s17def| |intersect| |infinityNorm| |subNode?| |subresultantSequence| + |stFunc1| |lazyPseudoRemainder| |complexForm| |constDsolve| + |arrayStack| |bezoutResultant| |idealiserMatrix| |inf| |leftFactor| + |smith| |sturmVariationsOf| |depth| |obj| |lyndonIfCan| + |leftDiscriminant| |rightScalarTimes!| |prepareSubResAlgo| + |inRadical?| |basisOfNucleus| |computeBasis| |roughSubIdeal?| + |positiveSolve| |d03edf| |bumprow| |cache| |dilog| |diagonal?| + |cycleTail| |rationalIfCan| |setRealSteps| |validExponential| + |integral?| |harmonic| |mathieu24| |log| |internalInfRittWu?| + |lineColorDefault| |OMputFloat| |sin| |patternMatchTimes| |power| + |pmComplexintegrate| |ratPoly| |lepol| |charpol| |polCase| |getStream| + |airyAi| |cos| |insertBottom!| |opeval| |subresultantVector| + |knownInfBasis| |reopen!| |reset| |Vectorise| |mathieu23| |pack!| + |magnitude| |tan| |basisOfRightNucloid| |mkAnswer| |exponential1| + |degreePartition| |prinpolINFO| |c06eaf| |splitNodeOf!| + |leftScalarTimes!| |binaryFunction| |cot| |tanIfCan| |prime?| |imagE| + |write| |critMonD1| |rightRecip| |numFunEvals| |generate| |sec| + |normalizedAssociate| |fintegrate| |useSingleFactorBound?| |rules| + |factor1| |messagePrint| |e04naf| |npcoef| |quotientByP| |csc| + |simpson| |check| |cyclic| |save| |restorePrecision| |viewZoomDefault| + |double?| |f01bsf| |dark| |incrementBy| |printStatement| + |cyclicEqual?| |Aleph| |second| |sdf2lst| |tubeRadiusDefault| + |musserTrials| |ratpart| |search| |maximumExponent| |expand| |asin| + |equiv| |third| |principal?| |OMencodingSGML| |cAtan| |cAsin| |hclf| + |getMultiplicationMatrix| |modifyPoint| |filterWhile| |printInfo!| + |acos| |length| |middle| ** |doubleComplex?| |remainder| |e02dcf| + |indiceSubResultantEuclidean| |integrate| |bag| |sPol| |filterUntil| + |lastSubResultant| |atan| |scripts| |leastAffineMultiple| |flatten| + |rightMult| |pleskenSplit| |OMputObject| |maxrow| + |rightRegularRepresentation| |splitSquarefree| |select| + |mainPrimitivePart| |acot| |e02adf| |df2ef| |d03faf| EQ |has?| + |BasicMethod| |color| |asec| |numberOfCycles| |returns| |f02ajf| + |createLowComplexityNormalBasis| |singleFactorBound| |cCsc| |iExquo| + |resultantEuclidean| |acscIfCan| |complexNumeric| |coerceImages| + |rischDE| |reduceByQuasiMonic| |graphs| |sizeMultiplication| |testDim| + |maxColIndex| |acsc| |makeSUP| |extendedSubResultantGcd| |csch2sinh| + |headRemainder| |solveLinearlyOverQ| |cLog| |internalZeroSetSplit| + |addPoint2| |kernels| |badValues| |showTheRoutinesTable| |lowerCase?| + |mapExponents| |reciprocalPolynomial| |expintfldpoly| |addPointLast| + |fortran| SEGMENT |univariate| |interReduce| |countRealRoots| + |topPredicate| |solveRetract| |rightTrim| |cCoth| |makeRecord| + |torsion?| |nullSpace| |extractBottom!| |s19aaf| + |radicalOfLeftTraceForm| |OMsupportsSymbol?| |leftTrim| |zeroOf| + |divisorCascade| |OMgetEndBind| |iilog| |outerProduct| |cfirst| + |associative?| |rename| |remove| |stiffnessAndStabilityOfODEIF| + |setProperties!| |parametric?| |summation| |factor| |overlabel| + |eigenvalues| |consnewpol| |octon| |conjugates| |lazyGintegrate| + |saturate| |critMTonD1| |sqrt| |stopTableInvSet!| |zeroVector| + |ReduceOrder| |last| |iFTable| |dequeue!| |exactQuotient| |enqueue!| + |real| |leftLcm| |padecf| |linearlyDependent?| |e04ucf| |assoc| + |firstSubsetGray| |myDegree| |setlast!| |extractIndex| |plus!| |imag| + |moreAlgebraic?| |minPol| |bsolve| |OMputEndAtp| + |drawComplexVectorField| |updatD| |row| |fortranDoubleComplex| + |directProduct| |cAtanh| |s18aff| |sylvesterMatrix| |subResultantGcd| + |primPartElseUnitCanonical!| |limit| |f04asf| |algebraic?| |df2st| + |s21bcf| |normalise| |duplicates| |orOperands| |linearAssociatedExp| + |diff| |resultantReduit| |wholeRagits| |substring?| + |decreasePrecision| |numberOfOperations| |destruct| |debug3D| + |permutationGroup| |resultantReduitEuclidean| |roughEqualIdeals?| + |nonLinearPart| |OMputString| |OMgetBind| |evenlambert| |string| + |nextPrime| |or?| |sort!| |writeLine!| |pomopo!| |gcdcofactprim| + |hasTopPredicate?| |phiCoord| |suffix?| |physicalLength| |latex| + |complexNormalize| |nodeOf?| |extractProperty| |divideIfCan!| |d01alf| + |semiIndiceSubResultantEuclidean| |viewpoint| + |indicialEquationAtInfinity| |script| |approximants| |branchIfCan| + |iipow| |quadraticNorm| |simpsono| |inverseIntegralMatrix| |mapGen| + |mpsode| |prefix?| |extractTop!| |makeFR| |parametersOf| + |stiffnessAndStabilityFactor| |setMaxPoints| |getMeasure| + |integralMatrix| |e04dgf| |chiSquare| |slex| |computeInt| + |normalDeriv| |discreteLog| |equiv?| |maxPoints| |test| |reducedForm| + |iiexp| |genus| |alternative?| |tex| |clearFortranOutputStack| + |solveid| |LiePoly| |Hausdorff| |imagK| |tableForDiscreteLogarithm| + |e04gcf| |sinIfCan| |relationsIdeal| |binary| |leftTrace| |sequences| + ~= |monicDecomposeIfCan| |cond| |lflimitedint| |f02axf| + |stripCommentsAndBlanks| |leftRankPolynomial| |status| |rightPower| + |chainSubResultants| |doubleFloatFormat| |repSq| |viewThetaDefault| + |coerce| |partialQuotients| |subMatrix| |zoom| |coth2trigh| + |legendreP| |tab1| |hMonic| |removeRedundantFactorsInPols| |construct| + LODO2FUN |symbol?| |list?| |rewriteSetWithReduction| + |removeSquaresIfCan| |firstDenom| |screenResolution3D| + |genericLeftDiscriminant| |clipPointsDefault| |iicot| |derivative| + |processTemplate| |monicCompleteDecompose| |signAround| + |mapUnivariateIfCan| |getOperands| |cAsec| |refine| |find| |twist| + |acotIfCan| |prem| |B1solve| |digit?| |explicitEntries?| + |numberOfImproperPartitions| |showClipRegion| |bivariate?| + |getVariableOrder| |OMReadError?| |countable?| |leftUnit| |c06frf| + |iiacsc| |exponential| |mr| |checkForZero| |exprToUPS| |palgintegrate| + |hasoln| |matrixGcd| |cons| |nthr| |packageCall| |mainSquareFreePart| + |withPredicates| |removeZeroes| |degree| |t| |createPrimitivePoly| + |quotient| |reverse| |leftGcd| |subspace| |list| |solve| |stop| + |airyBi| |belong?| |minus!| |setfirst!| |error| |varList| + |useSingleFactorBound| |const| |pile| |compound?| |car| |makingStats?| + |patternVariable| |poisson| |floor| |deepCopy| |bezoutMatrix| |vark| + |c06gsf| |assert| |integralBasis| |denominator| |cdr| |printCode| + |iibinom| |central?| |upperCase!| |leftOne| |setLabelValue| |presuper| + |companionBlocks| |extension| |setDifference| |ravel| |e04ycf| + |cylindrical| |genericRightDiscriminant| |rk4| |solid?| + |normalizeAtInfinity| |permutations| |collectUnder| |setIntersection| + |f02fjf| |OMread| |identityMatrix| |secIfCan| |subQuasiComponent?| + |basisOfCommutingElements| |colorDef| |LowTriBddDenomInv| + |eyeDistance| |normalElement| |setUnion| |gcdPrimitive| |nthRootIfCan| + |integer?| |iisin| |createMultiplicationMatrix| + |stoseInvertibleSetreg| |e02agf| |apply| |nsqfree| |element?| + |distFact| |chebyshevU| |graeffe| |minimumExponent| |returnType!| + |triangulate| |largest| |ffactor| |debug| |cyclicGroup| |content| + |semiResultantEuclidean2| |showSummary| |neglist| |isMult| |leftPower| + |OMputEndBind| |size| |startTableGcd!| |backOldPos| |explimitedint| + |ScanArabic| |unitsColorDefault| |bindings| |f2df| |e02aef| |e02bef| + |iprint| |asinIfCan| |showAllElements| |setelt| |bottom!| F2FG + |hostPlatform| |tanSum| |showAttributes| |transform| |f07aef| + |OMgetInteger| |univariatePolynomial| |s14aaf| |discriminant| + |bitCoef| |li| |anfactor| |transcendent?| |OMreadStr| |htrigs| + |semiDegreeSubResultantEuclidean| |seriesSolve| |unitNormal| + |multiset| |lowerCase!| |OMencodingBinary| |complexEigenvalues| + |first| |copy| |char| |cAcosh| |dmp2rfi| |numberOfComposites| |leaf?| + |rootSplit| |var2Steps| |makeSeries| |even?| |removeCoshSq| |rest| + |midpoints| |insertTop!| |lllp| |OMputVariable| |tValues| |fixedPoint| + |substitute| |brace| |commutativeEquality| |pr2dmp| |hdmpToP| + |removeSuperfluousQuasiComponents| |s13aaf| |getOperator| |kernel| + |autoCoerce| |bits| |inverse| |stFunc2| |rationalPoints| |plus| + |integerBound| |hexDigit| |removeDuplicates| |toScale| |solveInField| + |lighting| |draw| |setButtonValue| |elem?| |curry| |parts| |imagk| + |totalDifferential| |constantIfCan| |numerator| |OMgetEndAttr| + |RemainderList| |OMgetString| |areEquivalent?| |float| |cos2sec| + |numericIfCan| |mat| |s15adf| |radicalEigenvector| |binomThmExpt| + |primlimintfrac| |exprHasAlgebraicWeight| |power!| |numeric| |ParCond| + |hash| |removeSinSq| |say| |value| |zeroDim?| |e02bcf| + |realEigenvectors| |totalGroebner| |UpTriBddDenomInv| + |showFortranOutputStack| |radical| |compiledFunction| |lagrange| + |droot| |times| |functionIsFracPolynomial?| |leftExtendedGcd| + |createRandomElement| |frobenius| |internalLastSubResultant| + |makeObject| |goodPoint| |decimal| |count| |OMlistSymbols| |yellow| + |leftDivide| |rubiksGroup| |errorKind| |expandLog| |edf2efi| + |genericLeftMinimalPolynomial| |viewDeltaYDefault| |RittWuCompare| + |basisOfLeftNucleus| |unparse| |c06gqf| |e01baf| |rationalPower| + |coef| |makeUnit| |rewriteIdealWithHeadRemainder| |qqq| |clip| + |radPoly| |movedPoints| |split!| |bitTruth| |elColumn2!| |s17akf| + |monomials| |var2StepsDefault| |taylorRep| |monom| |divisor| + |copyInto!| |radicalSimplify| |space| |setsubMatrix!| |controlPanel| + |f02agf| |entries| |torsionIfCan| |lfunc| |pushdterm| + |primPartElseUnitCanonical| |iicosh| |linearAssociatedOrder| GE + |LiePolyIfCan| |permutationRepresentation| + |solveLinearPolynomialEquation| |makeprod| |complementaryBasis| + |moebiusMu| |selectOrPolynomials| |asimpson| GT |limitPlus| + |leadingBasisTerm| |common| |alphanumeric?| + |leftCharacteristicPolynomial| |getConstant| |lyndon| + |initiallyReduce| |prefix| |generic| |useEisensteinCriterion| |tRange| + |mainVariable| |meshFun2Var| |is?| |diagonal| |setColumn!| |round| + |factorSquareFree| |singularitiesOf| |sortConstraints| |normal01| + |quasiRegular| |nextColeman| |match?| |sec2cos| |credPol| |OMwrite| + |dominantTerm| |jacobian| |equation| |elRow1!| |froot| |euclideanSize| + |selectPolynomials| |printHeader| |rst| |asechIfCan| |deleteRoutine!| + |addBadValue| |iiasech| |atoms| |numberOfIrreduciblePoly| |coerceP| + |c02aff| |acothIfCan| |move| |binarySearchTree| |rotatey| + |clipBoolean| |property| |directory| |e01saf| |log2| + |hypergeometric0F1| |antisymmetricTensors| + |halfExtendedSubResultantGcd2| |setPosition| |selectPDERoutines| + |taylorIfCan| |iitan| |cycles| |unit?| |kmax| |newSubProgram| + |meatAxe| |SturmHabichtMultiple| |e02ajf| |level| + |SturmHabichtCoefficients| |safetyMargin| |recoverAfterFail| |setPoly| + |matrixDimensions| |lambert| |weierstrass| + |semiLastSubResultantEuclidean| |associatedSystem| |listOfLists| + |units| |selectsecond| |crest| |orbit| |fortranDouble| |OMgetApp| + |isList| |integralMatrixAtInfinity| |style| |resultantnaif| + |bezoutDiscriminant| |tubePlot| |tab| |number?| |normal?| + |coefficients| |sorted?| |modularFactor| |quadratic| |bivariateSLPEBR| + |createThreeSpace| |reverseLex| |trailingCoefficient| |checkPrecision| + |makeViewport2D| |upDateBranches| |removeSinhSq| |padicFraction| + |currentEnv| |callForm?| |conditionP| |polyPart| |nthRoot| |string?| + |setleaves!| |edf2fi| |vertConcat| |pdf2df| |tubeRadius| + |halfExtendedResultant2| |mapmult| |expandTrigProducts| |noKaratsuba| + |printInfo| |shiftRoots| NOT |brillhartIrreducible?| |intcompBasis| + |minRowIndex| |queue| |linearPart| |code| |OMUnknownSymbol?| |e01bff| + |monicDivide| |leftMult| OR |elRow2!| |f07fdf| |primitivePart| + |extractClosed| |tryFunctionalDecomposition| |c06ekf| + |balancedFactorisation| |uniform| |selectAndPolynomials| AND + |directSum| |selectMultiDimensionalRoutines| |birth| |empty| + |alternating| |inrootof| |completeHensel| |makeGraphImage| |bright| + |surface| |pushdown| |solveLinearPolynomialEquationByRecursion| |sum| + |lllip| |points| |equality| |tanintegrate| |left| |alphabetic| + |f04qaf| |rur| |generalizedEigenvectors| |dot| |rational| |nand| + |node| |trace2PowMod| |multiEuclidean| |numericalOptimization| |term?| + |setrest!| |right| |updateStatus!| |SFunction| |OMconnInDevice| + |besselY| |showIntensityFunctions| |mainCharacterization| |elliptic?| + |nor| |notelem| |s17dcf| |perfectNthPower?| |curryLeft| + |minimalPolynomial| |derivationCoordinates| |iiasin| |factorAndSplit| + |e02dff| |exquo| |cyclicEntries| |OMgetFloat| |solveLinear| + |drawComplex| |lazyPseudoQuotient| |satisfy?| |rdHack1| |subset?| + |node?| |constant?| |selectfirst| |invmod| |fibonacci| |div| + |pseudoQuotient| |delete| |zeroSetSplit| |reduceLODE| |index| + |closeComponent| |listLoops| |subTriSet?| |hitherPlane| |An| + |numberOfFractionalTerms| |close!| |complexRoots| |sizePascalTriangle| + |quo| |graphImage| |cschIfCan| |d01gaf| |LazardQuotient| |psolve| + |setchildren!| |expextendedint| |mainCoefficients| |s14abf| + |cycleEntry| |changeNameToObjf| |fillPascalTriangle| |comp| + |quasiRegular?| |makeResult| |headReduced?| |purelyAlgebraic?| + |resetAttributeButtons| |multisect| |operator| + |subResultantGcdEuclidean| |mapUp!| |vedf2vef| |properties| |iiatanh| + |rem| |PDESolve| |ODESolve| |lastSubResultantEuclidean| |tube| + |constantToUnaryFunction| |lfinfieldint| |linear| |irreducibleFactors| + |f01rdf| |pair| |upperCase?| |conditionsForIdempotents| |translate| + |contains?| |divergence| |makeop| |polygon?| |currentCategoryFrame| * + |rightZero| |primitivePart!| |increase| |c06ebf| |next| |unmakeSUP| + |d02bbf| |d03eef| |showTheSymbolTable| |prevPrime| |less?| + |partialDenominators| |frst| |polynomial| |stoseInvertible?sqfreg| + |infRittWu?| |stirling2| |minimize| |rangePascalTriangle| + |listRepresentation| |perfectNthRoot| |mix| |triangularSystems| + |createNormalPrimitivePoly| |partition| |fortranLiteralLine| + |coHeight| |pade| |fortranLiteral| |removeConstantTerm| + |changeMeasure| |f04atf| |initializeGroupForWordProblem| |alphabetic?| + |lieAlgebra?| |karatsuba| |edf2df| |setStatus| |rootPoly| |iisech| + |listConjugateBases| |polyRDE| |leftRemainder| |truncate| |submod| + GF2FG |rewriteSetByReducingWithParticularGenerators| |subtractIfCan| + |digamma| |s17agf| |duplicates?| |laplacian| |minPoints3D| |mainValue| + |basicSet| |numberOfComponents| |retract| |prolateSpheroidal| |sup| + |shanksDiscLogAlgorithm| |cSin| |createNormalPoly| |log10| + |genericRightMinimalPolynomial| |integers| |mainMonomial| |dimensions| + |enumerate| |functionIsOscillatory| |iiGamma| |makeEq| + |irreducibleRepresentation| |f04mbf| |argument| |leftQuotient| + |palgextint0| |f07adf| |enterPointData| |perfectSquare?| + |fixPredicate| |fi2df| |kovacic| |message| |stopTableGcd!| |conjugate| + |rightDivide| |expandPower| |twoFactor| |build| |separate| |pdct| + |logical?| |s18aef| |univariatePolynomialsGcds| |adaptive| |cTan| + |fmecg| |cCosh| |extensionDegree| |entry?| |ScanFloatIgnoreSpaces| + |solid| |extendedEuclidean| |plotPolar| |not| |primeFactor| + |showTheIFTable| |tracePowMod| |lazyPrem| |objectOf| |e01bef| + |createLowComplexityTable| |e02baf| |oneDimensionalArray| |isQuotient| + |hex| |isTimes| |genericPosition| |eulerPhi| |groebnerFactorize| + |reverse!| |expenseOfEvaluationIF| |gcdprim| |Beta| + |algebraicDecompose| |isExpt| |reseed| |OMgetEndApp| |infix| + |drawCurves| |mainKernel| |makeMulti| |retractable?| |cAcsch| |name| + |palgLODE0| |simplify| |innerint| |shift| |term| |characteristic| + |genericRightNorm| |OMgetObject| |dioSolve| |generalInfiniteProduct| + |specialTrigs| |chebyshevT| |relerror| |invertible?| |fortranInteger| + |roughUnitIdeal?| |fortranReal| |quadraticForm| |divisors| |digits| + |jordanAlgebra?| |separateFactors| |light| |thetaCoord| + |nextNormalPoly| |d01bbf| |atrapezoidal| |logGamma| |compBound| + |subst| |rowEchLocal| |oddInfiniteProduct| |leftZero| |printingInfo?| + |leadingIndex| |uniform01| |semicolonSeparate| |height| |setEmpty!| + |merge| |symmetricProduct| |constantCoefficientRicDE| |biRank| + |superscript| |rootKerSimp| |every?| |outputAsScript| |d02gbf| + |mapdiv| |pointSizeDefault| |integralRepresents| |sumSquares| + |deepExpand| |meshPar2Var| |increasePrecision| |max| |outputSpacing| + |primeFrobenius| |testModulus| |factorSquareFreeByRecursion| |mulmod| + |aCubic| |combineFeatureCompatibility| |someBasis| |fracPart| + |monicLeftDivide| |in?| |nextNormalPrimitivePoly| |sqfrFactor| + |positive?| |c06fqf| |more?| |init| |critT| |cycleSplit!| + |alternatingGroup| |OMParseError?| |cycleRagits| + |generalizedContinuumHypothesisAssumed| |fortranCarriageReturn| + |generalizedContinuumHypothesisAssumed?| |s17acf| |reify| + |invmultisect| |currentScope| |iitanh| |ramifiedAtInfinity?| |exp1| + |PollardSmallFactor| |factorials| |numFunEvals3D| |contract| |shade| + |objects| |cAcoth| |scripted?| |newTypeLists| |symmetricRemainder| + |region| |swapColumns!| |mainVariables| |decrease| |symmetricSquare| + |base| |semiResultantEuclidean1| |ode2| |imaginary| |normalizeIfCan| + |cyclicParents| |groebgen| |addMatchRestricted| |hspace| |or| + |fractRadix| |factorPolynomial| |rotate| |localAbs| |leastPower| + |newReduc| |OMputBind| |FormatArabic| |toseLastSubResultant| + |sumOfSquares| |and| |wordInGenerators| |romberg| |laguerreL| + |numberOfNormalPoly| |polygamma| |rightNorm| + |factorSquareFreePolynomial| |raisePolynomial| |primextintfrac| + |unexpand| |linearDependence| |nextIrreduciblePoly| |outputFloating| + |cAcsc| |addiag| |zero| |createPrimitiveElement| + |setLegalFortranSourceExtensions| |f02akf| |zeroSquareMatrix| + |systemCommand| |outputFixed| |rootBound| |e04mbf| |xCoord| + |euclideanNormalForm| |e01sff| |legendre| |getRef| |polar| |leader| + |f07fef| |divide| |makeViewport3D| |And| |stosePrepareSubResAlgo| + |resize| |terms| |critBonD| |dictionary| |cn| |tower| |complex?| + |expPot| |gcdcofact| |Or| |front| |endOfFile?| |child?| |geometric| + |unary?| |powerAssociative?| |c05pbf| |merge!| |Not| |iicsc| + |minGbasis| |decompose| |f02awf| |d02bhf| |insertMatch| |ratDenom| + |iicoth| |eigenvectors| |primaryDecomp| |maxrank| |lift| + |LagrangeInterpolation| |basis| |setAdaptive| |f01rcf| + |jordanAdmissible?| |infieldint| |over| |reduce| + |multiplyCoefficients| |bipolar| |external?| |trigs| |complexSolve| + |bumptab1| |paren| |previous| |iiacosh| |safeCeiling| |minimumDegree| + |pow| |pattern| |totolex| |HermiteIntegrate| |c05nbf| |iiabs| + |genericLeftTraceForm| |argumentListOf| |arguments| |iiacoth| + |representationType| |unitCanonical| |rationalFunction| |s13acf| + |d01akf| |rightFactorCandidate| |listOfMonoms| |e02bbf| |algDsolve| + |viewSizeDefault| |sturmSequence| |qinterval| |f01qdf| + |functionIsContinuousAtEndPoints| |outputForm| |discriminantEuclidean| + |iisec| |cCos| FG2F |cyclePartition| |minColIndex| |exprToGenUPS| + |localIntegralBasis| |times!| |initials| |insertRoot!| |identity| + |numberOfMonomials| |univariatePolynomials| |predicate| |approxSqrt| + |overlap| |leastMonomial| |tree| |associatorDependence| |interval| + |iiatan| |/\\| |OMUnknownCD?| |coercePreimagesImages| |ldf2vmf| + |rightTrace| |writable?| |bandedHessian| |f02abf| |cosh2sech| + |stFuncN| |s19abf| |palgRDE| |primlimitedint| |loadNativeModule| |\\/| + |linGenPos| |shallowCopy| |modularGcdPrimitive| |hyperelliptic| + |boundOfCauchy| |d01gbf| |nextPartition| |OMputApp| |squareFreePrim| + |axes| |numberOfFactors| |univariate?| |dihedral| |totalLex| |wreath| + |critB| |moebius| |result| |removeRoughlyRedundantFactorsInContents| + |univcase| BY |trivialIdeal?| |operators| |outputMeasure| |OMreceive| + |clearDenominator| |startTableInvSet!| |systemSizeIF| + |pointColorPalette| |denomRicDE| |infinite?| |mainMonomials| |xn| + |goto| |primintfldpoly| |size?| |selectNonFiniteRoutines| |concat!| + |internalIntegrate0| |quasiMonic?| |externalList| |generalTwoFactor| + |linkToFortran| |euclideanGroebner| |Is| |palginfieldint| + |returnTypeOf| |iiacos| |lquo| |cartesian| |reorder| |OMserve| + |algebraicCoefficients?| |startStats!| |trunc| |autoReduced?| + |maxPoints3D| |normal| |stronglyReduced?| |charthRoot| |cCot| + |mapSolve| |subscriptedVariables| |f2st| |range| |ocf2ocdf| + |rischNormalize| |rationalPoint?| |bit?| |indices| |cyclotomic| + |typeList| |rdregime| |constantRight| |cyclicSubmodule| |dmpToHdmp| + |untab| |parameters| |cardinality| |listexp| |symmetricDifference| + |hermite| |OMputEndObject| |back| |position!| |simplifyExp| + |subHeight| |lowerCase| |f01mcf| |squareFreeFactors| |nthExpon| + |invertibleSet| |readLineIfCan!| |coordinate| |collectUpper| |seed| + |stoseInvertibleSet| |kroneckerDelta| |integralAtInfinity?| + |setCondition!| |readIfCan!| |quote| |palgextint| |Si| + |changeThreshhold| |reduced?| |putGraph| |genericRightTrace| |box| + |prepareDecompose| |monomial?| |selectFiniteRoutines| + |lazyResidueClass| |clearTheSymbolTable| |write!| |lifting1| + |binomial| |imagi| |OMsetEncoding| |evenInfiniteProduct| |superHeight| + |interpolate| |applyRules| |OMbindTCP| |cTanh| |lintgcd| + |innerEigenvectors| |addMatch| |presub| |prefixRagits| + |symmetricGroup| |sylvesterSequence| |palgint| |setScreenResolution| + |blankSeparate| |weights| |irreducibleFactor| |fullDisplay| |ranges| + |perfectSqrt| |swap!| |s21bbf| |d01aqf| |replaceKthElement| |iifact| + |copies| |finiteBasis| |s20adf| |dimension| |f02aef| + |subResultantChain| |GospersMethod| |remove!| |iicsch| |rotatez| + |att2Result| |f02bbf| |f04maf| |initTable!| |problemPoints| + |lfextendedint| |normalForm| |op| |subNodeOf?| |tail| |OMgetSymbol| + |sqfree| |enterInCache| |cyclicCopy| |Frobenius| |horizConcat| + |janko2| |approxNthRoot| |one?| |recolor| |printTypes| |spherical| + |operation| |critpOrder| |stoseInvertibleSetsqfreg| |prime| |lprop| + |e01sbf| |setValue!| |subResultantsChain| |schema| |getButtonValue| + |tanhIfCan| |open?| |monomRDE| |maxRowIndex| |divideIfCan| + |deleteProperty!| |df2mf| |definingInequation| |antiCommutative?| + |dAndcExp| |singRicDE| |pdf2ef| |s17aff| |red| |leftExactQuotient| + |fortranComplex| |critM| |s17dgf| |mathieu11| |squareFree| + |lazyPremWithDefault| |reducedQPowers| |nthFractionalTerm| + |separateDegrees| |taylorQuoByVar| |toseInvertible?| |minrank| + |deepestTail| |setTex!| |OMgetEndAtp| |OMgetEndBVar| |gcdPolynomial| + |symbolIfCan| |setvalue!| |charClass| |exprHasWeightCosWXorSinWX| + |iflist2Result| |monomialIntegrate| |leftRecip| |f04jgf| |isOp| + |stoseSquareFreePart| |f04mcf| |ScanFloatIgnoreSpacesIfCan| + |OMputSymbol| |OMsupportsCD?| |reducedSystem| |s17ajf| |getGoodPrime| + |asecIfCan| |OMgetAttr| |expint| |loopPoints| |sumOfKthPowerDivisors| + |realZeros| |setleft!| |indicialEquations| |rootSimp| + |complexIntegrate| |unaryFunction| |getOrder| |orthonormalBasis| + |hasPredicate?| |composites| |selectIntegrationRoutines| = + |removeDuplicates!| |var1StepsDefault| |explogs2trigs| |logIfCan| + |inspect| |nary?| |chvar| |startPolynomial| |OMopenFile| + |quotedOperators| |LyndonWordsList| |member?| |basisOfRightNucleus| + |binaryTournament| |rationalApproximation| |henselFact| + |fixedPointExquo| |schwerpunkt| |distdfact| |primextendedint| + |generator| |symbolTableOf| |revert| |OMgetVariable| + |supDimElseRittWu?| |delta| < |prinb| |numberOfDivisors| + |compactFraction| |pointLists| |leftRank| |branchPoint?| |anticoord| + |s14baf| |mesh| |transcendenceDegree| > |transcendentalDecompose| + |resetNew| |rightCharacteristicPolynomial| |viewPhiDefault| |exponent| + |limitedIntegrate| |c06fpf| |polyRicDE| |rightExactQuotient| + |epilogue| |commonDenominator| <= |heapSort| |augment| |shiftLeft| + |mvar| |noncommutativeJordanAlgebra?| |normalDenom| |algebraicSort| + |c02agf| |pToHdmp| >= |OMgetAtp| |infiniteProduct| |rightUnits| + |isPlus| |makeCos| |create3Space| |lazy?| |characteristicSet| + |genericLeftNorm| |fortranLinkerArgs| |setprevious!| |splitConstant| + |c06gcf| |patternMatch| |exteriorDifferential| |ridHack1| |traverse| + |algint| |seriesToOutputForm| |datalist| |inc| |rule| |commutator| + |getPickedPoints| |paraboloidal| |createZechTable| |LyndonWordsList1| + |rightGcd| |possiblyNewVariety?| |totalfract| |LazardQuotient2| + + |mdeg| |pushNewContour| |exprex| |f02aff| |maxint| |eulerE| + |ParCondList| |OMgetEndError| |gderiv| |lambda| - + |lazyIrreducibleFactors| |generalLambert| |OMgetEndObject| |cap| + |iomode| |lo| |regularRepresentation| |andOperands| |exactQuotient!| + |laurentRep| |sinh| / |cSinh| |generic?| |call| |quartic| |freeOf?| + |notOperand| |lexico| |incr| |youngGroup| |shiftRight| |overset?| + |monicRightFactorIfCan| |tanQ| |cosh| |measure2Result| |extractPoint| + |formula| |normFactors| |nthExponent| |startTable!| |hi| |failed| + |postfix| |listYoungTableaus| |OMgetType| |internalDecompose| |true| + |tanh| |rightUnit| |checkRur| |exponentialOrder| |tan2trig| + |computeCycleLength| |innerSolve1| |squareTop| |OMreadFile| + |sayLength| |SturmHabicht| |coth| |infieldIntegrate| |bernoulliB| + |and?| |scanOneDimSubspaces| |categoryFrame| |f04adf| |OMputEndError| + |setPrologue!| |factorsOfCyclicGroupSize| |prinshINFO| |sech| + |buildSyntax| |partialFraction| |sh| |mergeFactors| |tableau| + |doublyTransitive?| |conical| |dflist| |curve| |f01qcf| |adaptive3D?| + |qelt| |csch| |stronglyReduce| |bandedJacobian| |weighted| + |solveLinearPolynomialEquationByFractions| |nrows| + |basisOfMiddleNucleus| |generalPosition| |leftMinimalPolynomial| |nil| + |currentSubProgram| |cyclic?| |bitLength| |vectorise| |exptMod| + |asinh| |monomRDEsys| |possiblyInfinite?| |ncols| |oddlambert| + |permutation| |prindINFO| |sechIfCan| |determinant| |laplace| |e01bhf| + |xRange| |acosh| |root?| |lhs| |minIndex| + |removeRoughlyRedundantFactorsInPol| |axesColorDefault| |factorset| + |isobaric?| |stopMusserTrials| |inverseLaplace| |quatern| |monic?| + |nextLatticePermutation| |yRange| |atanh| |imagj| |rhs| |extract!| + |mkIntegral| |weakBiRank| |tanAn| |basisOfLeftNucloid| |low| |lyndon?| + |approximate| |retractIfCan| |aQuartic| |brillhartTrials| |Lazard2| + |zRange| |acoth| |getDatabase| |shellSort| |rightRankPolynomial| + |module| |maxdeg| |complex| |squareFreeLexTriangular| |f02adf| |sign| + |cycle| |hue| |updatF| |map!| |asech| |stoseLastSubResultant| + |dimensionOfIrreducibleRepresentation| |outputList| |acosIfCan| + |inconsistent?| |cycleElt| |heap| |makeTerm| |coth2tanh| + |generalizedEigenvector| |interpretString| |qsetelt!| + |indiceSubResultant| |members| |dihedralGroup| |rootNormalize| + |firstUncouplingMatrix| |setProperty| |arity| |mathieu12| + |reducedDiscriminant| |multiEuclideanTree| |setScreenResolution3D| + |multiple| |getBadValues| |pToDmp| |viewDefaults| |escape| + |lfextlimint| |stirling1| |getIdentifier| |lfintegrate| |nextSublist| + |redPol| |stoseInvertible?| |applyQuote| |copy!| |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) ((-842) -12 (|has| |#1| (-286)) (|has| |#1| (-842))) ((-853) -3321 (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-932) -12 (|has| |#1| (-932)) (|has| |#1| (-1111))) ((-966 (-385 (-525))) |has| |#1| (-966 (-385 (-525)))) ((-966 (-525)) |has| |#1| (-966 (-525))) ((-966 |#1|) . T) ((-981 #0#) -3321 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-981 |#1|) . T) ((-981 $) . T) ((-975) . T) ((-982) . T) ((-1030) . T) ((-1018) . T) ((-1065) |has| |#1| (-327)) ((-1111) |has| |#1| (-1111)) ((-1114) |has| |#1| (-1111)) ((-1125) . 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-385 (-525))) -3150 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-37 |#1|) . T) ((-37 $) -3150 (|has| |#1| (-517)) (|has| |#1| (-327)) (|has| |#1| (-341)) (|has| |#1| (-286))) ((-34) |has| |#1| (-1111)) ((-91) |has| |#1| (-1111)) ((-97) . T) ((-107 #0# #0#) -3150 (|has| |#1| (-327)) (|has| |#1| (-341))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-126) . T) ((-136) -3150 (|has| |#1| (-327)) (|has| |#1| (-136))) ((-138) |has| |#1| (-138)) ((-565 (-796)) . T) ((-160) . T) ((-566 (-157 (-205))) |has| |#1| (-951)) ((-566 (-157 (-357))) |has| |#1| (-951)) ((-566 (-501)) |has| |#1| (-566 (-501))) ((-566 (-825 (-357))) |has| |#1| (-566 (-825 (-357)))) ((-566 (-825 (-525))) |has| |#1| (-566 (-825 (-525)))) ((-566 #1=(-1085 |#1|)) . T) ((-211 |#1|) . 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T) ((-37 |#2|) |has| |#2| (-160)) ((-97) -3150 (|has| |#2| (-1018)) (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-734)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3150 (|has| |#2| (-975)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-107 $ $) |has| |#2| (-160)) ((-126) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-734)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126))) ((-565 (-796)) -3150 (|has| |#2| (-1018)) (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-734)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-565 (-796))) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-565 (-1171 |#2|)) . T) ((-160) |has| |#2| (-160)) ((-211 |#2|) |has| |#2| (-975)) ((-213) -12 (|has| |#2| (-213)) (|has| |#2| (-975))) ((-265 #0=(-525) |#2|) . T) ((-267 #0# |#2|) . T) ((-288 |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((-346) |has| |#2| (-346)) ((-355 |#2|) |has| |#2| (-975)) ((-389 |#2|) |has| |#2| (-1018)) ((-464 |#2|) . T) ((-558 #0# |#2|) . T) ((-486 |#2| |#2|) -12 (|has| |#2| (-288 |#2|)) (|has| |#2| (-1018))) ((-593 |#2|) -3150 (|has| |#2| (-975)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-593 $) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-160))) ((-587 (-525)) -12 (|has| |#2| (-587 (-525))) (|has| |#2| (-975))) ((-587 |#2|) |has| |#2| (-975)) ((-659 |#2|) -3150 (|has| |#2| (-341)) (|has| |#2| (-160))) ((-668) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-160))) ((-732) |has| |#2| (-786)) ((-733) -3150 (|has| |#2| (-786)) (|has| |#2| (-734))) ((-734) |has| |#2| (-734)) ((-735) -3150 (|has| |#2| (-786)) (|has| |#2| (-734))) ((-736) -3150 (|has| |#2| (-786)) (|has| |#2| (-734))) ((-786) |has| |#2| (-786)) ((-788) -3150 (|has| |#2| (-786)) (|has| |#2| (-734))) ((-833 (-1089)) -12 (|has| |#2| (-833 (-1089))) (|has| |#2| (-975))) ((-966 (-385 (-525))) -12 (|has| |#2| (-966 (-385 (-525)))) (|has| |#2| (-1018))) ((-966 (-525)) -12 (|has| |#2| (-966 (-525))) (|has| |#2| (-1018))) ((-966 |#2|) |has| |#2| (-1018)) ((-981 |#2|) -3150 (|has| |#2| (-975)) (|has| |#2| (-341)) (|has| |#2| (-160))) ((-981 $) |has| |#2| (-160)) ((-975) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-160))) ((-982) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-160))) ((-1030) -3150 (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-160))) ((-1018) -3150 (|has| |#2| (-1018)) (|has| |#2| (-975)) (|has| |#2| (-786)) (|has| |#2| (-734)) (|has| |#2| (-346)) (|has| |#2| (-341)) (|has| |#2| (-160)) (|has| |#2| (-126)) (|has| |#2| (-25))) ((-1125) . T) ((-1178 |#2|) |has| |#2| (-341))) +((-1350 (((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 21)) (-3618 ((|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|) 23)) (-1257 (((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)) 18))) +(((-219 |#1| |#2| |#3|) (-10 -7 (-15 -1350 ((-220 |#1| |#3|) (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -3618 (|#3| (-1 |#3| |#2| |#3|) (-220 |#1| |#2|) |#3|)) (-15 -1257 ((-220 |#1| |#3|) (-1 |#3| |#2|) (-220 |#1| |#2|)))) (-712) (-1125) (-1125)) (T -219)) +((-1257 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-220 *5 *6)) (-14 *5 (-712)) (-4 *6 (-1125)) (-4 *7 (-1125)) (-5 *2 (-220 *5 *7)) (-5 *1 (-219 *5 *6 *7)))) (-3618 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-220 *5 *6)) (-14 *5 (-712)) (-4 *6 (-1125)) (-4 *2 (-1125)) (-5 *1 (-219 *5 *6 *2)))) (-1350 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-220 *6 *7)) (-14 *6 (-712)) (-4 *7 (-1125)) (-4 *5 (-1125)) (-5 *2 (-220 *6 *5)) (-5 *1 (-219 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 #0=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-97) . T) ((-107 #0# #0#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-565 (-796)) . T) ((-160) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-160))) ((-566 (-501)) -12 (|has| |#1| (-566 (-501))) (|has| |#3| (-566 (-501)))) ((-566 (-825 (-357))) -12 (|has| |#1| (-566 (-825 (-357)))) (|has| |#3| (-566 (-825 (-357))))) ((-566 (-825 (-525))) -12 (|has| |#1| (-566 (-825 (-525)))) (|has| |#3| (-566 (-825 (-525))))) ((-211 |#1|) . T) ((-213) |has| |#1| (-213)) ((-269) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-288 $) . T) ((-304 |#1| |#4|) . T) ((-355 |#1|) . T) ((-389 |#1|) . T) ((-429) -3150 (|has| |#1| (-842)) (|has| |#1| (-429))) ((-486 |#2| |#1|) |has| |#1| (-213)) ((-486 |#2| $) |has| |#1| (-213)) ((-486 |#3| |#1|) . T) ((-486 |#3| $) . T) ((-486 $ $) . T) ((-517) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-593 #0#) |has| |#1| (-37 (-385 (-525)))) ((-593 |#1|) . T) ((-593 $) . T) ((-587 (-525)) |has| |#1| (-587 (-525))) ((-587 |#1|) . T) ((-659 #0#) |has| |#1| (-37 (-385 (-525)))) ((-659 |#1|) |has| |#1| (-160)) ((-659 $) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429))) ((-668) . T) ((-788) |has| |#1| (-788)) ((-833 (-1089)) |has| |#1| (-833 (-1089))) ((-833 |#3|) . T) ((-819 (-357)) -12 (|has| |#1| (-819 (-357))) (|has| |#3| (-819 (-357)))) ((-819 (-525)) -12 (|has| |#1| (-819 (-525))) (|has| |#3| (-819 (-525)))) ((-882 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| #0=(-712)) . T) ((-25) . T) ((-37 #1=(-385 (-525))) |has| |#1| (-37 (-385 (-525)))) ((-37 |#1|) |has| |#1| (-160)) ((-37 $) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341))) ((-97) . T) ((-107 #1# #1#) |has| |#1| (-37 (-385 (-525)))) ((-107 |#1| |#1|) . T) ((-107 $ $) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-126) . T) ((-136) |has| |#1| (-136)) ((-138) |has| |#1| (-138)) ((-565 (-796)) . T) ((-160) -3150 (|has| |#1| (-842)) (|has| |#1| (-517)) (|has| |#1| (-429)) (|has| |#1| (-341)) (|has| |#1| (-160))) ((-566 (-501)) -12 (|has| (-1003) (-566 (-501))) (|has| |#1| (-566 (-501)))) ((-566 (-825 (-357))) -12 (|has| (-1003) (-566 (-825 (-357)))) (|has| |#1| (-566 (-825 (-357))))) ((-566 (-825 (-525))) -12 (|has| (-1003) (-566 (-825 (-525)))) (|has| |#1| (-566 (-825 (-525))))) ((-211 |#1|) . T) ((-213) . 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38) (($ $ $) 35)) (-4036 (($ $ $) 26)) (** (($ $ (-854)) NIL) (($ $ (-712)) 40)) (* (($ (-854) $) NIL) (($ (-712) $) NIL) (($ (-525) $) 32) (($ $ $) 31))) (((-1197 |#1|) (-13 (-160) (-346) (-566 (-525)) (-1065)) (-854)) (T -1197)) NIL (-13 (-160) (-346) (-566 (-525)) (-1065)) @@ -4917,4 +4917,4 @@ NIL NIL NIL NIL -((-3 3144498 3144503 3144508 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3144483 3144488 3144493 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3144468 3144473 3144478 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3144453 3144458 3144463 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1197 3143583 3144328 3144405 "ZMOD" 3144410 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1196 3142693 3142857 3143066 "ZLINDEP" 3143415 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1195 3132097 3133842 3135794 "ZDSOLVE" 3140842 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1194 3131343 3131484 3131673 "YSTREAM" 3131943 NIL YSTREAM (NIL T) -7 NIL NIL) (-1193 3129112 3130648 3130851 "XRPOLY" 3131186 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1192 3125574 3126903 3127485 "XPR" 3128576 NIL XPR (NIL T T) -8 NIL NIL) (-1191 3123288 3124909 3125112 "XPOLY" 3125405 NIL XPOLY (NIL T) -8 NIL NIL) (-1190 3121102 3122480 3122534 "XPOLYC" 3122819 NIL XPOLYC (NIL T T) -9 NIL 3122932) (-1189 3117474 3119619 3120007 "XPBWPOLY" 3120760 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1188 3113402 3115715 3115757 "XF" 3116378 NIL XF (NIL T) -9 NIL 3116777) (-1187 3113023 3113111 3113280 "XF-" 3113285 NIL XF- (NIL T T) -8 NIL NIL) (-1186 3108403 3109702 3109756 "XFALG" 3111904 NIL XFALG (NIL T T) -9 NIL 3112691) (-1185 3107540 3107644 3107848 "XEXPPKG" 3108295 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1184 3105639 3107391 3107486 "XDPOLY" 3107491 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1183 3104518 3105128 3105170 "XALG" 3105232 NIL XALG (NIL T) -9 NIL 3105351) (-1182 3097994 3102502 3102995 "WUTSET" 3104110 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1181 3095806 3096613 3096964 "WP" 3097776 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1180 3094692 3094890 3095185 "WFFINTBS" 3095603 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1179 3092596 3093023 3093485 "WEIER" 3094264 NIL WEIER (NIL T) -7 NIL NIL) (-1178 3091745 3092169 3092211 "VSPACE" 3092347 NIL VSPACE (NIL T) -9 NIL 3092421) (-1177 3091583 3091610 3091701 "VSPACE-" 3091706 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1176 3091329 3091372 3091443 "VOID" 3091534 T VOID (NIL) -8 NIL NIL) (-1175 3089465 3089824 3090230 "VIEW" 3090945 T VIEW (NIL) -7 NIL NIL) (-1174 3085890 3086528 3087265 "VIEWDEF" 3088750 T VIEWDEF (NIL) -7 NIL NIL) (-1173 3075228 3077438 3079611 "VIEW3D" 3083739 T VIEW3D (NIL) -8 NIL NIL) (-1172 3067510 3069139 3070718 "VIEW2D" 3073671 T VIEW2D (NIL) -8 NIL NIL) (-1171 3062919 3067280 3067372 "VECTOR" 3067453 NIL VECTOR (NIL T) -8 NIL NIL) (-1170 3061496 3061755 3062073 "VECTOR2" 3062649 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1169 3055036 3059288 3059331 "VECTCAT" 3060319 NIL VECTCAT (NIL T) -9 NIL 3060903) (-1168 3054050 3054304 3054694 "VECTCAT-" 3054699 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1167 3053531 3053701 3053821 "VARIABLE" 3053965 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1166 3053464 3053469 3053499 "UTYPE" 3053504 T UTYPE (NIL) -9 NIL NIL) (-1165 3052299 3052453 3052714 "UTSODETL" 3053290 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1164 3049739 3050199 3050723 "UTSODE" 3051840 NIL UTSODE (NIL T T) -7 NIL NIL) (-1163 3041583 3047379 3047867 "UTS" 3049308 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1162 3032928 3038293 3038335 "UTSCAT" 3039436 NIL UTSCAT (NIL T) -9 NIL 3040193) (-1161 3030283 3030999 3031987 "UTSCAT-" 3031992 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1160 3029914 3029957 3030088 "UTS2" 3030234 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1159 3024190 3026755 3026798 "URAGG" 3028868 NIL URAGG (NIL T) -9 NIL 3029590) (-1158 3021129 3021992 3023115 "URAGG-" 3023120 NIL URAGG- (NIL T T) -8 NIL NIL) (-1157 3016815 3019746 3020217 "UPXSSING" 3020793 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1156 3008706 3015936 3016216 "UPXS" 3016592 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1155 3001735 3008611 3008682 "UPXSCONS" 3008687 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1154 2992024 2998854 2998915 "UPXSCCA" 2999564 NIL UPXSCCA (NIL T T) -9 NIL 2999805) (-1153 2991663 2991748 2991921 "UPXSCCA-" 2991926 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1152 2981874 2988477 2988519 "UPXSCAT" 2989162 NIL UPXSCAT (NIL T) -9 NIL 2989770) (-1151 2981308 2981387 2981564 "UPXS2" 2981789 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1150 2979962 2980215 2980566 "UPSQFREE" 2981051 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1149 2973853 2976908 2976962 "UPSCAT" 2978111 NIL UPSCAT (NIL T T) -9 NIL 2978885) (-1148 2973058 2973265 2973591 "UPSCAT-" 2973596 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1147 2959144 2967181 2967223 "UPOLYC" 2969301 NIL UPOLYC (NIL T) -9 NIL 2970522) (-1146 2950474 2952899 2956045 "UPOLYC-" 2956050 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1145 2950105 2950148 2950279 "UPOLYC2" 2950425 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1144 2941524 2949674 2949811 "UP" 2950015 NIL UP (NIL NIL T) -8 NIL NIL) (-1143 2940867 2940974 2941137 "UPMP" 2941413 NIL UPMP (NIL T T) -7 NIL NIL) (-1142 2940420 2940501 2940640 "UPDIVP" 2940780 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1141 2938988 2939237 2939553 "UPDECOMP" 2940169 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1140 2938223 2938335 2938520 "UPCDEN" 2938872 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1139 2937746 2937815 2937962 "UP2" 2938148 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1138 2936263 2936950 2937227 "UNISEG" 2937504 NIL UNISEG (NIL T) -8 NIL NIL) (-1137 2935478 2935605 2935810 "UNISEG2" 2936106 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1136 2934538 2934718 2934944 "UNIFACT" 2935294 NIL UNIFACT (NIL T) -7 NIL NIL) (-1135 2918434 2933719 2933969 "ULS" 2934345 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1134 2906399 2918339 2918410 "ULSCONS" 2918415 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1133 2889149 2901162 2901223 "ULSCCAT" 2901935 NIL ULSCCAT (NIL T T) -9 NIL 2902231) (-1132 2888200 2888445 2888832 "ULSCCAT-" 2888837 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1131 2878190 2884707 2884749 "ULSCAT" 2885605 NIL ULSCAT (NIL T) -9 NIL 2886335) (-1130 2877624 2877703 2877880 "ULS2" 2878105 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1129 2876022 2876989 2877019 "UFD" 2877231 T UFD (NIL) -9 NIL 2877345) (-1128 2875816 2875862 2875957 "UFD-" 2875962 NIL UFD- (NIL T) -8 NIL NIL) (-1127 2874898 2875081 2875297 "UDVO" 2875622 T UDVO (NIL) -7 NIL NIL) (-1126 2872714 2873123 2873594 "UDPO" 2874462 NIL UDPO (NIL T) -7 NIL NIL) (-1125 2872647 2872652 2872682 "TYPE" 2872687 T TYPE (NIL) -9 NIL NIL) (-1124 2871618 2871820 2872060 "TWOFACT" 2872441 NIL TWOFACT (NIL T) -7 NIL NIL) (-1123 2870556 2870893 2871156 "TUPLE" 2871390 NIL TUPLE (NIL T) -8 NIL NIL) (-1122 2868247 2868766 2869305 "TUBETOOL" 2870039 T TUBETOOL (NIL) -7 NIL NIL) (-1121 2867096 2867301 2867542 "TUBE" 2868040 NIL TUBE (NIL T) -8 NIL NIL) (-1120 2861820 2866074 2866356 "TS" 2866848 NIL TS (NIL T) -8 NIL NIL) (-1119 2850524 2854616 2854712 "TSETCAT" 2859946 NIL TSETCAT (NIL T T T T) -9 NIL 2861477) (-1118 2845259 2846857 2848747 "TSETCAT-" 2848752 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1117 2839522 2840368 2841310 "TRMANIP" 2844395 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1116 2838963 2839026 2839189 "TRIMAT" 2839454 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1115 2836769 2837006 2837369 "TRIGMNIP" 2838712 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1114 2836289 2836402 2836432 "TRIGCAT" 2836645 T TRIGCAT (NIL) -9 NIL NIL) (-1113 2835958 2836037 2836178 "TRIGCAT-" 2836183 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1112 2832857 2834818 2835098 "TREE" 2835713 NIL TREE (NIL T) -8 NIL NIL) (-1111 2832131 2832659 2832689 "TRANFUN" 2832724 T TRANFUN (NIL) -9 NIL 2832790) (-1110 2831410 2831601 2831881 "TRANFUN-" 2831886 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1109 2831214 2831246 2831307 "TOPSP" 2831371 T TOPSP (NIL) -7 NIL NIL) (-1108 2830566 2830681 2830834 "TOOLSIGN" 2831095 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1107 2829227 2829743 2829982 "TEXTFILE" 2830349 T TEXTFILE (NIL) -8 NIL NIL) (-1106 2827092 2827606 2828044 "TEX" 2828811 T TEX (NIL) -8 NIL NIL) (-1105 2826873 2826904 2826976 "TEX1" 2827055 NIL TEX1 (NIL T) -7 NIL NIL) (-1104 2826521 2826584 2826674 "TEMUTL" 2826805 T TEMUTL (NIL) -7 NIL NIL) (-1103 2824675 2824955 2825280 "TBCMPPK" 2826244 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1102 2816564 2822836 2822892 "TBAGG" 2823292 NIL TBAGG (NIL T T) -9 NIL 2823503) (-1101 2811634 2813122 2814876 "TBAGG-" 2814881 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1100 2811018 2811125 2811270 "TANEXP" 2811523 NIL TANEXP (NIL T) -7 NIL NIL) (-1099 2804519 2810875 2810968 "TABLE" 2810973 NIL TABLE (NIL T T) -8 NIL NIL) (-1098 2803931 2804030 2804168 "TABLEAU" 2804416 NIL TABLEAU (NIL T) -8 NIL NIL) (-1097 2798539 2799759 2801007 "TABLBUMP" 2802717 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1096 2797967 2798067 2798195 "SYSTEM" 2798433 T SYSTEM (NIL) -7 NIL NIL) (-1095 2794430 2795125 2795908 "SYSSOLP" 2797218 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1094 2790721 2791429 2792163 "SYNTAX" 2793718 T SYNTAX (NIL) -8 NIL NIL) (-1093 2787855 2788463 2789101 "SYMTAB" 2790105 T SYMTAB (NIL) -8 NIL NIL) (-1092 2783104 2784006 2784989 "SYMS" 2786894 T SYMS (NIL) -8 NIL NIL) (-1091 2780337 2782564 2782793 "SYMPOLY" 2782909 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1090 2779857 2779932 2780054 "SYMFUNC" 2780249 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1089 2775834 2777094 2777916 "SYMBOL" 2779057 T SYMBOL (NIL) -8 NIL NIL) (-1088 2769373 2771062 2772782 "SWITCH" 2774136 T SWITCH (NIL) -8 NIL NIL) (-1087 2762603 2768200 2768502 "SUTS" 2769128 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1086 2754493 2761724 2762004 "SUPXS" 2762380 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1085 2745985 2754114 2754239 "SUP" 2754402 NIL SUP (NIL T) -8 NIL NIL) (-1084 2745144 2745271 2745488 "SUPFRACF" 2745853 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1083 2744769 2744828 2744939 "SUP2" 2745079 NIL SUP2 (NIL T T) -7 NIL NIL) (-1082 2743187 2743461 2743823 "SUMRF" 2744468 NIL SUMRF (NIL T) -7 NIL NIL) (-1081 2742504 2742570 2742768 "SUMFS" 2743108 NIL SUMFS (NIL T T) -7 NIL NIL) (-1080 2726440 2741685 2741935 "SULS" 2742311 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1079 2725762 2725965 2726105 "SUCH" 2726348 NIL SUCH (NIL T T) -8 NIL NIL) (-1078 2719689 2720701 2721659 "SUBSPACE" 2724850 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1077 2719119 2719209 2719373 "SUBRESP" 2719577 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1076 2712488 2713784 2715095 "STTF" 2717855 NIL STTF (NIL T) -7 NIL NIL) (-1075 2706661 2707781 2708928 "STTFNC" 2711388 NIL STTFNC (NIL T) -7 NIL NIL) (-1074 2698012 2699879 2701672 "STTAYLOR" 2704902 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1073 2691256 2697876 2697959 "STRTBL" 2697964 NIL STRTBL (NIL T) -8 NIL NIL) (-1072 2686647 2691211 2691242 "STRING" 2691247 T STRING (NIL) -8 NIL NIL) (-1071 2681536 2686021 2686051 "STRICAT" 2686110 T STRICAT (NIL) -9 NIL 2686172) (-1070 2674252 2679059 2679679 "STREAM" 2680951 NIL STREAM (NIL T) -8 NIL NIL) (-1069 2673762 2673839 2673983 "STREAM3" 2674169 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1068 2672744 2672927 2673162 "STREAM2" 2673575 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1067 2672432 2672484 2672577 "STREAM1" 2672686 NIL STREAM1 (NIL T) -7 NIL NIL) (-1066 2671448 2671629 2671860 "STINPROD" 2672248 NIL STINPROD (NIL T) -7 NIL NIL) (-1065 2671027 2671211 2671241 "STEP" 2671321 T STEP (NIL) -9 NIL 2671399) (-1064 2664570 2670926 2671003 "STBL" 2671008 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1063 2659746 2663793 2663836 "STAGG" 2663989 NIL STAGG (NIL T) -9 NIL 2664078) (-1062 2657448 2658050 2658922 "STAGG-" 2658927 NIL STAGG- (NIL T T) -8 NIL NIL) (-1061 2655643 2657218 2657310 "STACK" 2657391 NIL STACK (NIL T) -8 NIL NIL) (-1060 2648374 2653790 2654245 "SREGSET" 2655273 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1059 2640814 2642182 2643694 "SRDCMPK" 2646980 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1058 2633782 2638255 2638285 "SRAGG" 2639588 T SRAGG (NIL) -9 NIL 2640196) (-1057 2632799 2633054 2633433 "SRAGG-" 2633438 NIL SRAGG- (NIL T) -8 NIL NIL) (-1056 2627248 2631718 2632145 "SQMATRIX" 2632418 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1055 2621000 2623968 2624694 "SPLTREE" 2626594 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1054 2616990 2617656 2618302 "SPLNODE" 2620426 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1053 2616037 2616270 2616300 "SPFCAT" 2616744 T SPFCAT (NIL) -9 NIL NIL) (-1052 2614774 2614984 2615248 "SPECOUT" 2615795 T SPECOUT (NIL) -7 NIL NIL) (-1051 2614535 2614575 2614644 "SPADPRSR" 2614727 T SPADPRSR (NIL) -7 NIL NIL) (-1050 2606558 2608305 2608347 "SPACEC" 2612670 NIL SPACEC (NIL T) -9 NIL 2614486) (-1049 2604729 2606491 2606539 "SPACE3" 2606544 NIL SPACE3 (NIL T) -8 NIL NIL) (-1048 2603481 2603652 2603943 "SORTPAK" 2604534 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1047 2601537 2601840 2602258 "SOLVETRA" 2603145 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1046 2600548 2600770 2601044 "SOLVESER" 2601310 NIL SOLVESER (NIL T) -7 NIL NIL) (-1045 2595768 2596649 2597651 "SOLVERAD" 2599600 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1044 2591583 2592192 2592921 "SOLVEFOR" 2595135 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1043 2585883 2590935 2591031 "SNTSCAT" 2591036 NIL SNTSCAT (NIL T T T T) -9 NIL 2591106) (-1042 2579987 2584214 2584604 "SMTS" 2585573 NIL SMTS (NIL T T T) -8 NIL NIL) (-1041 2574397 2579876 2579952 "SMP" 2579957 NIL SMP (NIL T T) -8 NIL NIL) (-1040 2572556 2572857 2573255 "SMITH" 2574094 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1039 2565521 2569717 2569819 "SMATCAT" 2571159 NIL SMATCAT (NIL NIL T T T) -9 NIL 2571708) (-1038 2562462 2563285 2564462 "SMATCAT-" 2564467 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1037 2560176 2561699 2561742 "SKAGG" 2562003 NIL SKAGG (NIL T) -9 NIL 2562138) (-1036 2556234 2559280 2559558 "SINT" 2559920 T SINT (NIL) -8 NIL NIL) (-1035 2556006 2556044 2556110 "SIMPAN" 2556190 T SIMPAN (NIL) -7 NIL NIL) (-1034 2554844 2555065 2555340 "SIGNRF" 2555765 NIL SIGNRF (NIL T) -7 NIL NIL) (-1033 2553653 2553804 2554094 "SIGNEF" 2554673 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1032 2551343 2551797 2552303 "SHP" 2553194 NIL SHP (NIL T NIL) -7 NIL NIL) (-1031 2545196 2551244 2551320 "SHDP" 2551325 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1030 2544686 2544878 2544908 "SGROUP" 2545060 T SGROUP (NIL) -9 NIL 2545147) (-1029 2544456 2544508 2544612 "SGROUP-" 2544617 NIL SGROUP- (NIL T) -8 NIL NIL) (-1028 2541292 2541989 2542712 "SGCF" 2543755 T SGCF (NIL) -7 NIL NIL) (-1027 2535691 2540743 2540839 "SFRTCAT" 2540844 NIL SFRTCAT (NIL T T T T) -9 NIL 2540882) (-1026 2529151 2530166 2531300 "SFRGCD" 2534674 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1025 2522317 2523388 2524572 "SFQCMPK" 2528084 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1024 2521939 2522028 2522138 "SFORT" 2522258 NIL SFORT (NIL T T) -8 NIL NIL) (-1023 2521084 2521779 2521900 "SEXOF" 2521905 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1022 2520218 2520965 2521033 "SEX" 2521038 T SEX (NIL) -8 NIL NIL) (-1021 2514995 2515684 2515779 "SEXCAT" 2519550 NIL SEXCAT (NIL T T T T T) -9 NIL 2520169) (-1020 2512175 2514929 2514977 "SET" 2514982 NIL SET (NIL T) -8 NIL NIL) (-1019 2510426 2510888 2511193 "SETMN" 2511916 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1018 2510034 2510160 2510190 "SETCAT" 2510307 T SETCAT (NIL) -9 NIL 2510391) (-1017 2509814 2509866 2509965 "SETCAT-" 2509970 NIL SETCAT- (NIL T) -8 NIL NIL) (-1016 2506202 2508276 2508319 "SETAGG" 2509189 NIL SETAGG (NIL T) -9 NIL 2509529) (-1015 2505660 2505776 2506013 "SETAGG-" 2506018 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1014 2504864 2505157 2505218 "SEGXCAT" 2505504 NIL SEGXCAT (NIL T T) -9 NIL 2505624) (-1013 2503920 2504530 2504712 "SEG" 2504717 NIL SEG (NIL T) -8 NIL NIL) (-1012 2502827 2503040 2503083 "SEGCAT" 2503665 NIL SEGCAT (NIL T) -9 NIL 2503903) (-1011 2501876 2502206 2502406 "SEGBIND" 2502662 NIL SEGBIND (NIL T) -8 NIL NIL) (-1010 2501497 2501556 2501669 "SEGBIND2" 2501811 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1009 2500716 2500842 2501046 "SEG2" 2501341 NIL SEG2 (NIL T T) -7 NIL NIL) (-1008 2500153 2500651 2500698 "SDVAR" 2500703 NIL SDVAR (NIL T) -8 NIL NIL) (-1007 2492405 2499926 2500054 "SDPOL" 2500059 NIL SDPOL (NIL T) -8 NIL NIL) (-1006 2490998 2491264 2491583 "SCPKG" 2492120 NIL SCPKG (NIL T) -7 NIL NIL) (-1005 2490135 2490314 2490514 "SCOPE" 2490820 T SCOPE (NIL) -8 NIL NIL) (-1004 2489356 2489489 2489668 "SCACHE" 2489990 NIL SCACHE (NIL T) -7 NIL NIL) (-1003 2488795 2489116 2489201 "SAOS" 2489293 T SAOS (NIL) -8 NIL NIL) (-1002 2488360 2488395 2488568 "SAERFFC" 2488754 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1001 2482254 2488257 2488337 "SAE" 2488342 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1000 2481847 2481882 2482041 "SAEFACT" 2482213 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-999 2480173 2480487 2480886 "RURPK" 2481513 NIL RURPK (NIL T NIL) -7 NIL NIL) (-998 2478826 2479103 2479410 "RULESET" 2480009 NIL RULESET (NIL T T T) -8 NIL NIL) (-997 2476034 2476537 2476998 "RULE" 2478508 NIL RULE (NIL T T T) -8 NIL NIL) (-996 2475676 2475831 2475912 "RULECOLD" 2475986 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-995 2470568 2471362 2472278 "RSETGCD" 2474875 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-994 2459883 2464935 2465029 "RSETCAT" 2469094 NIL RSETCAT (NIL T T T T) -9 NIL 2470191) (-993 2457814 2458353 2459173 "RSETCAT-" 2459178 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-992 2450244 2451619 2453135 "RSDCMPK" 2456413 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-991 2448262 2448703 2448775 "RRCC" 2449851 NIL RRCC (NIL T T) -9 NIL 2450195) (-990 2447616 2447790 2448066 "RRCC-" 2448071 NIL RRCC- (NIL T T T) -8 NIL NIL) (-989 2421983 2431608 2431672 "RPOLCAT" 2442174 NIL RPOLCAT (NIL T T T) -9 NIL 2445332) (-988 2413487 2415825 2418943 "RPOLCAT-" 2418948 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-987 2404553 2411717 2412197 "ROUTINE" 2413027 T ROUTINE (NIL) -8 NIL NIL) (-986 2401258 2404109 2404256 "ROMAN" 2404426 T ROMAN (NIL) -8 NIL NIL) (-985 2399544 2400129 2400386 "ROIRC" 2401064 NIL ROIRC (NIL T T) -8 NIL NIL) (-984 2395949 2398253 2398281 "RNS" 2398577 T RNS (NIL) -9 NIL 2398847) (-983 2394463 2394846 2395377 "RNS-" 2395450 NIL RNS- (NIL T) -8 NIL NIL) (-982 2393889 2394297 2394325 "RNG" 2394330 T RNG (NIL) -9 NIL 2394351) (-981 2393287 2393649 2393689 "RMODULE" 2393749 NIL RMODULE (NIL T) -9 NIL 2393791) (-980 2392139 2392233 2392563 "RMCAT2" 2393188 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-979 2388853 2391322 2391643 "RMATRIX" 2391874 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-978 2381850 2384084 2384196 "RMATCAT" 2387505 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2388487) (-977 2381229 2381376 2381679 "RMATCAT-" 2381684 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-976 2380799 2380874 2381000 "RINTERP" 2381148 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-975 2379850 2380414 2380442 "RING" 2380552 T RING (NIL) -9 NIL 2380646) (-974 2379645 2379689 2379783 "RING-" 2379788 NIL RING- (NIL T) -8 NIL NIL) (-973 2378493 2378730 2378986 "RIDIST" 2379409 T RIDIST (NIL) -7 NIL NIL) (-972 2369815 2377967 2378170 "RGCHAIN" 2378342 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-971 2366820 2367434 2368102 "RF" 2369179 NIL RF (NIL T) -7 NIL NIL) (-970 2366469 2366532 2366633 "RFFACTOR" 2366751 NIL RFFACTOR (NIL T) -7 NIL NIL) (-969 2366197 2366232 2366327 "RFFACT" 2366428 NIL RFFACT (NIL T) -7 NIL NIL) (-968 2364327 2364691 2365071 "RFDIST" 2365837 T RFDIST (NIL) -7 NIL NIL) (-967 2363785 2363877 2364037 "RETSOL" 2364229 NIL RETSOL (NIL T T) -7 NIL NIL) (-966 2363378 2363458 2363499 "RETRACT" 2363689 NIL RETRACT (NIL T) -9 NIL NIL) (-965 2363230 2363255 2363339 "RETRACT-" 2363344 NIL RETRACT- (NIL T T) -8 NIL NIL) (-964 2356088 2362887 2363012 "RESULT" 2363125 T RESULT (NIL) -8 NIL NIL) (-963 2354673 2355362 2355559 "RESRING" 2355991 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-962 2354313 2354362 2354458 "RESLATC" 2354610 NIL RESLATC (NIL T) -7 NIL NIL) (-961 2354022 2354056 2354161 "REPSQ" 2354272 NIL REPSQ (NIL T) -7 NIL NIL) (-960 2351453 2352033 2352633 "REP" 2353442 T REP (NIL) -7 NIL NIL) (-959 2351154 2351188 2351297 "REPDB" 2351412 NIL REPDB (NIL T) -7 NIL NIL) (-958 2345099 2346478 2347698 "REP2" 2349966 NIL REP2 (NIL T) -7 NIL NIL) (-957 2341505 2342186 2342991 "REP1" 2344326 NIL REP1 (NIL T) -7 NIL NIL) (-956 2334251 2339666 2340118 "REGSET" 2341136 NIL REGSET (NIL T T T T) -8 NIL NIL) (-955 2333072 2333407 2333655 "REF" 2334036 NIL REF (NIL T) -8 NIL NIL) (-954 2332453 2332556 2332721 "REDORDER" 2332956 NIL REDORDER (NIL T T) -7 NIL NIL) (-953 2328422 2331687 2331908 "RECLOS" 2332284 NIL RECLOS (NIL T) -8 NIL NIL) (-952 2327479 2327660 2327873 "REALSOLV" 2328229 T REALSOLV (NIL) -7 NIL NIL) (-951 2327327 2327368 2327396 "REAL" 2327401 T REAL (NIL) -9 NIL 2327436) (-950 2323818 2324620 2325502 "REAL0Q" 2326492 NIL REAL0Q (NIL T) -7 NIL NIL) (-949 2319429 2320417 2321476 "REAL0" 2322799 NIL REAL0 (NIL T) -7 NIL NIL) (-948 2318837 2318909 2319114 "RDIV" 2319351 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-947 2317910 2318084 2318295 "RDIST" 2318659 NIL RDIST (NIL T) -7 NIL NIL) (-946 2316514 2316801 2317170 "RDETRS" 2317618 NIL RDETRS (NIL T T) -7 NIL NIL) (-945 2314335 2314789 2315324 "RDETR" 2316056 NIL RDETR (NIL T T) -7 NIL NIL) (-944 2312951 2313229 2313630 "RDEEFS" 2314051 NIL RDEEFS (NIL T T) -7 NIL NIL) (-943 2311451 2311757 2312186 "RDEEF" 2312639 NIL RDEEF (NIL T T) -7 NIL NIL) (-942 2305736 2308668 2308696 "RCFIELD" 2309973 T RCFIELD (NIL) -9 NIL 2310703) (-941 2303805 2304309 2305002 "RCFIELD-" 2305075 NIL RCFIELD- (NIL T) -8 NIL NIL) (-940 2300137 2301922 2301963 "RCAGG" 2303034 NIL RCAGG (NIL T) -9 NIL 2303499) (-939 2299768 2299862 2300022 "RCAGG-" 2300027 NIL RCAGG- (NIL T T) -8 NIL NIL) (-938 2299112 2299224 2299386 "RATRET" 2299652 NIL RATRET (NIL T) -7 NIL NIL) (-937 2298669 2298736 2298855 "RATFACT" 2299040 NIL RATFACT (NIL T) -7 NIL NIL) (-936 2297984 2298104 2298254 "RANDSRC" 2298539 T RANDSRC (NIL) -7 NIL NIL) (-935 2297721 2297765 2297836 "RADUTIL" 2297933 T RADUTIL (NIL) -7 NIL NIL) (-934 2290728 2296464 2296781 "RADIX" 2297436 NIL RADIX (NIL NIL) -8 NIL NIL) (-933 2282298 2290572 2290700 "RADFF" 2290705 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-932 2281950 2282025 2282053 "RADCAT" 2282210 T RADCAT (NIL) -9 NIL NIL) (-931 2281735 2281783 2281880 "RADCAT-" 2281885 NIL RADCAT- (NIL T) -8 NIL NIL) (-930 2279886 2281510 2281599 "QUEUE" 2281679 NIL QUEUE (NIL T) -8 NIL NIL) (-929 2276383 2279823 2279868 "QUAT" 2279873 NIL QUAT (NIL T) -8 NIL NIL) (-928 2276021 2276064 2276191 "QUATCT2" 2276334 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-927 2269815 2273195 2273235 "QUATCAT" 2274014 NIL QUATCAT (NIL T) -9 NIL 2274779) (-926 2265959 2266996 2268383 "QUATCAT-" 2268477 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-925 2263480 2265044 2265085 "QUAGG" 2265460 NIL QUAGG (NIL T) -9 NIL 2265635) (-924 2262405 2262878 2263050 "QFORM" 2263352 NIL QFORM (NIL NIL T) -8 NIL NIL) (-923 2253702 2258960 2259000 "QFCAT" 2259658 NIL QFCAT (NIL T) -9 NIL 2260651) (-922 2249274 2250475 2252066 "QFCAT-" 2252160 NIL QFCAT- (NIL T T) -8 NIL NIL) (-921 2248912 2248955 2249082 "QFCAT2" 2249225 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-920 2248372 2248482 2248612 "QEQUAT" 2248802 T QEQUAT (NIL) -8 NIL NIL) (-919 2241558 2242629 2243811 "QCMPACK" 2247305 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-918 2239134 2239555 2239983 "QALGSET" 2241213 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-917 2238379 2238553 2238785 "QALGSET2" 2238954 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-916 2237070 2237293 2237610 "PWFFINTB" 2238152 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-915 2235258 2235426 2235779 "PUSHVAR" 2236884 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-914 2231176 2232230 2232271 "PTRANFN" 2234155 NIL PTRANFN (NIL T) -9 NIL NIL) (-913 2229588 2229879 2230200 "PTPACK" 2230887 NIL PTPACK (NIL T) -7 NIL NIL) (-912 2229224 2229281 2229388 "PTFUNC2" 2229525 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-911 2223701 2228042 2228082 "PTCAT" 2228450 NIL PTCAT (NIL T) -9 NIL 2228612) (-910 2223359 2223394 2223518 "PSQFR" 2223660 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-909 2221954 2222252 2222586 "PSEUDLIN" 2223057 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-908 2208762 2211126 2213449 "PSETPK" 2219714 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-907 2201849 2204563 2204657 "PSETCAT" 2207638 NIL PSETCAT (NIL T T T T) -9 NIL 2208452) (-906 2199687 2200321 2201140 "PSETCAT-" 2201145 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-905 2199036 2199201 2199229 "PSCURVE" 2199497 T PSCURVE (NIL) -9 NIL 2199664) (-904 2195488 2197014 2197078 "PSCAT" 2197914 NIL PSCAT (NIL T T T) -9 NIL 2198154) (-903 2194552 2194768 2195167 "PSCAT-" 2195172 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-902 2193204 2193837 2194051 "PRTITION" 2194358 T PRTITION (NIL) -8 NIL NIL) (-901 2182302 2184508 2186696 "PRS" 2191066 NIL PRS (NIL T T) -7 NIL NIL) (-900 2180161 2181653 2181693 "PRQAGG" 2181876 NIL PRQAGG (NIL T) -9 NIL 2181978) (-899 2179732 2179834 2179862 "PROPLOG" 2180047 T PROPLOG (NIL) -9 NIL NIL) (-898 2176855 2177420 2177947 "PROPFRML" 2179237 NIL PROPFRML (NIL T) -8 NIL NIL) (-897 2176315 2176425 2176555 "PROPERTY" 2176745 T PROPERTY (NIL) -8 NIL NIL) (-896 2170089 2174481 2175301 "PRODUCT" 2175541 NIL PRODUCT (NIL T T) -8 NIL NIL) (-895 2167365 2169549 2169782 "PR" 2169900 NIL PR (NIL T T) -8 NIL NIL) (-894 2167161 2167193 2167252 "PRINT" 2167326 T PRINT (NIL) -7 NIL NIL) (-893 2166501 2166618 2166770 "PRIMES" 2167041 NIL PRIMES (NIL T) -7 NIL NIL) (-892 2164566 2164967 2165433 "PRIMELT" 2166080 NIL PRIMELT (NIL T) -7 NIL NIL) (-891 2164295 2164344 2164372 "PRIMCAT" 2164496 T PRIMCAT (NIL) -9 NIL NIL) (-890 2160456 2164233 2164278 "PRIMARR" 2164283 NIL PRIMARR (NIL T) -8 NIL NIL) (-889 2159463 2159641 2159869 "PRIMARR2" 2160274 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-888 2159106 2159162 2159273 "PREASSOC" 2159401 NIL PREASSOC (NIL T T) -7 NIL NIL) (-887 2158581 2158714 2158742 "PPCURVE" 2158947 T PPCURVE (NIL) -9 NIL 2159083) (-886 2155940 2156339 2156931 "POLYROOT" 2158162 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-885 2149846 2155546 2155705 "POLY" 2155813 NIL POLY (NIL T) -8 NIL NIL) (-884 2149231 2149289 2149522 "POLYLIFT" 2149782 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-883 2145516 2145965 2146593 "POLYCATQ" 2148776 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-882 2132557 2137954 2138018 "POLYCAT" 2141503 NIL POLYCAT (NIL T T T) -9 NIL 2143430) (-881 2126008 2127869 2130252 "POLYCAT-" 2130257 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-880 2125597 2125665 2125784 "POLY2UP" 2125934 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-879 2125233 2125290 2125397 "POLY2" 2125534 NIL POLY2 (NIL T T) -7 NIL NIL) (-878 2123918 2124157 2124433 "POLUTIL" 2125007 NIL POLUTIL (NIL T T) -7 NIL NIL) (-877 2122280 2122557 2122887 "POLTOPOL" 2123640 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-876 2117803 2122217 2122262 "POINT" 2122267 NIL POINT (NIL T) -8 NIL NIL) (-875 2115990 2116347 2116722 "PNTHEORY" 2117448 T PNTHEORY (NIL) -7 NIL NIL) (-874 2114418 2114715 2115124 "PMTOOLS" 2115688 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-873 2114011 2114089 2114206 "PMSYM" 2114334 NIL PMSYM (NIL T) -7 NIL NIL) (-872 2113521 2113590 2113764 "PMQFCAT" 2113936 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-871 2112876 2112986 2113142 "PMPRED" 2113398 NIL PMPRED (NIL T) -7 NIL NIL) (-870 2112272 2112358 2112519 "PMPREDFS" 2112777 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-869 2110918 2111126 2111510 "PMPLCAT" 2112034 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-868 2110450 2110529 2110681 "PMLSAGG" 2110833 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-867 2109927 2110003 2110183 "PMKERNEL" 2110368 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-866 2109544 2109619 2109732 "PMINS" 2109846 NIL PMINS (NIL T) -7 NIL NIL) (-865 2108974 2109043 2109258 "PMFS" 2109469 NIL PMFS (NIL T T T) -7 NIL NIL) (-864 2108205 2108323 2108527 "PMDOWN" 2108851 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-863 2107368 2107527 2107709 "PMASS" 2108043 T PMASS (NIL) -7 NIL NIL) (-862 2106642 2106753 2106916 "PMASSFS" 2107254 NIL PMASSFS (NIL T T) -7 NIL NIL) (-861 2106297 2106365 2106459 "PLOTTOOL" 2106568 T PLOTTOOL (NIL) -7 NIL NIL) (-860 2100919 2102108 2103256 "PLOT" 2105169 T PLOT (NIL) -8 NIL NIL) (-859 2096733 2097767 2098688 "PLOT3D" 2100018 T PLOT3D (NIL) -8 NIL NIL) (-858 2095645 2095822 2096057 "PLOT1" 2096537 NIL PLOT1 (NIL T) -7 NIL NIL) (-857 2071039 2075711 2080562 "PLEQN" 2090911 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-856 2070357 2070479 2070659 "PINTERP" 2070904 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-855 2070050 2070097 2070200 "PINTERPA" 2070304 NIL PINTERPA (NIL T T) -7 NIL NIL) (-854 2069277 2069844 2069937 "PI" 2069977 T PI (NIL) -8 NIL NIL) (-853 2067669 2068654 2068682 "PID" 2068864 T PID (NIL) -9 NIL 2068998) (-852 2067394 2067431 2067519 "PICOERCE" 2067626 NIL PICOERCE (NIL T) -7 NIL NIL) (-851 2066714 2066853 2067029 "PGROEB" 2067250 NIL PGROEB (NIL T) -7 NIL NIL) (-850 2062301 2063115 2064020 "PGE" 2065829 T PGE (NIL) -7 NIL NIL) (-849 2060425 2060671 2061037 "PGCD" 2062018 NIL PGCD (NIL T T T T) -7 NIL NIL) (-848 2059763 2059866 2060027 "PFRPAC" 2060309 NIL PFRPAC (NIL T) -7 NIL NIL) (-847 2056378 2058311 2058664 "PFR" 2059442 NIL PFR (NIL T) -8 NIL NIL) (-846 2054767 2055011 2055336 "PFOTOOLS" 2056125 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-845 2053300 2053539 2053890 "PFOQ" 2054524 NIL PFOQ (NIL T T T) -7 NIL NIL) (-844 2051777 2051989 2052351 "PFO" 2053084 NIL PFO (NIL T T T T T) -7 NIL NIL) (-843 2048300 2051666 2051735 "PF" 2051740 NIL PF (NIL NIL) -8 NIL NIL) (-842 2045729 2047010 2047038 "PFECAT" 2047623 T PFECAT (NIL) -9 NIL 2048007) (-841 2045174 2045328 2045542 "PFECAT-" 2045547 NIL PFECAT- (NIL T) -8 NIL NIL) (-840 2043778 2044029 2044330 "PFBRU" 2044923 NIL PFBRU (NIL T T) -7 NIL NIL) (-839 2041645 2041996 2042428 "PFBR" 2043429 NIL PFBR (NIL T T T T) -7 NIL NIL) (-838 2037497 2039021 2039697 "PERM" 2041002 NIL PERM (NIL T) -8 NIL NIL) (-837 2032762 2033704 2034574 "PERMGRP" 2036660 NIL PERMGRP (NIL T) -8 NIL NIL) (-836 2030833 2031826 2031867 "PERMCAT" 2032313 NIL PERMCAT (NIL T) -9 NIL 2032618) (-835 2030488 2030529 2030652 "PERMAN" 2030786 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-834 2027928 2030057 2030188 "PENDTREE" 2030390 NIL PENDTREE (NIL T) -8 NIL NIL) (-833 2026001 2026779 2026820 "PDRING" 2027477 NIL PDRING (NIL T) -9 NIL 2027762) (-832 2025104 2025322 2025684 "PDRING-" 2025689 NIL PDRING- (NIL T T) -8 NIL NIL) (-831 2022245 2022996 2023687 "PDEPROB" 2024433 T PDEPROB (NIL) -8 NIL NIL) (-830 2019816 2020312 2020861 "PDEPACK" 2021716 T PDEPACK (NIL) -7 NIL NIL) (-829 2018728 2018918 2019169 "PDECOMP" 2019615 NIL PDECOMP (NIL T T) -7 NIL NIL) (-828 2016340 2017155 2017183 "PDECAT" 2017968 T PDECAT (NIL) -9 NIL 2018679) (-827 2016093 2016126 2016215 "PCOMP" 2016301 NIL PCOMP (NIL T T) -7 NIL NIL) (-826 2014300 2014896 2015192 "PBWLB" 2015823 NIL PBWLB (NIL T) -8 NIL NIL) (-825 2006808 2008377 2009713 "PATTERN" 2012985 NIL PATTERN (NIL T) -8 NIL NIL) (-824 2006440 2006497 2006606 "PATTERN2" 2006745 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-823 2004197 2004585 2005042 "PATTERN1" 2006029 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-822 2001592 2002146 2002627 "PATRES" 2003762 NIL PATRES (NIL T T) -8 NIL NIL) (-821 2001156 2001223 2001355 "PATRES2" 2001519 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-820 1999053 1999453 1999858 "PATMATCH" 2000825 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-819 1998590 1998773 1998814 "PATMAB" 1998921 NIL PATMAB (NIL T) -9 NIL 1999004) (-818 1997135 1997444 1997702 "PATLRES" 1998395 NIL PATLRES (NIL T T T) -8 NIL NIL) (-817 1996681 1996804 1996845 "PATAB" 1996850 NIL PATAB (NIL T) -9 NIL 1997022) (-816 1994162 1994694 1995267 "PARTPERM" 1996128 T PARTPERM (NIL) -7 NIL NIL) (-815 1993783 1993846 1993948 "PARSURF" 1994093 NIL PARSURF (NIL T) -8 NIL NIL) (-814 1993415 1993472 1993581 "PARSU2" 1993720 NIL PARSU2 (NIL T T) -7 NIL NIL) (-813 1993179 1993219 1993286 "PARSER" 1993368 T PARSER (NIL) -7 NIL NIL) (-812 1992800 1992863 1992965 "PARSCURV" 1993110 NIL PARSCURV (NIL T) -8 NIL NIL) (-811 1992432 1992489 1992598 "PARSC2" 1992737 NIL PARSC2 (NIL T T) -7 NIL NIL) (-810 1992071 1992129 1992226 "PARPCURV" 1992368 NIL PARPCURV (NIL T) -8 NIL NIL) (-809 1991703 1991760 1991869 "PARPC2" 1992008 NIL PARPC2 (NIL T T) -7 NIL NIL) (-808 1991223 1991309 1991428 "PAN2EXPR" 1991604 T PAN2EXPR (NIL) -7 NIL NIL) (-807 1990029 1990344 1990572 "PALETTE" 1991015 T PALETTE (NIL) -8 NIL NIL) (-806 1988497 1989034 1989394 "PAIR" 1989715 NIL PAIR (NIL T T) -8 NIL NIL) (-805 1982347 1987756 1987950 "PADICRC" 1988352 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-804 1975555 1981693 1981877 "PADICRAT" 1982195 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-803 1973859 1975492 1975537 "PADIC" 1975542 NIL PADIC (NIL NIL) -8 NIL NIL) (-802 1971064 1972638 1972678 "PADICCT" 1973259 NIL PADICCT (NIL NIL) -9 NIL 1973541) (-801 1970021 1970221 1970489 "PADEPAC" 1970851 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-800 1969233 1969366 1969572 "PADE" 1969883 NIL PADE (NIL T T T) -7 NIL NIL) (-799 1967244 1968076 1968391 "OWP" 1969001 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-798 1966353 1966849 1967021 "OVAR" 1967112 NIL OVAR (NIL NIL) -8 NIL NIL) (-797 1965617 1965738 1965899 "OUT" 1966212 T OUT (NIL) -7 NIL NIL) (-796 1954671 1956842 1959012 "OUTFORM" 1963467 T OUTFORM (NIL) -8 NIL NIL) (-795 1954079 1954400 1954489 "OSI" 1954602 T OSI (NIL) -8 NIL NIL) (-794 1952824 1953051 1953336 "ORTHPOL" 1953826 NIL ORTHPOL (NIL T) -7 NIL NIL) (-793 1950195 1952485 1952623 "OREUP" 1952767 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-792 1947591 1949888 1950014 "ORESUP" 1950137 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-791 1945126 1945626 1946186 "OREPCTO" 1947080 NIL OREPCTO (NIL T T) -7 NIL NIL) (-790 1939036 1941242 1941282 "OREPCAT" 1943603 NIL OREPCAT (NIL T) -9 NIL 1944706) (-789 1936184 1936966 1938023 "OREPCAT-" 1938028 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-788 1935362 1935634 1935662 "ORDSET" 1935971 T ORDSET (NIL) -9 NIL 1936135) (-787 1934881 1935003 1935196 "ORDSET-" 1935201 NIL ORDSET- (NIL T) -8 NIL NIL) (-786 1933495 1934296 1934324 "ORDRING" 1934526 T ORDRING (NIL) -9 NIL 1934650) (-785 1933140 1933234 1933378 "ORDRING-" 1933383 NIL ORDRING- (NIL T) -8 NIL NIL) (-784 1932516 1932997 1933025 "ORDMON" 1933030 T ORDMON (NIL) -9 NIL 1933051) (-783 1931678 1931825 1932020 "ORDFUNS" 1932365 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-782 1931190 1931549 1931577 "ORDFIN" 1931582 T ORDFIN (NIL) -9 NIL 1931603) (-781 1927702 1929776 1930185 "ORDCOMP" 1930814 NIL ORDCOMP (NIL T) -8 NIL NIL) (-780 1926968 1927095 1927281 "ORDCOMP2" 1927562 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-779 1923475 1924358 1925195 "OPTPROB" 1926151 T OPTPROB (NIL) -8 NIL NIL) (-778 1920317 1920946 1921640 "OPTPACK" 1922801 T OPTPACK (NIL) -7 NIL NIL) (-777 1918043 1918779 1918807 "OPTCAT" 1919622 T OPTCAT (NIL) -9 NIL 1920268) (-776 1917811 1917850 1917916 "OPQUERY" 1917997 T OPQUERY (NIL) -7 NIL NIL) (-775 1914947 1916138 1916638 "OP" 1917343 NIL OP (NIL T) -8 NIL NIL) (-774 1911712 1913744 1914113 "ONECOMP" 1914611 NIL ONECOMP (NIL T) -8 NIL NIL) (-773 1911017 1911132 1911306 "ONECOMP2" 1911584 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-772 1910436 1910542 1910672 "OMSERVER" 1910907 T OMSERVER (NIL) -7 NIL NIL) (-771 1907325 1909877 1909917 "OMSAGG" 1909978 NIL OMSAGG (NIL T) -9 NIL 1910042) (-770 1905948 1906211 1906493 "OMPKG" 1907063 T OMPKG (NIL) -7 NIL NIL) (-769 1905378 1905481 1905509 "OM" 1905808 T OM (NIL) -9 NIL NIL) (-768 1903917 1904930 1905098 "OMLO" 1905259 NIL OMLO (NIL T T) -8 NIL NIL) (-767 1902847 1902994 1903220 "OMEXPR" 1903743 NIL OMEXPR (NIL T) -7 NIL NIL) (-766 1902165 1902393 1902529 "OMERR" 1902731 T OMERR (NIL) -8 NIL NIL) (-765 1901343 1901586 1901746 "OMERRK" 1902025 T OMERRK (NIL) -8 NIL NIL) (-764 1900821 1901020 1901128 "OMENC" 1901255 T OMENC (NIL) -8 NIL NIL) (-763 1894716 1895901 1897072 "OMDEV" 1899670 T OMDEV (NIL) -8 NIL NIL) (-762 1893785 1893956 1894150 "OMCONN" 1894542 T OMCONN (NIL) -8 NIL NIL) (-761 1892401 1893387 1893415 "OINTDOM" 1893420 T OINTDOM (NIL) -9 NIL 1893441) (-760 1888163 1889393 1890108 "OFMONOID" 1891718 NIL OFMONOID (NIL T) -8 NIL NIL) (-759 1887601 1888100 1888145 "ODVAR" 1888150 NIL ODVAR (NIL T) -8 NIL NIL) (-758 1884726 1887098 1887283 "ODR" 1887476 NIL ODR (NIL T T NIL) -8 NIL NIL) (-757 1877032 1884505 1884629 "ODPOL" 1884634 NIL ODPOL (NIL T) -8 NIL NIL) (-756 1870855 1876904 1877009 "ODP" 1877014 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-755 1869621 1869836 1870111 "ODETOOLS" 1870629 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-754 1866590 1867246 1867962 "ODESYS" 1868954 NIL ODESYS (NIL T T) -7 NIL NIL) (-753 1861494 1862402 1863425 "ODERTRIC" 1865665 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-752 1860920 1861002 1861196 "ODERED" 1861406 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-751 1857822 1858370 1859045 "ODERAT" 1860343 NIL ODERAT (NIL T T) -7 NIL NIL) (-750 1854790 1855254 1855850 "ODEPRRIC" 1857351 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-749 1852659 1853228 1853737 "ODEPROB" 1854301 T ODEPROB (NIL) -8 NIL NIL) (-748 1849191 1849674 1850320 "ODEPRIM" 1852138 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-747 1848444 1848546 1848804 "ODEPAL" 1849083 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-746 1844646 1845427 1846281 "ODEPACK" 1847610 T ODEPACK (NIL) -7 NIL NIL) (-745 1843683 1843790 1844018 "ODEINT" 1844535 NIL ODEINT (NIL T T) -7 NIL NIL) (-744 1837784 1839209 1840656 "ODEIFTBL" 1842256 T ODEIFTBL (NIL) -8 NIL NIL) (-743 1833128 1833914 1834872 "ODEEF" 1836943 NIL ODEEF (NIL T T) -7 NIL NIL) (-742 1832465 1832554 1832783 "ODECONST" 1833033 NIL ODECONST (NIL T T T) -7 NIL NIL) (-741 1830623 1831256 1831284 "ODECAT" 1831887 T ODECAT (NIL) -9 NIL 1832416) (-740 1827495 1830335 1830454 "OCT" 1830536 NIL OCT (NIL T) -8 NIL NIL) (-739 1827133 1827176 1827303 "OCTCT2" 1827446 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-738 1821967 1824405 1824445 "OC" 1825541 NIL OC (NIL T) -9 NIL 1826398) (-737 1819194 1819942 1820932 "OC-" 1821026 NIL OC- (NIL T T) -8 NIL NIL) (-736 1818573 1819015 1819043 "OCAMON" 1819048 T OCAMON (NIL) -9 NIL 1819069) (-735 1818027 1818434 1818462 "OASGP" 1818467 T OASGP (NIL) -9 NIL 1818487) (-734 1817315 1817778 1817806 "OAMONS" 1817846 T OAMONS (NIL) -9 NIL 1817889) (-733 1816756 1817163 1817191 "OAMON" 1817196 T OAMON (NIL) -9 NIL 1817216) (-732 1816061 1816553 1816581 "OAGROUP" 1816586 T OAGROUP (NIL) -9 NIL 1816606) (-731 1815751 1815801 1815889 "NUMTUBE" 1816005 NIL NUMTUBE (NIL T) -7 NIL NIL) (-730 1809324 1810842 1812378 "NUMQUAD" 1814235 T NUMQUAD (NIL) -7 NIL NIL) (-729 1805080 1806068 1807093 "NUMODE" 1808319 T NUMODE (NIL) -7 NIL NIL) (-728 1802484 1803330 1803358 "NUMINT" 1804275 T NUMINT (NIL) -9 NIL 1805031) (-727 1801432 1801629 1801847 "NUMFMT" 1802286 T NUMFMT (NIL) -7 NIL NIL) (-726 1787814 1790748 1793278 "NUMERIC" 1798941 NIL NUMERIC (NIL T) -7 NIL NIL) (-725 1782215 1787267 1787361 "NTSCAT" 1787366 NIL NTSCAT (NIL T T T T) -9 NIL 1787404) (-724 1781409 1781574 1781767 "NTPOLFN" 1782054 NIL NTPOLFN (NIL T) -7 NIL NIL) (-723 1769225 1778251 1779061 "NSUP" 1780631 NIL NSUP (NIL T) -8 NIL NIL) (-722 1768861 1768918 1769025 "NSUP2" 1769162 NIL NSUP2 (NIL T T) -7 NIL NIL) (-721 1758823 1768640 1768770 "NSMP" 1768775 NIL NSMP (NIL T T) -8 NIL NIL) (-720 1757255 1757556 1757913 "NREP" 1758511 NIL NREP (NIL T) -7 NIL NIL) (-719 1755846 1756098 1756456 "NPCOEF" 1756998 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-718 1754912 1755027 1755243 "NORMRETR" 1755727 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-717 1752965 1753255 1753662 "NORMPK" 1754620 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-716 1752650 1752678 1752802 "NORMMA" 1752931 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-715 1752477 1752607 1752636 "NONE" 1752641 T NONE (NIL) -8 NIL NIL) (-714 1752266 1752295 1752364 "NONE1" 1752441 NIL NONE1 (NIL T) -7 NIL NIL) (-713 1751751 1751813 1751998 "NODE1" 1752198 NIL NODE1 (NIL T T) -7 NIL NIL) (-712 1750044 1750914 1751169 "NNI" 1751516 T NNI (NIL) -8 NIL NIL) (-711 1748464 1748777 1749141 "NLINSOL" 1749712 NIL NLINSOL (NIL T) -7 NIL NIL) (-710 1744631 1745599 1746521 "NIPROB" 1747562 T NIPROB (NIL) -8 NIL NIL) (-709 1743388 1743622 1743924 "NFINTBAS" 1744393 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-708 1742096 1742327 1742608 "NCODIV" 1743156 NIL NCODIV (NIL T T) -7 NIL NIL) (-707 1741858 1741895 1741970 "NCNTFRAC" 1742053 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-706 1740038 1740402 1740822 "NCEP" 1741483 NIL NCEP (NIL T) -7 NIL NIL) (-705 1738950 1739689 1739717 "NASRING" 1739827 T NASRING (NIL) -9 NIL 1739901) (-704 1738745 1738789 1738883 "NASRING-" 1738888 NIL NASRING- (NIL T) -8 NIL NIL) (-703 1737899 1738398 1738426 "NARNG" 1738543 T NARNG (NIL) -9 NIL 1738634) (-702 1737591 1737658 1737792 "NARNG-" 1737797 NIL NARNG- (NIL T) -8 NIL NIL) (-701 1736470 1736677 1736912 "NAGSP" 1737376 T NAGSP (NIL) -7 NIL NIL) (-700 1727894 1729540 1731175 "NAGS" 1734855 T NAGS (NIL) -7 NIL NIL) (-699 1726458 1726762 1727089 "NAGF07" 1727587 T NAGF07 (NIL) -7 NIL NIL) (-698 1721040 1722320 1723616 "NAGF04" 1725182 T NAGF04 (NIL) -7 NIL NIL) (-697 1714072 1715670 1717287 "NAGF02" 1719443 T NAGF02 (NIL) -7 NIL NIL) (-696 1709336 1710426 1711533 "NAGF01" 1712985 T NAGF01 (NIL) -7 NIL NIL) (-695 1702996 1704554 1706131 "NAGE04" 1707779 T NAGE04 (NIL) -7 NIL NIL) (-694 1694237 1696340 1698452 "NAGE02" 1700904 T NAGE02 (NIL) -7 NIL NIL) (-693 1690230 1691167 1692121 "NAGE01" 1693303 T NAGE01 (NIL) -7 NIL NIL) (-692 1688037 1688568 1689123 "NAGD03" 1689695 T NAGD03 (NIL) -7 NIL NIL) (-691 1679823 1681742 1683687 "NAGD02" 1686112 T NAGD02 (NIL) -7 NIL NIL) (-690 1673682 1675095 1676523 "NAGD01" 1678415 T NAGD01 (NIL) -7 NIL NIL) (-689 1669939 1670749 1671574 "NAGC06" 1672877 T NAGC06 (NIL) -7 NIL NIL) (-688 1668416 1668745 1669098 "NAGC05" 1669606 T NAGC05 (NIL) -7 NIL NIL) (-687 1667800 1667917 1668059 "NAGC02" 1668294 T NAGC02 (NIL) -7 NIL NIL) (-686 1666862 1667419 1667459 "NAALG" 1667538 NIL NAALG (NIL T) -9 NIL 1667599) (-685 1666697 1666726 1666816 "NAALG-" 1666821 NIL NAALG- (NIL T T) -8 NIL NIL) (-684 1660647 1661755 1662942 "MULTSQFR" 1665593 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-683 1659966 1660041 1660225 "MULTFACT" 1660559 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-682 1653160 1657071 1657123 "MTSCAT" 1658183 NIL MTSCAT (NIL T T) -9 NIL 1658697) (-681 1652872 1652926 1653018 "MTHING" 1653100 NIL MTHING (NIL T) -7 NIL NIL) (-680 1652664 1652697 1652757 "MSYSCMD" 1652832 T MSYSCMD (NIL) -7 NIL NIL) (-679 1648776 1651419 1651739 "MSET" 1652377 NIL MSET (NIL T) -8 NIL NIL) (-678 1645872 1648338 1648379 "MSETAGG" 1648384 NIL MSETAGG (NIL T) -9 NIL 1648418) (-677 1641728 1643270 1644011 "MRING" 1645175 NIL MRING (NIL T T) -8 NIL NIL) (-676 1641298 1641365 1641494 "MRF2" 1641655 NIL MRF2 (NIL T T T) -7 NIL NIL) (-675 1640916 1640951 1641095 "MRATFAC" 1641257 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-674 1638528 1638823 1639254 "MPRFF" 1640621 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-673 1632548 1638383 1638479 "MPOLY" 1638484 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-672 1632038 1632073 1632281 "MPCPF" 1632507 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-671 1631554 1631597 1631780 "MPC3" 1631989 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-670 1630755 1630836 1631055 "MPC2" 1631469 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-669 1629056 1629393 1629783 "MONOTOOL" 1630415 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-668 1628181 1628516 1628544 "MONOID" 1628821 T MONOID (NIL) -9 NIL 1628993) (-667 1627559 1627722 1627965 "MONOID-" 1627970 NIL MONOID- (NIL T) -8 NIL NIL) (-666 1618540 1624526 1624585 "MONOGEN" 1625259 NIL MONOGEN (NIL T T) -9 NIL 1625715) (-665 1615758 1616493 1617493 "MONOGEN-" 1617612 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-664 1614618 1615038 1615066 "MONADWU" 1615458 T MONADWU (NIL) -9 NIL 1615696) (-663 1613990 1614149 1614397 "MONADWU-" 1614402 NIL MONADWU- (NIL T) -8 NIL NIL) (-662 1613376 1613594 1613622 "MONAD" 1613829 T MONAD (NIL) -9 NIL 1613941) (-661 1613061 1613139 1613271 "MONAD-" 1613276 NIL MONAD- (NIL T) -8 NIL NIL) (-660 1611312 1611974 1612253 "MOEBIUS" 1612814 NIL MOEBIUS (NIL T) -8 NIL NIL) (-659 1610706 1611084 1611124 "MODULE" 1611129 NIL MODULE (NIL T) -9 NIL 1611155) (-658 1610274 1610370 1610560 "MODULE-" 1610565 NIL MODULE- (NIL T T) -8 NIL NIL) (-657 1607945 1608640 1608966 "MODRING" 1610099 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-656 1604901 1606066 1606583 "MODOP" 1607477 NIL MODOP (NIL T T) -8 NIL NIL) (-655 1603088 1603540 1603881 "MODMONOM" 1604700 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-654 1592767 1601292 1601714 "MODMON" 1602716 NIL MODMON (NIL T T) -8 NIL NIL) (-653 1589893 1591611 1591887 "MODFIELD" 1592642 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-652 1588897 1589174 1589364 "MMLFORM" 1589723 T MMLFORM (NIL) -8 NIL NIL) (-651 1588423 1588466 1588645 "MMAP" 1588848 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-650 1586660 1587437 1587477 "MLO" 1587894 NIL MLO (NIL T) -9 NIL 1588135) (-649 1584027 1584542 1585144 "MLIFT" 1586141 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-648 1583418 1583502 1583656 "MKUCFUNC" 1583938 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-647 1583017 1583087 1583210 "MKRECORD" 1583341 NIL MKRECORD (NIL T T) -7 NIL NIL) (-646 1582065 1582226 1582454 "MKFUNC" 1582828 NIL MKFUNC (NIL T) -7 NIL NIL) (-645 1581453 1581557 1581713 "MKFLCFN" 1581948 NIL MKFLCFN (NIL T) -7 NIL NIL) (-644 1580879 1581246 1581335 "MKCHSET" 1581397 NIL MKCHSET (NIL T) -8 NIL NIL) (-643 1580156 1580258 1580443 "MKBCFUNC" 1580772 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-642 1576840 1579710 1579846 "MINT" 1580040 T MINT (NIL) -8 NIL NIL) (-641 1575652 1575895 1576172 "MHROWRED" 1576595 NIL MHROWRED (NIL T) -7 NIL NIL) (-640 1570923 1574097 1574521 "MFLOAT" 1575248 T MFLOAT (NIL) -8 NIL NIL) (-639 1570280 1570356 1570527 "MFINFACT" 1570835 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-638 1566595 1567443 1568327 "MESH" 1569416 T MESH (NIL) -7 NIL NIL) (-637 1564985 1565297 1565650 "MDDFACT" 1566282 NIL MDDFACT (NIL T) -7 NIL NIL) (-636 1561828 1564145 1564186 "MDAGG" 1564441 NIL MDAGG (NIL T) -9 NIL 1564584) (-635 1551526 1561121 1561328 "MCMPLX" 1561641 T MCMPLX (NIL) -8 NIL NIL) (-634 1550667 1550813 1551013 "MCDEN" 1551375 NIL MCDEN (NIL T T) -7 NIL NIL) (-633 1548557 1548827 1549207 "MCALCFN" 1550397 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-632 1546179 1546702 1547263 "MATSTOR" 1548028 NIL MATSTOR (NIL T) -7 NIL NIL) (-631 1542188 1545554 1545801 "MATRIX" 1545964 NIL MATRIX (NIL T) -8 NIL NIL) (-630 1537957 1538661 1539397 "MATLIN" 1541545 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-629 1528155 1531293 1531369 "MATCAT" 1536207 NIL MATCAT (NIL T T T) -9 NIL 1537624) (-628 1524520 1525533 1526888 "MATCAT-" 1526893 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-627 1523122 1523275 1523606 "MATCAT2" 1524355 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-626 1521234 1521558 1521942 "MAPPKG3" 1522797 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-625 1520215 1520388 1520610 "MAPPKG2" 1521058 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-624 1518714 1518998 1519325 "MAPPKG1" 1519921 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-623 1518325 1518383 1518506 "MAPHACK3" 1518650 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-622 1517917 1517978 1518092 "MAPHACK2" 1518257 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-621 1517355 1517458 1517600 "MAPHACK1" 1517808 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-620 1515463 1516057 1516360 "MAGMA" 1517084 NIL MAGMA (NIL T) -8 NIL NIL) (-619 1511937 1513707 1514167 "M3D" 1515036 NIL M3D (NIL T) -8 NIL NIL) (-618 1506093 1510308 1510349 "LZSTAGG" 1511131 NIL LZSTAGG (NIL T) -9 NIL 1511426) (-617 1502066 1503224 1504681 "LZSTAGG-" 1504686 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-616 1499182 1499959 1500445 "LWORD" 1501612 NIL LWORD (NIL T) -8 NIL NIL) (-615 1492342 1498953 1499087 "LSQM" 1499092 NIL LSQM (NIL NIL T) -8 NIL NIL) (-614 1491566 1491705 1491933 "LSPP" 1492197 NIL LSPP (NIL T T T T) -7 NIL NIL) (-613 1489378 1489679 1490135 "LSMP" 1491255 NIL LSMP (NIL T T T T) -7 NIL NIL) (-612 1486157 1486831 1487561 "LSMP1" 1488680 NIL LSMP1 (NIL T) -7 NIL NIL) (-611 1480084 1485326 1485367 "LSAGG" 1485429 NIL LSAGG (NIL T) -9 NIL 1485507) (-610 1476779 1477703 1478916 "LSAGG-" 1478921 NIL LSAGG- (NIL T T) -8 NIL NIL) (-609 1474405 1475923 1476172 "LPOLY" 1476574 NIL LPOLY (NIL T T) -8 NIL NIL) (-608 1473987 1474072 1474195 "LPEFRAC" 1474314 NIL LPEFRAC (NIL T) -7 NIL NIL) (-607 1472334 1473081 1473334 "LO" 1473819 NIL LO (NIL T T T) -8 NIL NIL) (-606 1471988 1472100 1472128 "LOGIC" 1472239 T LOGIC (NIL) -9 NIL 1472319) (-605 1471850 1471873 1471944 "LOGIC-" 1471949 NIL LOGIC- (NIL T) -8 NIL NIL) (-604 1471043 1471183 1471376 "LODOOPS" 1471706 NIL LODOOPS (NIL T T) -7 NIL NIL) (-603 1468461 1470960 1471025 "LODO" 1471030 NIL LODO (NIL T NIL) -8 NIL NIL) (-602 1467007 1467242 1467593 "LODOF" 1468208 NIL LODOF (NIL T T) -7 NIL NIL) (-601 1463427 1465863 1465903 "LODOCAT" 1466335 NIL LODOCAT (NIL T) -9 NIL 1466546) (-600 1463161 1463219 1463345 "LODOCAT-" 1463350 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-599 1460475 1463002 1463120 "LODO2" 1463125 NIL LODO2 (NIL T T) -8 NIL NIL) (-598 1457904 1460412 1460457 "LODO1" 1460462 NIL LODO1 (NIL T) -8 NIL NIL) (-597 1456767 1456932 1457243 "LODEEF" 1457727 NIL LODEEF (NIL T T T) -7 NIL NIL) (-596 1452054 1454898 1454939 "LNAGG" 1455886 NIL LNAGG (NIL T) -9 NIL 1456330) (-595 1451201 1451415 1451757 "LNAGG-" 1451762 NIL LNAGG- (NIL T T) -8 NIL NIL) (-594 1447366 1448128 1448766 "LMOPS" 1450617 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-593 1446764 1447126 1447166 "LMODULE" 1447226 NIL LMODULE (NIL T) -9 NIL 1447268) (-592 1444010 1446409 1446532 "LMDICT" 1446674 NIL LMDICT (NIL T) -8 NIL NIL) (-591 1437237 1442956 1443254 "LIST" 1443745 NIL LIST (NIL T) -8 NIL NIL) (-590 1436762 1436836 1436975 "LIST3" 1437157 NIL LIST3 (NIL T T T) -7 NIL NIL) (-589 1435769 1435947 1436175 "LIST2" 1436580 NIL LIST2 (NIL T T) -7 NIL NIL) (-588 1433903 1434215 1434614 "LIST2MAP" 1435416 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-587 1432616 1433296 1433336 "LINEXP" 1433589 NIL LINEXP (NIL T) -9 NIL 1433737) (-586 1431263 1431523 1431820 "LINDEP" 1432368 NIL LINDEP (NIL T T) -7 NIL NIL) (-585 1428030 1428749 1429526 "LIMITRF" 1430518 NIL LIMITRF (NIL T) -7 NIL NIL) (-584 1426310 1426605 1427020 "LIMITPS" 1427725 NIL LIMITPS (NIL T T) -7 NIL NIL) (-583 1420765 1425821 1426049 "LIE" 1426131 NIL LIE (NIL T T) -8 NIL NIL) (-582 1419816 1420259 1420299 "LIECAT" 1420439 NIL LIECAT (NIL T) -9 NIL 1420590) (-581 1419657 1419684 1419772 "LIECAT-" 1419777 NIL LIECAT- (NIL T T) -8 NIL NIL) (-580 1412269 1419106 1419271 "LIB" 1419512 T LIB (NIL) -8 NIL NIL) (-579 1407906 1408787 1409722 "LGROBP" 1411386 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-578 1405772 1406046 1406408 "LF" 1407627 NIL LF (NIL T T) -7 NIL NIL) (-577 1404612 1405304 1405332 "LFCAT" 1405539 T LFCAT (NIL) -9 NIL 1405678) (-576 1401524 1402150 1402836 "LEXTRIPK" 1403978 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-575 1398230 1399094 1399597 "LEXP" 1401104 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-574 1396628 1396941 1397342 "LEADCDET" 1397912 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-573 1395824 1395898 1396125 "LAZM3PK" 1396549 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-572 1390741 1393903 1394440 "LAUPOL" 1395337 NIL LAUPOL (NIL T T) -8 NIL NIL) (-571 1390308 1390352 1390519 "LAPLACE" 1390691 NIL LAPLACE (NIL T T) -7 NIL NIL) (-570 1388236 1389409 1389660 "LA" 1390141 NIL LA (NIL T T T) -8 NIL NIL) (-569 1387299 1387893 1387933 "LALG" 1387994 NIL LALG (NIL T) -9 NIL 1388052) (-568 1387014 1387073 1387208 "LALG-" 1387213 NIL LALG- (NIL T T) -8 NIL NIL) (-567 1385924 1386111 1386408 "KOVACIC" 1386814 NIL KOVACIC (NIL T T) -7 NIL NIL) (-566 1385759 1385783 1385824 "KONVERT" 1385886 NIL KONVERT (NIL T) -9 NIL NIL) (-565 1385594 1385618 1385659 "KOERCE" 1385721 NIL KOERCE (NIL T) -9 NIL NIL) (-564 1383328 1384088 1384481 "KERNEL" 1385233 NIL KERNEL (NIL T) -8 NIL NIL) (-563 1382830 1382911 1383041 "KERNEL2" 1383242 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-562 1376682 1381370 1381424 "KDAGG" 1381801 NIL KDAGG (NIL T T) -9 NIL 1382007) (-561 1376211 1376335 1376540 "KDAGG-" 1376545 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-560 1369386 1375872 1376027 "KAFILE" 1376089 NIL KAFILE (NIL T) -8 NIL NIL) (-559 1363841 1368897 1369125 "JORDAN" 1369207 NIL JORDAN (NIL T T) -8 NIL NIL) (-558 1360141 1362047 1362101 "IXAGG" 1363030 NIL IXAGG (NIL T T) -9 NIL 1363489) (-557 1359060 1359366 1359785 "IXAGG-" 1359790 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1354645 1358982 1359041 "IVECTOR" 1359046 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1353411 1353648 1353914 "ITUPLE" 1354412 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1351847 1352024 1352330 "ITRIGMNP" 1353233 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1350592 1350796 1351079 "ITFUN3" 1351623 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1350224 1350281 1350390 "ITFUN2" 1350529 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1348026 1349097 1349394 "ITAYLOR" 1349959 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1337014 1342212 1343371 "ISUPS" 1346899 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1336118 1336258 1336494 "ISUMP" 1336861 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1331382 1335919 1335998 "ISTRING" 1336071 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1330595 1330676 1330891 "IRURPK" 1331296 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1329531 1329732 1329972 "IRSN" 1330375 T IRSN (NIL) -7 NIL NIL) (-545 1327566 1327921 1328356 "IRRF2F" 1329169 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1327313 1327351 1327427 "IRREDFFX" 1327522 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1325928 1326187 1326486 "IROOT" 1327046 NIL IROOT (NIL T) -7 NIL NIL) (-542 1322566 1323617 1324307 "IR" 1325270 NIL IR (NIL T) -8 NIL NIL) (-541 1320179 1320674 1321240 "IR2" 1322044 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1319255 1319368 1319588 "IR2F" 1320062 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1319046 1319080 1319140 "IPRNTPK" 1319215 T IPRNTPK (NIL) -7 NIL NIL) (-538 1315600 1318935 1319004 "IPF" 1319009 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1313917 1315525 1315582 "IPADIC" 1315587 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1313416 1313474 1313663 "INVLAPLA" 1313853 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1303065 1305418 1307804 "INTTR" 1311080 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1299413 1300154 1301017 "INTTOOLS" 1302251 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1298999 1299090 1299207 "INTSLPE" 1299316 T INTSLPE (NIL) -7 NIL NIL) (-532 1296949 1298922 1298981 "INTRVL" 1298986 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1294556 1295068 1295642 "INTRF" 1296434 NIL INTRF (NIL T) -7 NIL NIL) (-530 1293971 1294068 1294209 "INTRET" 1294454 NIL INTRET (NIL T) -7 NIL NIL) (-529 1291973 1292362 1292831 "INTRAT" 1293579 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1289206 1289789 1290414 "INTPM" 1291458 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1285915 1286514 1287258 "INTPAF" 1288592 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1281158 1282104 1283139 "INTPACK" 1284900 T INTPACK (NIL) -7 NIL NIL) (-525 1278012 1280887 1281014 "INT" 1281051 T INT (NIL) -8 NIL NIL) (-524 1277264 1277416 1277624 "INTHERTR" 1277854 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1276703 1276783 1276971 "INTHERAL" 1277178 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1274549 1274992 1275449 "INTHEORY" 1276266 T INTHEORY (NIL) -7 NIL NIL) (-521 1265871 1267492 1269270 "INTG0" 1272901 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1246444 1251234 1256044 "INTFTBL" 1261081 T INTFTBL (NIL) -8 NIL NIL) (-519 1245693 1245831 1246004 "INTFACT" 1246303 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1243084 1243530 1244093 "INTEF" 1245247 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1241546 1242295 1242323 "INTDOM" 1242624 T INTDOM (NIL) -9 NIL 1242831) (-516 1240915 1241089 1241331 "INTDOM-" 1241336 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1237408 1239340 1239394 "INTCAT" 1240193 NIL INTCAT (NIL T) -9 NIL 1240512) (-514 1236881 1236983 1237111 "INTBIT" 1237300 T INTBIT (NIL) -7 NIL NIL) (-513 1235556 1235710 1236023 "INTALG" 1236726 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1235013 1235103 1235273 "INTAF" 1235460 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1228467 1234823 1234963 "INTABL" 1234968 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1223418 1226147 1226175 "INS" 1227143 T INS (NIL) -9 NIL 1227824) (-509 1220658 1221429 1222403 "INS-" 1222476 NIL INS- (NIL T) -8 NIL NIL) (-508 1219437 1219664 1219961 "INPSIGN" 1220411 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1218555 1218672 1218869 "INPRODPF" 1219317 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1217449 1217566 1217803 "INPRODFF" 1218435 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1216449 1216601 1216861 "INNMFACT" 1217285 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1215646 1215743 1215931 "INMODGCD" 1216348 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1214155 1214399 1214723 "INFSP" 1215391 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1213339 1213456 1213639 "INFPROD0" 1214035 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1210349 1211508 1211999 "INFORM" 1212856 T INFORM (NIL) -8 NIL NIL) (-500 1209959 1210019 1210117 "INFORM1" 1210284 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1209482 1209571 1209685 "INFINITY" 1209865 T INFINITY (NIL) -7 NIL NIL) (-498 1208099 1208348 1208669 "INEP" 1209230 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1207375 1207996 1208061 "INDE" 1208066 NIL INDE (NIL T) -8 NIL NIL) (-496 1206939 1207007 1207124 "INCRMAPS" 1207302 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1202250 1203175 1204119 "INBFF" 1206027 NIL INBFF (NIL T) -7 NIL NIL) (-494 1198745 1202095 1202198 "IMATRIX" 1202203 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1197457 1197580 1197895 "IMATQF" 1198601 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1195677 1195904 1196241 "IMATLIN" 1197213 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1190303 1195601 1195659 "ILIST" 1195664 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1188256 1190163 1190276 "IIARRAY2" 1190281 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1183624 1188167 1188231 "IFF" 1188236 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1178667 1182916 1183104 "IFARRAY" 1183481 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1177874 1178571 1178644 "IFAMON" 1178649 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1177458 1177523 1177577 "IEVALAB" 1177784 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1177133 1177201 1177361 "IEVALAB-" 1177366 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1176791 1177047 1177110 "IDPO" 1177115 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1176068 1176680 1176755 "IDPOAMS" 1176760 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1175402 1175957 1176032 "IDPOAM" 1176037 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1174488 1174738 1174791 "IDPC" 1175204 NIL IDPC (NIL T T) -9 NIL 1175353) (-480 1173984 1174380 1174453 "IDPAM" 1174458 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1173387 1173876 1173949 "IDPAG" 1173954 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1169642 1170490 1171385 "IDECOMP" 1172544 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1162515 1163565 1164612 "IDEAL" 1168678 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1161679 1161791 1161990 "ICDEN" 1162399 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1160778 1161159 1161306 "ICARD" 1161552 T ICARD (NIL) -8 NIL NIL) (-474 1158850 1159163 1159566 "IBPTOOLS" 1160455 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1154464 1158470 1158583 "IBITS" 1158769 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1151187 1151763 1152458 "IBATOOL" 1153881 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1148967 1149428 1149961 "IBACHIN" 1150722 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1146844 1148813 1148916 "IARRAY2" 1148921 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1142997 1146770 1146827 "IARRAY1" 1146832 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1136935 1141415 1141893 "IAN" 1142539 T IAN (NIL) -8 NIL NIL) (-467 1136446 1136503 1136676 "IALGFACT" 1136872 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1135974 1136087 1136115 "HYPCAT" 1136322 T HYPCAT (NIL) -9 NIL NIL) (-465 1135512 1135629 1135815 "HYPCAT-" 1135820 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1132192 1133523 1133564 "HOAGG" 1134545 NIL HOAGG (NIL T) -9 NIL 1135224) (-463 1130786 1131185 1131711 "HOAGG-" 1131716 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1124616 1130227 1130393 "HEXADEC" 1130640 T HEXADEC (NIL) -8 NIL NIL) (-461 1123364 1123586 1123849 "HEUGCD" 1124393 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1122467 1123201 1123331 "HELLFDIV" 1123336 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1120695 1122244 1122332 "HEAP" 1122411 NIL HEAP (NIL T) -8 NIL NIL) (-458 1114562 1120610 1120672 "HDP" 1120677 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1108274 1114199 1114350 "HDMP" 1114463 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1107599 1107738 1107902 "HB" 1108130 T HB (NIL) -7 NIL NIL) (-455 1101096 1107445 1107549 "HASHTBL" 1107554 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1098849 1100724 1100903 "HACKPI" 1100937 T HACKPI (NIL) -8 NIL NIL) (-453 1094545 1098703 1098815 "GTSET" 1098820 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1088071 1094423 1094521 "GSTBL" 1094526 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1080304 1087107 1087371 "GSERIES" 1087862 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1079327 1079780 1079808 "GROUP" 1080069 T GROUP (NIL) -9 NIL 1080228) (-449 1078443 1078666 1079010 "GROUP-" 1079015 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1076812 1077131 1077518 "GROEBSOL" 1078120 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1075753 1076015 1076066 "GRMOD" 1076595 NIL GRMOD (NIL T T) -9 NIL 1076763) (-446 1075521 1075557 1075685 "GRMOD-" 1075690 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1070847 1071875 1072875 "GRIMAGE" 1074541 T GRIMAGE (NIL) -8 NIL NIL) (-444 1069314 1069574 1069898 "GRDEF" 1070543 T GRDEF (NIL) -7 NIL NIL) (-443 1068758 1068874 1069015 "GRAY" 1069193 T GRAY (NIL) -7 NIL NIL) (-442 1067992 1068372 1068423 "GRALG" 1068576 NIL GRALG (NIL T T) -9 NIL 1068668) (-441 1067653 1067726 1067889 "GRALG-" 1067894 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1064461 1067242 1067418 "GPOLSET" 1067560 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1063817 1063874 1064131 "GOSPER" 1064398 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1059576 1060255 1060781 "GMODPOL" 1063516 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1058581 1058765 1059003 "GHENSEL" 1059388 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1052647 1053490 1054516 "GENUPS" 1057665 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1052344 1052395 1052484 "GENUFACT" 1052590 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1051756 1051833 1051998 "GENPGCD" 1052262 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1051230 1051265 1051478 "GENMFACT" 1051715 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1049798 1050053 1050360 "GENEEZ" 1050973 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1043672 1049411 1049572 "GDMP" 1049721 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1033052 1037443 1038549 "GCNAALG" 1042655 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1031474 1032346 1032374 "GCDDOM" 1032629 T GCDDOM (NIL) -9 NIL 1032786) (-428 1030944 1031071 1031286 "GCDDOM-" 1031291 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1029616 1029801 1030105 "GB" 1030723 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1018236 1020562 1022954 "GBINTERN" 1027307 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1016073 1016365 1016786 "GBF" 1017911 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1014854 1015019 1015286 "GBEUCLID" 1015889 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1014203 1014328 1014477 "GAUSSFAC" 1014725 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1012580 1012882 1013195 "GALUTIL" 1013922 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1010897 1011171 1011494 "GALPOLYU" 1012307 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1008286 1008576 1008981 "GALFACTU" 1010594 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1000092 1001591 1003199 "GALFACT" 1006718 NIL GALFACT (NIL T) -7 NIL NIL) (-418 997480 998138 998166 "FVFUN" 999322 T FVFUN (NIL) -9 NIL 1000042) (-417 996746 996928 996956 "FVC" 997247 T FVC (NIL) -9 NIL 997430) (-416 996388 996543 996624 "FUNCTION" 996698 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 994058 994609 995098 "FT" 995919 T FT (NIL) -8 NIL NIL) (-414 992876 993359 993562 "FTEM" 993875 T FTEM (NIL) -8 NIL NIL) (-413 991141 991429 991831 "FSUPFACT" 992568 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 989538 989827 990159 "FST" 990829 T FST (NIL) -8 NIL NIL) (-411 988713 988819 989013 "FSRED" 989420 NIL FSRED (NIL T T) -7 NIL NIL) (-410 987392 987647 988001 "FSPRMELT" 988428 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 984477 984915 985414 "FSPECF" 986955 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 966851 975408 975448 "FS" 979286 NIL FS (NIL T) -9 NIL 981568) (-407 955501 958491 962547 "FS-" 962844 NIL FS- (NIL T T) -8 NIL NIL) (-406 955017 955071 955247 "FSINT" 955442 NIL FSINT (NIL T T) -7 NIL NIL) (-405 953298 954010 954313 "FSERIES" 954796 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 952316 952432 952662 "FSCINT" 953178 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 948551 951261 951302 "FSAGG" 951672 NIL FSAGG (NIL T) -9 NIL 951931) (-402 946313 946914 947710 "FSAGG-" 947805 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 945355 945498 945725 "FSAGG2" 946166 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 943014 943293 943846 "FS2UPS" 945073 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 942600 942643 942796 "FS2" 942965 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 941460 941631 941939 "FS2EXPXP" 942425 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 940886 941001 941153 "FRUTIL" 941340 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 932306 936385 937741 "FR" 939562 NIL FR (NIL T) -8 NIL NIL) (-395 927383 930026 930066 "FRNAALG" 931462 NIL FRNAALG (NIL T) -9 NIL 932069) (-394 923061 924132 925407 "FRNAALG-" 926157 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 922699 922742 922869 "FRNAAF2" 923012 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 921064 921556 921850 "FRMOD" 922512 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 918786 919455 919771 "FRIDEAL" 920855 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 917985 918072 918359 "FRIDEAL2" 918693 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 917243 917651 917692 "FRETRCT" 917697 NIL FRETRCT (NIL T) -9 NIL 917868) (-388 916355 916586 916937 "FRETRCT-" 916942 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 913565 914785 914844 "FRAMALG" 915726 NIL FRAMALG (NIL T T) -9 NIL 916018) (-386 911698 912154 912784 "FRAMALG-" 913007 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 905600 911173 911449 "FRAC" 911454 NIL FRAC (NIL T) -8 NIL NIL) (-384 905236 905293 905400 "FRAC2" 905537 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 904872 904929 905036 "FR2" 905173 NIL FR2 (NIL T T) -7 NIL NIL) (-382 899546 902459 902487 "FPS" 903606 T FPS (NIL) -9 NIL 904162) (-381 898995 899104 899268 "FPS-" 899414 NIL FPS- (NIL T) -8 NIL NIL) (-380 896444 898141 898169 "FPC" 898394 T FPC (NIL) -9 NIL 898536) (-379 896237 896277 896374 "FPC-" 896379 NIL FPC- (NIL T) -8 NIL NIL) (-378 895116 895726 895767 "FPATMAB" 895772 NIL FPATMAB (NIL T) -9 NIL 895924) (-377 892816 893292 893718 "FPARFRAC" 894753 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 888209 888708 889390 "FORTRAN" 892248 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 885925 886425 886964 "FORT" 887690 T FORT (NIL) -7 NIL NIL) (-374 883601 884163 884191 "FORTFN" 885251 T FORTFN (NIL) -9 NIL 885875) (-373 883365 883415 883443 "FORTCAT" 883502 T FORTCAT (NIL) -9 NIL 883564) (-372 881425 881908 882307 "FORMULA" 882986 T FORMULA (NIL) -8 NIL NIL) (-371 881213 881243 881312 "FORMULA1" 881389 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 880736 880788 880961 "FORDER" 881155 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 879832 879996 880189 "FOP" 880563 T FOP (NIL) -7 NIL NIL) (-368 878440 879112 879286 "FNLA" 879714 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 877109 877498 877526 "FNCAT" 878098 T FNCAT (NIL) -9 NIL 878391) (-366 876675 877068 877096 "FNAME" 877101 T FNAME (NIL) -8 NIL NIL) (-365 875335 876308 876336 "FMTC" 876341 T FMTC (NIL) -9 NIL 876376) (-364 871653 872860 873488 "FMONOID" 874740 NIL FMONOID (NIL T) -8 NIL NIL) (-363 870873 871396 871544 "FM" 871549 NIL FM (NIL T T) -8 NIL NIL) (-362 868297 868943 868971 "FMFUN" 870115 T FMFUN (NIL) -9 NIL 870823) (-361 867566 867747 867775 "FMC" 868065 T FMC (NIL) -9 NIL 868247) (-360 864796 865630 865683 "FMCAT" 866865 NIL FMCAT (NIL T T) -9 NIL 867359) (-359 863691 864564 864663 "FM1" 864741 NIL FM1 (NIL T T) -8 NIL NIL) (-358 861465 861881 862375 "FLOATRP" 863242 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 854951 859121 859751 "FLOAT" 860855 T FLOAT (NIL) -8 NIL NIL) (-356 852389 852889 853467 "FLOATCP" 854418 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 851178 852026 852066 "FLINEXP" 852071 NIL FLINEXP (NIL T) -9 NIL 852164) (-354 850333 850568 850895 "FLINEXP-" 850900 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 849409 849553 849777 "FLASORT" 850185 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 846628 847470 847522 "FLALG" 848749 NIL FLALG (NIL T T) -9 NIL 849216) (-351 840413 844115 844156 "FLAGG" 845418 NIL FLAGG (NIL T) -9 NIL 846070) (-350 839139 839478 839968 "FLAGG-" 839973 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 838181 838324 838551 "FLAGG2" 838992 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 835154 836172 836231 "FINRALG" 837359 NIL FINRALG (NIL T T) -9 NIL 837867) (-347 834314 834543 834882 "FINRALG-" 834887 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 833721 833934 833962 "FINITE" 834158 T FINITE (NIL) -9 NIL 834265) (-345 826181 828342 828382 "FINAALG" 832049 NIL FINAALG (NIL T) -9 NIL 833502) (-344 821522 822563 823707 "FINAALG-" 825086 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 820917 821277 821380 "FILE" 821452 NIL FILE (NIL T) -8 NIL NIL) (-342 819602 819914 819968 "FILECAT" 820652 NIL FILECAT (NIL T T) -9 NIL 820868) (-341 817465 819021 819049 "FIELD" 819089 T FIELD (NIL) -9 NIL 819169) (-340 816085 816470 816981 "FIELD-" 816986 NIL FIELD- (NIL T) -8 NIL NIL) (-339 813900 814722 815068 "FGROUP" 815772 NIL FGROUP (NIL T) -8 NIL NIL) (-338 812990 813154 813374 "FGLMICPK" 813732 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 808792 812915 812972 "FFX" 812977 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 808393 808454 808589 "FFSLPE" 808725 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 804386 805165 805961 "FFPOLY" 807629 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 803890 803926 804135 "FFPOLY2" 804344 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 799711 803809 803872 "FFP" 803877 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 795079 799622 799686 "FF" 799691 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 790175 794422 794612 "FFNBX" 794933 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 785084 789310 789568 "FFNBP" 790029 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 779687 784368 784579 "FFNB" 784917 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 778519 778717 779032 "FFINTBAS" 779484 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 774743 776983 777011 "FFIELDC" 777631 T FFIELDC (NIL) -9 NIL 778007) (-326 773406 773776 774273 "FFIELDC-" 774278 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 772976 773021 773145 "FFHOM" 773348 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 770674 771158 771675 "FFF" 772491 NIL FFF (NIL T) -7 NIL NIL) (-323 766262 770416 770517 "FFCGX" 770617 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 761864 765994 766101 "FFCGP" 766205 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 757017 761591 761699 "FFCG" 761800 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 738963 748086 748172 "FFCAT" 753337 NIL FFCAT (NIL T T T) -9 NIL 754824) (-319 734161 735208 736522 "FFCAT-" 737752 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 733572 733615 733850 "FFCAT2" 734112 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 722772 726562 727779 "FEXPR" 732427 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 721772 722207 722248 "FEVALAB" 722332 NIL FEVALAB (NIL T) -9 NIL 722593) (-315 720931 721141 721479 "FEVALAB-" 721484 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 719524 720314 720517 "FDIV" 720830 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 716591 717306 717421 "FDIVCAT" 718989 NIL FDIVCAT (NIL T T T T) -9 NIL 719426) (-312 716353 716380 716550 "FDIVCAT-" 716555 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 715573 715660 715937 "FDIV2" 716260 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 714259 714518 714807 "FCPAK1" 715304 T FCPAK1 (NIL) -7 NIL NIL) (-309 713387 713759 713900 "FCOMP" 714150 NIL FCOMP (NIL T) -8 NIL NIL) (-308 697022 700436 703997 "FC" 709846 T FC (NIL) -8 NIL NIL) (-307 689618 693664 693704 "FAXF" 695506 NIL FAXF (NIL T) -9 NIL 696197) (-306 686897 687552 688377 "FAXF-" 688842 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 681997 686273 686449 "FARRAY" 686754 NIL FARRAY (NIL T) -8 NIL NIL) (-304 677388 679459 679511 "FAMR" 680523 NIL FAMR (NIL T T) -9 NIL 680983) (-303 676279 676581 677015 "FAMR-" 677020 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 675475 676201 676254 "FAMONOID" 676259 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 673308 673992 674045 "FAMONC" 674986 NIL FAMONC (NIL T T) -9 NIL 675371) (-300 672000 673062 673199 "FAGROUP" 673204 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 669803 670122 670524 "FACUTIL" 671681 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 668902 669087 669309 "FACTFUNC" 669613 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 661222 668153 668365 "EXPUPXS" 668758 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 658705 659245 659831 "EXPRTUBE" 660656 T EXPRTUBE (NIL) -7 NIL NIL) (-295 654899 655491 656228 "EXPRODE" 658044 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 640058 653558 653984 "EXPR" 654505 NIL EXPR (NIL T) -8 NIL NIL) (-293 634486 635073 635885 "EXPR2UPS" 639356 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 634122 634179 634286 "EXPR2" 634423 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 625476 633259 633554 "EXPEXPAN" 633960 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 625303 625433 625462 "EXIT" 625467 T EXIT (NIL) -8 NIL NIL) (-289 624930 624992 625105 "EVALCYC" 625235 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 624471 624589 624630 "EVALAB" 624800 NIL EVALAB (NIL T) -9 NIL 624904) (-287 623952 624074 624295 "EVALAB-" 624300 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 621415 622727 622755 "EUCDOM" 623310 T EUCDOM (NIL) -9 NIL 623660) (-285 619820 620262 620852 "EUCDOM-" 620857 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 607398 610146 612886 "ESTOOLS" 617100 T ESTOOLS (NIL) -7 NIL NIL) (-283 607034 607091 607198 "ESTOOLS2" 607335 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 606785 606827 606907 "ESTOOLS1" 606986 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 600723 602447 602475 "ES" 605239 T ES (NIL) -9 NIL 606645) (-280 595670 596957 598774 "ES-" 598938 NIL ES- (NIL T) -8 NIL NIL) (-279 592045 592805 593585 "ESCONT" 594910 T ESCONT (NIL) -7 NIL NIL) (-278 591790 591822 591904 "ESCONT1" 592007 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 591465 591515 591615 "ES2" 591734 NIL ES2 (NIL T T) -7 NIL NIL) (-276 591095 591153 591262 "ES1" 591401 NIL ES1 (NIL T T) -7 NIL NIL) (-275 590311 590440 590616 "ERROR" 590939 T ERROR (NIL) -7 NIL NIL) (-274 583814 590170 590261 "EQTBL" 590266 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 576251 579132 580579 "EQ" 582400 NIL -2639 (NIL T) -8 NIL NIL) (-272 575883 575940 576049 "EQ2" 576188 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 571175 572221 573314 "EP" 574822 NIL EP (NIL T) -7 NIL NIL) (-270 569758 570058 570375 "ENV" 570878 T ENV (NIL) -8 NIL NIL) (-269 568918 569482 569510 "ENTIRER" 569515 T ENTIRER (NIL) -9 NIL 569560) (-268 565374 566873 567243 "EMR" 568717 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 564518 564703 564757 "ELTAGG" 565137 NIL ELTAGG (NIL T T) -9 NIL 565348) (-266 564237 564299 564440 "ELTAGG-" 564445 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 564026 564055 564109 "ELTAB" 564193 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 563152 563298 563497 "ELFUTS" 563877 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 562894 562950 562978 "ELEMFUN" 563083 T ELEMFUN (NIL) -9 NIL NIL) (-262 562764 562785 562853 "ELEMFUN-" 562858 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 557656 560865 560906 "ELAGG" 561846 NIL ELAGG (NIL T) -9 NIL 562309) (-260 555941 556375 557038 "ELAGG-" 557043 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 554598 554878 555173 "ELABEXPR" 555666 T ELABEXPR (NIL) -8 NIL NIL) (-258 547466 549265 550092 "EFUPXS" 553874 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 540916 542717 543527 "EFULS" 546742 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 538347 538705 539183 "EFSTRUC" 540548 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 527419 528984 530544 "EF" 536862 NIL EF (NIL T T) -7 NIL NIL) (-254 526520 526904 527053 "EAB" 527290 T EAB (NIL) -8 NIL NIL) (-253 525733 526479 526507 "E04UCFA" 526512 T E04UCFA (NIL) -8 NIL NIL) (-252 524946 525692 525720 "E04NAFA" 525725 T E04NAFA (NIL) -8 NIL NIL) (-251 524159 524905 524933 "E04MBFA" 524938 T E04MBFA (NIL) -8 NIL NIL) (-250 523372 524118 524146 "E04JAFA" 524151 T E04JAFA (NIL) -8 NIL NIL) (-249 522587 523331 523359 "E04GCFA" 523364 T E04GCFA (NIL) -8 NIL NIL) (-248 521802 522546 522574 "E04FDFA" 522579 T E04FDFA (NIL) -8 NIL NIL) (-247 521015 521761 521789 "E04DGFA" 521794 T E04DGFA (NIL) -8 NIL NIL) (-246 515200 516545 517907 "E04AGNT" 519673 T E04AGNT (NIL) -7 NIL NIL) (-245 513927 514407 514447 "DVARCAT" 514922 NIL DVARCAT (NIL T) -9 NIL 515120) (-244 513131 513343 513657 "DVARCAT-" 513662 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 505993 512933 513060 "DSMP" 513065 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 500803 501938 503006 "DROPT" 504945 T DROPT (NIL) -8 NIL NIL) (-241 500468 500527 500625 "DROPT1" 500738 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 495583 496709 497846 "DROPT0" 499351 T DROPT0 (NIL) -7 NIL NIL) (-239 493928 494253 494639 "DRAWPT" 495217 T DRAWPT (NIL) -7 NIL NIL) (-238 488515 489438 490517 "DRAW" 492902 NIL DRAW (NIL T) -7 NIL NIL) (-237 488148 488201 488319 "DRAWHACK" 488456 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 486879 487148 487439 "DRAWCX" 487877 T DRAWCX (NIL) -7 NIL NIL) (-235 486397 486465 486615 "DRAWCURV" 486805 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 476868 478827 480942 "DRAWCFUN" 484302 T DRAWCFUN (NIL) -7 NIL NIL) (-233 473682 475564 475605 "DQAGG" 476234 NIL DQAGG (NIL T) -9 NIL 476507) (-232 462189 468927 469009 "DPOLCAT" 470847 NIL DPOLCAT (NIL T T T T) -9 NIL 471391) (-231 457029 458375 460332 "DPOLCAT-" 460337 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 451113 456891 456988 "DPMO" 456993 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445100 450894 451060 "DPMM" 451065 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 444613 444711 444831 "DOMAIN" 445000 T DOMAIN (NIL) -8 NIL NIL) (-227 438325 444250 444401 "DMP" 444514 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 437925 437981 438125 "DLP" 438263 NIL DLP (NIL T) -7 NIL NIL) (-225 431569 437026 437253 "DLIST" 437730 NIL DLIST (NIL T) -8 NIL NIL) (-224 428416 430425 430466 "DLAGG" 431016 NIL DLAGG (NIL T) -9 NIL 431245) (-223 427126 427818 427846 "DIVRING" 427996 T DIVRING (NIL) -9 NIL 428104) (-222 426114 426367 426760 "DIVRING-" 426765 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424216 424573 424979 "DISPLAY" 425728 T DISPLAY (NIL) -7 NIL NIL) (-220 418105 424130 424193 "DIRPROD" 424198 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 416953 417156 417421 "DIRPROD2" 417898 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 406584 412589 412642 "DIRPCAT" 413050 NIL DIRPCAT (NIL NIL T) -9 NIL 413877) (-217 403910 404552 405433 "DIRPCAT-" 405770 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403197 403357 403543 "DIOSP" 403744 T DIOSP (NIL) -7 NIL NIL) (-215 399900 402110 402151 "DIOPS" 402585 NIL DIOPS (NIL T) -9 NIL 402814) (-214 399449 399563 399754 "DIOPS-" 399759 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398321 398959 398987 "DIFRING" 399174 T DIFRING (NIL) -9 NIL 399283) (-212 397967 398044 398196 "DIFRING-" 398201 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 395757 397039 397079 "DIFEXT" 397438 NIL DIFEXT (NIL T) -9 NIL 397731) (-210 394043 394471 395136 "DIFEXT-" 395141 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391366 393576 393617 "DIAGG" 393622 NIL DIAGG (NIL T) -9 NIL 393642) (-208 390750 390907 391159 "DIAGG-" 391164 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386215 389709 389986 "DHMATRIX" 390519 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 381827 382736 383746 "DFSFUN" 385225 T DFSFUN (NIL) -7 NIL NIL) (-205 376613 380541 380906 "DFLOAT" 381482 T DFLOAT (NIL) -8 NIL NIL) (-204 374846 375127 375522 "DFINTTLS" 376321 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 371879 372881 373279 "DERHAM" 374513 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 369728 371654 371743 "DEQUEUE" 371823 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 368946 369079 369274 "DEGRED" 369590 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365346 366091 366943 "DEFINTRF" 368174 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 362877 363346 363944 "DEFINTEF" 364865 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 356707 362318 362484 "DECIMAL" 362731 T DECIMAL (NIL) -8 NIL NIL) (-197 354219 354677 355183 "DDFACT" 356251 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 353815 353858 354009 "DBLRESP" 354170 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351525 351859 352228 "DBASE" 353573 NIL DBASE (NIL T) -8 NIL NIL) (-194 350660 351484 351512 "D03FAFA" 351517 T D03FAFA (NIL) -8 NIL NIL) (-193 349796 350619 350647 "D03EEFA" 350652 T D03EEFA (NIL) -8 NIL NIL) (-192 347746 348212 348701 "D03AGNT" 349327 T D03AGNT (NIL) -7 NIL NIL) (-191 347064 347705 347733 "D02EJFA" 347738 T D02EJFA (NIL) -8 NIL NIL) (-190 346382 347023 347051 "D02CJFA" 347056 T D02CJFA (NIL) -8 NIL NIL) (-189 345700 346341 346369 "D02BHFA" 346374 T D02BHFA (NIL) -8 NIL NIL) (-188 345018 345659 345687 "D02BBFA" 345692 T D02BBFA (NIL) -8 NIL NIL) (-187 338216 339804 341410 "D02AGNT" 343432 T D02AGNT (NIL) -7 NIL NIL) (-186 335985 336507 337053 "D01WGTS" 337690 T D01WGTS (NIL) -7 NIL NIL) (-185 335088 335944 335972 "D01TRNS" 335977 T D01TRNS (NIL) -8 NIL NIL) (-184 334191 335047 335075 "D01GBFA" 335080 T D01GBFA (NIL) -8 NIL NIL) (-183 333294 334150 334178 "D01FCFA" 334183 T D01FCFA (NIL) -8 NIL NIL) (-182 332397 333253 333281 "D01ASFA" 333286 T D01ASFA (NIL) -8 NIL NIL) (-181 331500 332356 332384 "D01AQFA" 332389 T D01AQFA (NIL) -8 NIL NIL) (-180 330603 331459 331487 "D01APFA" 331492 T D01APFA (NIL) -8 NIL NIL) (-179 329706 330562 330590 "D01ANFA" 330595 T D01ANFA (NIL) -8 NIL NIL) (-178 328809 329665 329693 "D01AMFA" 329698 T D01AMFA (NIL) -8 NIL NIL) (-177 327912 328768 328796 "D01ALFA" 328801 T D01ALFA (NIL) -8 NIL NIL) (-176 327015 327871 327899 "D01AKFA" 327904 T D01AKFA (NIL) -8 NIL NIL) (-175 326118 326974 327002 "D01AJFA" 327007 T D01AJFA (NIL) -8 NIL NIL) (-174 319422 320971 322530 "D01AGNT" 324579 T D01AGNT (NIL) -7 NIL NIL) (-173 318759 318887 319039 "CYCLOTOM" 319290 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315494 316207 316934 "CYCLES" 318052 T CYCLES (NIL) -7 NIL NIL) (-171 314806 314940 315111 "CVMP" 315355 NIL CVMP (NIL T) -7 NIL NIL) (-170 312587 312845 313220 "CTRIGMNP" 314534 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312192 312275 312380 "CTORCALL" 312502 T CTORCALL (NIL) -8 NIL NIL) (-168 311566 311665 311818 "CSTTOOLS" 312089 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307365 308022 308780 "CRFP" 310878 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306412 306597 306825 "CRAPACK" 307169 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 305796 305897 306101 "CPMATCH" 306288 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305521 305549 305655 "CPIMA" 305762 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 301885 302557 303275 "COORDSYS" 304856 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301269 301398 301548 "CONTOUR" 301755 T CONTOUR (NIL) -8 NIL NIL) (-161 297130 299272 299764 "CONTFRAC" 300809 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296284 296848 296876 "COMRING" 296881 T COMRING (NIL) -9 NIL 296932) (-159 295365 295642 295826 "COMPPROP" 296120 T COMPPROP (NIL) -8 NIL NIL) (-158 295026 295061 295189 "COMPLPAT" 295324 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 285007 294835 294944 "COMPLEX" 294949 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 284643 284700 284807 "COMPLEX2" 284944 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284361 284396 284494 "COMPFACT" 284602 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 268696 278990 279030 "COMPCAT" 280032 NIL COMPCAT (NIL T) -9 NIL 281425) (-153 258211 261135 264762 "COMPCAT-" 265118 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 257942 257970 258072 "COMMUPC" 258177 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 257737 257770 257829 "COMMONOP" 257903 T COMMONOP (NIL) -7 NIL NIL) (-150 257320 257488 257575 "COMM" 257670 T COMM (NIL) -8 NIL NIL) (-149 256569 256763 256791 "COMBOPC" 257129 T COMBOPC (NIL) -9 NIL 257304) (-148 255465 255675 255917 "COMBINAT" 256359 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 251663 252236 252876 "COMBF" 254887 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250449 250779 251014 "COLOR" 251448 T COLOR (NIL) -8 NIL NIL) (-145 250089 250136 250261 "CMPLXRT" 250396 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245591 246619 247699 "CLIP" 249029 T CLIP (NIL) -7 NIL NIL) (-143 243929 244699 244937 "CLIF" 245419 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240152 242076 242117 "CLAGG" 243046 NIL CLAGG (NIL T) -9 NIL 243582) (-141 238574 239031 239614 "CLAGG-" 239619 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238118 238203 238343 "CINTSLPE" 238483 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235619 236090 236638 "CHVAR" 237646 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 234842 235406 235434 "CHARZ" 235439 T CHARZ (NIL) -9 NIL 235453) (-137 234596 234636 234714 "CHARPOL" 234796 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 233703 234300 234328 "CHARNZ" 234375 T CHARNZ (NIL) -9 NIL 234430) (-135 231728 232393 232728 "CHAR" 233388 T CHAR (NIL) -8 NIL NIL) (-134 231454 231515 231543 "CFCAT" 231654 T CFCAT (NIL) -9 NIL NIL) (-133 230699 230810 230992 "CDEN" 231338 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 226691 229852 230132 "CCLASS" 230439 T CCLASS (NIL) -8 NIL NIL) (-131 226610 226636 226671 "CATEGORY" 226676 T -10 (NIL) -8 NIL NIL) (-130 221662 222639 223392 "CARTEN" 225913 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 220770 220918 221139 "CARTEN2" 221509 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219068 219922 220178 "CARD" 220534 T CARD (NIL) -8 NIL NIL) (-127 218441 218769 218797 "CACHSET" 218929 T CACHSET (NIL) -9 NIL 219006) (-126 217938 218234 218262 "CABMON" 218312 T CABMON (NIL) -9 NIL 218368) (-125 217426 217740 217820 "BYTE" 217878 T BYTE (NIL) -8 NIL NIL) (-124 213374 217373 217407 "BYTEARY" 217412 T BYTEARY (NIL) -8 NIL NIL) (-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 +((-3 3144482 3144487 3144492 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3144467 3144472 3144477 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3144452 3144457 3144462 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3144437 3144442 3144447 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1197 3143567 3144312 3144389 "ZMOD" 3144394 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1196 3142677 3142841 3143050 "ZLINDEP" 3143399 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1195 3132081 3133826 3135778 "ZDSOLVE" 3140826 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1194 3131327 3131468 3131657 "YSTREAM" 3131927 NIL YSTREAM (NIL T) -7 NIL NIL) (-1193 3129096 3130632 3130835 "XRPOLY" 3131170 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1192 3125558 3126887 3127469 "XPR" 3128560 NIL XPR (NIL T T) -8 NIL NIL) (-1191 3123272 3124893 3125096 "XPOLY" 3125389 NIL XPOLY (NIL T) -8 NIL NIL) (-1190 3121086 3122464 3122518 "XPOLYC" 3122803 NIL XPOLYC (NIL T T) -9 NIL 3122916) (-1189 3117458 3119603 3119991 "XPBWPOLY" 3120744 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1188 3113386 3115699 3115741 "XF" 3116362 NIL XF (NIL T) -9 NIL 3116761) (-1187 3113007 3113095 3113264 "XF-" 3113269 NIL XF- (NIL T T) -8 NIL NIL) (-1186 3108387 3109686 3109740 "XFALG" 3111888 NIL XFALG (NIL T T) -9 NIL 3112675) (-1185 3107524 3107628 3107832 "XEXPPKG" 3108279 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1184 3105623 3107375 3107470 "XDPOLY" 3107475 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1183 3104502 3105112 3105154 "XALG" 3105216 NIL XALG (NIL T) -9 NIL 3105335) (-1182 3097978 3102486 3102979 "WUTSET" 3104094 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1181 3095790 3096597 3096948 "WP" 3097760 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1180 3094676 3094874 3095169 "WFFINTBS" 3095587 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1179 3092580 3093007 3093469 "WEIER" 3094248 NIL WEIER (NIL T) -7 NIL NIL) (-1178 3091729 3092153 3092195 "VSPACE" 3092331 NIL VSPACE (NIL T) -9 NIL 3092405) (-1177 3091567 3091594 3091685 "VSPACE-" 3091690 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1176 3091313 3091356 3091427 "VOID" 3091518 T VOID (NIL) -8 NIL NIL) (-1175 3089449 3089808 3090214 "VIEW" 3090929 T VIEW (NIL) -7 NIL NIL) (-1174 3085874 3086512 3087249 "VIEWDEF" 3088734 T VIEWDEF (NIL) -7 NIL NIL) (-1173 3075212 3077422 3079595 "VIEW3D" 3083723 T VIEW3D (NIL) -8 NIL NIL) (-1172 3067494 3069123 3070702 "VIEW2D" 3073655 T VIEW2D (NIL) -8 NIL NIL) (-1171 3062903 3067264 3067356 "VECTOR" 3067437 NIL VECTOR (NIL T) -8 NIL NIL) (-1170 3061480 3061739 3062057 "VECTOR2" 3062633 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1169 3055020 3059272 3059315 "VECTCAT" 3060303 NIL VECTCAT (NIL T) -9 NIL 3060887) (-1168 3054034 3054288 3054678 "VECTCAT-" 3054683 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1167 3053515 3053685 3053805 "VARIABLE" 3053949 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1166 3053448 3053453 3053483 "UTYPE" 3053488 T UTYPE (NIL) -9 NIL NIL) (-1165 3052283 3052437 3052698 "UTSODETL" 3053274 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1164 3049723 3050183 3050707 "UTSODE" 3051824 NIL UTSODE (NIL T T) -7 NIL NIL) (-1163 3041567 3047363 3047851 "UTS" 3049292 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1162 3032912 3038277 3038319 "UTSCAT" 3039420 NIL UTSCAT (NIL T) -9 NIL 3040177) (-1161 3030267 3030983 3031971 "UTSCAT-" 3031976 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1160 3029898 3029941 3030072 "UTS2" 3030218 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1159 3024174 3026739 3026782 "URAGG" 3028852 NIL URAGG (NIL T) -9 NIL 3029574) (-1158 3021113 3021976 3023099 "URAGG-" 3023104 NIL URAGG- (NIL T T) -8 NIL NIL) (-1157 3016799 3019730 3020201 "UPXSSING" 3020777 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1156 3008690 3015920 3016200 "UPXS" 3016576 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1155 3001719 3008595 3008666 "UPXSCONS" 3008671 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1154 2992008 2998838 2998899 "UPXSCCA" 2999548 NIL UPXSCCA (NIL T T) -9 NIL 2999789) (-1153 2991647 2991732 2991905 "UPXSCCA-" 2991910 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1152 2981858 2988461 2988503 "UPXSCAT" 2989146 NIL UPXSCAT (NIL T) -9 NIL 2989754) (-1151 2981292 2981371 2981548 "UPXS2" 2981773 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1150 2979946 2980199 2980550 "UPSQFREE" 2981035 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1149 2973837 2976892 2976946 "UPSCAT" 2978095 NIL UPSCAT (NIL T T) -9 NIL 2978869) (-1148 2973042 2973249 2973575 "UPSCAT-" 2973580 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1147 2959128 2967165 2967207 "UPOLYC" 2969285 NIL UPOLYC (NIL T) -9 NIL 2970506) (-1146 2950458 2952883 2956029 "UPOLYC-" 2956034 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1145 2950089 2950132 2950263 "UPOLYC2" 2950409 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1144 2941508 2949658 2949795 "UP" 2949999 NIL UP (NIL NIL T) -8 NIL NIL) (-1143 2940851 2940958 2941121 "UPMP" 2941397 NIL UPMP (NIL T T) -7 NIL NIL) (-1142 2940404 2940485 2940624 "UPDIVP" 2940764 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1141 2938972 2939221 2939537 "UPDECOMP" 2940153 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1140 2938207 2938319 2938504 "UPCDEN" 2938856 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1139 2937730 2937799 2937946 "UP2" 2938132 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1138 2936247 2936934 2937211 "UNISEG" 2937488 NIL UNISEG (NIL T) -8 NIL NIL) (-1137 2935462 2935589 2935794 "UNISEG2" 2936090 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1136 2934522 2934702 2934928 "UNIFACT" 2935278 NIL UNIFACT (NIL T) -7 NIL NIL) (-1135 2918418 2933703 2933953 "ULS" 2934329 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1134 2906383 2918323 2918394 "ULSCONS" 2918399 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1133 2889133 2901146 2901207 "ULSCCAT" 2901919 NIL ULSCCAT (NIL T T) -9 NIL 2902215) (-1132 2888184 2888429 2888816 "ULSCCAT-" 2888821 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1131 2878174 2884691 2884733 "ULSCAT" 2885589 NIL ULSCAT (NIL T) -9 NIL 2886319) (-1130 2877608 2877687 2877864 "ULS2" 2878089 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1129 2876006 2876973 2877003 "UFD" 2877215 T UFD (NIL) -9 NIL 2877329) (-1128 2875800 2875846 2875941 "UFD-" 2875946 NIL UFD- (NIL T) -8 NIL NIL) (-1127 2874882 2875065 2875281 "UDVO" 2875606 T UDVO (NIL) -7 NIL NIL) (-1126 2872698 2873107 2873578 "UDPO" 2874446 NIL UDPO (NIL T) -7 NIL NIL) (-1125 2872631 2872636 2872666 "TYPE" 2872671 T TYPE (NIL) -9 NIL NIL) (-1124 2871602 2871804 2872044 "TWOFACT" 2872425 NIL TWOFACT (NIL T) -7 NIL NIL) (-1123 2870540 2870877 2871140 "TUPLE" 2871374 NIL TUPLE (NIL T) -8 NIL NIL) (-1122 2868231 2868750 2869289 "TUBETOOL" 2870023 T TUBETOOL (NIL) -7 NIL NIL) (-1121 2867080 2867285 2867526 "TUBE" 2868024 NIL TUBE (NIL T) -8 NIL NIL) (-1120 2861804 2866058 2866340 "TS" 2866832 NIL TS (NIL T) -8 NIL NIL) (-1119 2850508 2854600 2854696 "TSETCAT" 2859930 NIL TSETCAT (NIL T T T T) -9 NIL 2861461) (-1118 2845243 2846841 2848731 "TSETCAT-" 2848736 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1117 2839506 2840352 2841294 "TRMANIP" 2844379 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1116 2838947 2839010 2839173 "TRIMAT" 2839438 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1115 2836753 2836990 2837353 "TRIGMNIP" 2838696 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1114 2836273 2836386 2836416 "TRIGCAT" 2836629 T TRIGCAT (NIL) -9 NIL NIL) (-1113 2835942 2836021 2836162 "TRIGCAT-" 2836167 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1112 2832841 2834802 2835082 "TREE" 2835697 NIL TREE (NIL T) -8 NIL NIL) (-1111 2832115 2832643 2832673 "TRANFUN" 2832708 T TRANFUN (NIL) -9 NIL 2832774) (-1110 2831394 2831585 2831865 "TRANFUN-" 2831870 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1109 2831198 2831230 2831291 "TOPSP" 2831355 T TOPSP (NIL) -7 NIL NIL) (-1108 2830550 2830665 2830818 "TOOLSIGN" 2831079 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1107 2829211 2829727 2829966 "TEXTFILE" 2830333 T TEXTFILE (NIL) -8 NIL NIL) (-1106 2827076 2827590 2828028 "TEX" 2828795 T TEX (NIL) -8 NIL NIL) (-1105 2826857 2826888 2826960 "TEX1" 2827039 NIL TEX1 (NIL T) -7 NIL NIL) (-1104 2826505 2826568 2826658 "TEMUTL" 2826789 T TEMUTL (NIL) -7 NIL NIL) (-1103 2824659 2824939 2825264 "TBCMPPK" 2826228 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1102 2816548 2822820 2822876 "TBAGG" 2823276 NIL TBAGG (NIL T T) -9 NIL 2823487) (-1101 2811618 2813106 2814860 "TBAGG-" 2814865 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1100 2811002 2811109 2811254 "TANEXP" 2811507 NIL TANEXP (NIL T) -7 NIL NIL) (-1099 2804503 2810859 2810952 "TABLE" 2810957 NIL TABLE (NIL T T) -8 NIL NIL) (-1098 2803915 2804014 2804152 "TABLEAU" 2804400 NIL TABLEAU (NIL T) -8 NIL NIL) (-1097 2798523 2799743 2800991 "TABLBUMP" 2802701 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1096 2797951 2798051 2798179 "SYSTEM" 2798417 T SYSTEM (NIL) -7 NIL NIL) (-1095 2794414 2795109 2795892 "SYSSOLP" 2797202 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1094 2790705 2791413 2792147 "SYNTAX" 2793702 T SYNTAX (NIL) -8 NIL NIL) (-1093 2787839 2788447 2789085 "SYMTAB" 2790089 T SYMTAB (NIL) -8 NIL NIL) (-1092 2783088 2783990 2784973 "SYMS" 2786878 T SYMS (NIL) -8 NIL NIL) (-1091 2780321 2782548 2782777 "SYMPOLY" 2782893 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1090 2779841 2779916 2780038 "SYMFUNC" 2780233 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1089 2775818 2777078 2777900 "SYMBOL" 2779041 T SYMBOL (NIL) -8 NIL NIL) (-1088 2769357 2771046 2772766 "SWITCH" 2774120 T SWITCH (NIL) -8 NIL NIL) (-1087 2762587 2768184 2768486 "SUTS" 2769112 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1086 2754477 2761708 2761988 "SUPXS" 2762364 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1085 2745969 2754098 2754223 "SUP" 2754386 NIL SUP (NIL T) -8 NIL NIL) (-1084 2745128 2745255 2745472 "SUPFRACF" 2745837 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1083 2744753 2744812 2744923 "SUP2" 2745063 NIL SUP2 (NIL T T) -7 NIL NIL) (-1082 2743171 2743445 2743807 "SUMRF" 2744452 NIL SUMRF (NIL T) -7 NIL NIL) (-1081 2742488 2742554 2742752 "SUMFS" 2743092 NIL SUMFS (NIL T T) -7 NIL NIL) (-1080 2726424 2741669 2741919 "SULS" 2742295 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1079 2725746 2725949 2726089 "SUCH" 2726332 NIL SUCH (NIL T T) -8 NIL NIL) (-1078 2719673 2720685 2721643 "SUBSPACE" 2724834 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1077 2719103 2719193 2719357 "SUBRESP" 2719561 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1076 2712472 2713768 2715079 "STTF" 2717839 NIL STTF (NIL T) -7 NIL NIL) (-1075 2706645 2707765 2708912 "STTFNC" 2711372 NIL STTFNC (NIL T) -7 NIL NIL) (-1074 2697996 2699863 2701656 "STTAYLOR" 2704886 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1073 2691240 2697860 2697943 "STRTBL" 2697948 NIL STRTBL (NIL T) -8 NIL NIL) (-1072 2686631 2691195 2691226 "STRING" 2691231 T STRING (NIL) -8 NIL NIL) (-1071 2681520 2686005 2686035 "STRICAT" 2686094 T STRICAT (NIL) -9 NIL 2686156) (-1070 2674236 2679043 2679663 "STREAM" 2680935 NIL STREAM (NIL T) -8 NIL NIL) (-1069 2673746 2673823 2673967 "STREAM3" 2674153 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1068 2672728 2672911 2673146 "STREAM2" 2673559 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1067 2672416 2672468 2672561 "STREAM1" 2672670 NIL STREAM1 (NIL T) -7 NIL NIL) (-1066 2671432 2671613 2671844 "STINPROD" 2672232 NIL STINPROD (NIL T) -7 NIL NIL) (-1065 2671011 2671195 2671225 "STEP" 2671305 T STEP (NIL) -9 NIL 2671383) (-1064 2664554 2670910 2670987 "STBL" 2670992 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1063 2659730 2663777 2663820 "STAGG" 2663973 NIL STAGG (NIL T) -9 NIL 2664062) (-1062 2657432 2658034 2658906 "STAGG-" 2658911 NIL STAGG- (NIL T T) -8 NIL NIL) (-1061 2655627 2657202 2657294 "STACK" 2657375 NIL STACK (NIL T) -8 NIL NIL) (-1060 2648358 2653774 2654229 "SREGSET" 2655257 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1059 2640798 2642166 2643678 "SRDCMPK" 2646964 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1058 2633766 2638239 2638269 "SRAGG" 2639572 T SRAGG (NIL) -9 NIL 2640180) (-1057 2632783 2633038 2633417 "SRAGG-" 2633422 NIL SRAGG- (NIL T) -8 NIL NIL) (-1056 2627232 2631702 2632129 "SQMATRIX" 2632402 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1055 2620984 2623952 2624678 "SPLTREE" 2626578 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1054 2616974 2617640 2618286 "SPLNODE" 2620410 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1053 2616021 2616254 2616284 "SPFCAT" 2616728 T SPFCAT (NIL) -9 NIL NIL) (-1052 2614758 2614968 2615232 "SPECOUT" 2615779 T SPECOUT (NIL) -7 NIL NIL) (-1051 2614519 2614559 2614628 "SPADPRSR" 2614711 T SPADPRSR (NIL) -7 NIL NIL) (-1050 2606542 2608289 2608331 "SPACEC" 2612654 NIL SPACEC (NIL T) -9 NIL 2614470) (-1049 2604713 2606475 2606523 "SPACE3" 2606528 NIL SPACE3 (NIL T) -8 NIL NIL) (-1048 2603465 2603636 2603927 "SORTPAK" 2604518 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1047 2601521 2601824 2602242 "SOLVETRA" 2603129 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1046 2600532 2600754 2601028 "SOLVESER" 2601294 NIL SOLVESER (NIL T) -7 NIL NIL) (-1045 2595752 2596633 2597635 "SOLVERAD" 2599584 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1044 2591567 2592176 2592905 "SOLVEFOR" 2595119 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1043 2585867 2590919 2591015 "SNTSCAT" 2591020 NIL SNTSCAT (NIL T T T T) -9 NIL 2591090) (-1042 2579971 2584198 2584588 "SMTS" 2585557 NIL SMTS (NIL T T T) -8 NIL NIL) (-1041 2574381 2579860 2579936 "SMP" 2579941 NIL SMP (NIL T T) -8 NIL NIL) (-1040 2572540 2572841 2573239 "SMITH" 2574078 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1039 2565505 2569701 2569803 "SMATCAT" 2571143 NIL SMATCAT (NIL NIL T T T) -9 NIL 2571692) (-1038 2562446 2563269 2564446 "SMATCAT-" 2564451 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1037 2560160 2561683 2561726 "SKAGG" 2561987 NIL SKAGG (NIL T) -9 NIL 2562122) (-1036 2556218 2559264 2559542 "SINT" 2559904 T SINT (NIL) -8 NIL NIL) (-1035 2555990 2556028 2556094 "SIMPAN" 2556174 T SIMPAN (NIL) -7 NIL NIL) (-1034 2554828 2555049 2555324 "SIGNRF" 2555749 NIL SIGNRF (NIL T) -7 NIL NIL) (-1033 2553637 2553788 2554078 "SIGNEF" 2554657 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1032 2551327 2551781 2552287 "SHP" 2553178 NIL SHP (NIL T NIL) -7 NIL NIL) (-1031 2545180 2551228 2551304 "SHDP" 2551309 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1030 2544670 2544862 2544892 "SGROUP" 2545044 T SGROUP (NIL) -9 NIL 2545131) (-1029 2544440 2544492 2544596 "SGROUP-" 2544601 NIL SGROUP- (NIL T) -8 NIL NIL) (-1028 2541276 2541973 2542696 "SGCF" 2543739 T SGCF (NIL) -7 NIL NIL) (-1027 2535675 2540727 2540823 "SFRTCAT" 2540828 NIL SFRTCAT (NIL T T T T) -9 NIL 2540866) (-1026 2529135 2530150 2531284 "SFRGCD" 2534658 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1025 2522301 2523372 2524556 "SFQCMPK" 2528068 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1024 2521923 2522012 2522122 "SFORT" 2522242 NIL SFORT (NIL T T) -8 NIL NIL) (-1023 2521068 2521763 2521884 "SEXOF" 2521889 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1022 2520202 2520949 2521017 "SEX" 2521022 T SEX (NIL) -8 NIL NIL) (-1021 2514979 2515668 2515763 "SEXCAT" 2519534 NIL SEXCAT (NIL T T T T T) -9 NIL 2520153) (-1020 2512159 2514913 2514961 "SET" 2514966 NIL SET (NIL T) -8 NIL NIL) (-1019 2510410 2510872 2511177 "SETMN" 2511900 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1018 2510018 2510144 2510174 "SETCAT" 2510291 T SETCAT (NIL) -9 NIL 2510375) (-1017 2509798 2509850 2509949 "SETCAT-" 2509954 NIL SETCAT- (NIL T) -8 NIL NIL) (-1016 2506186 2508260 2508303 "SETAGG" 2509173 NIL SETAGG (NIL T) -9 NIL 2509513) (-1015 2505644 2505760 2505997 "SETAGG-" 2506002 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1014 2504848 2505141 2505202 "SEGXCAT" 2505488 NIL SEGXCAT (NIL T T) -9 NIL 2505608) (-1013 2503904 2504514 2504696 "SEG" 2504701 NIL SEG (NIL T) -8 NIL NIL) (-1012 2502811 2503024 2503067 "SEGCAT" 2503649 NIL SEGCAT (NIL T) -9 NIL 2503887) (-1011 2501860 2502190 2502390 "SEGBIND" 2502646 NIL SEGBIND (NIL T) -8 NIL NIL) (-1010 2501481 2501540 2501653 "SEGBIND2" 2501795 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1009 2500700 2500826 2501030 "SEG2" 2501325 NIL SEG2 (NIL T T) -7 NIL NIL) (-1008 2500137 2500635 2500682 "SDVAR" 2500687 NIL SDVAR (NIL T) -8 NIL NIL) (-1007 2492389 2499910 2500038 "SDPOL" 2500043 NIL SDPOL (NIL T) -8 NIL NIL) (-1006 2490982 2491248 2491567 "SCPKG" 2492104 NIL SCPKG (NIL T) -7 NIL NIL) (-1005 2490119 2490298 2490498 "SCOPE" 2490804 T SCOPE (NIL) -8 NIL NIL) (-1004 2489340 2489473 2489652 "SCACHE" 2489974 NIL SCACHE (NIL T) -7 NIL NIL) (-1003 2488779 2489100 2489185 "SAOS" 2489277 T SAOS (NIL) -8 NIL NIL) (-1002 2488344 2488379 2488552 "SAERFFC" 2488738 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1001 2482238 2488241 2488321 "SAE" 2488326 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1000 2481831 2481866 2482025 "SAEFACT" 2482197 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-999 2480157 2480471 2480870 "RURPK" 2481497 NIL RURPK (NIL T NIL) -7 NIL NIL) (-998 2478810 2479087 2479394 "RULESET" 2479993 NIL RULESET (NIL T T T) -8 NIL NIL) (-997 2476018 2476521 2476982 "RULE" 2478492 NIL RULE (NIL T T T) -8 NIL NIL) (-996 2475660 2475815 2475896 "RULECOLD" 2475970 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-995 2470552 2471346 2472262 "RSETGCD" 2474859 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-994 2459867 2464919 2465013 "RSETCAT" 2469078 NIL RSETCAT (NIL T T T T) -9 NIL 2470175) (-993 2457798 2458337 2459157 "RSETCAT-" 2459162 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-992 2450228 2451603 2453119 "RSDCMPK" 2456397 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-991 2448246 2448687 2448759 "RRCC" 2449835 NIL RRCC (NIL T T) -9 NIL 2450179) (-990 2447600 2447774 2448050 "RRCC-" 2448055 NIL RRCC- (NIL T T T) -8 NIL NIL) (-989 2421967 2431592 2431656 "RPOLCAT" 2442158 NIL RPOLCAT (NIL T T T) -9 NIL 2445316) (-988 2413471 2415809 2418927 "RPOLCAT-" 2418932 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-987 2404537 2411701 2412181 "ROUTINE" 2413011 T ROUTINE (NIL) -8 NIL NIL) (-986 2401242 2404093 2404240 "ROMAN" 2404410 T ROMAN (NIL) -8 NIL NIL) (-985 2399528 2400113 2400370 "ROIRC" 2401048 NIL ROIRC (NIL T T) -8 NIL NIL) (-984 2395933 2398237 2398265 "RNS" 2398561 T RNS (NIL) -9 NIL 2398831) (-983 2394447 2394830 2395361 "RNS-" 2395434 NIL RNS- (NIL T) -8 NIL NIL) (-982 2393873 2394281 2394309 "RNG" 2394314 T RNG (NIL) -9 NIL 2394335) (-981 2393271 2393633 2393673 "RMODULE" 2393733 NIL RMODULE (NIL T) -9 NIL 2393775) (-980 2392123 2392217 2392547 "RMCAT2" 2393172 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-979 2388837 2391306 2391627 "RMATRIX" 2391858 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-978 2381834 2384068 2384180 "RMATCAT" 2387489 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2388471) (-977 2381213 2381360 2381663 "RMATCAT-" 2381668 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-976 2380783 2380858 2380984 "RINTERP" 2381132 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-975 2379834 2380398 2380426 "RING" 2380536 T RING (NIL) -9 NIL 2380630) (-974 2379629 2379673 2379767 "RING-" 2379772 NIL RING- (NIL T) -8 NIL NIL) (-973 2378477 2378714 2378970 "RIDIST" 2379393 T RIDIST (NIL) -7 NIL NIL) (-972 2369799 2377951 2378154 "RGCHAIN" 2378326 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-971 2366804 2367418 2368086 "RF" 2369163 NIL RF (NIL T) -7 NIL NIL) (-970 2366453 2366516 2366617 "RFFACTOR" 2366735 NIL RFFACTOR (NIL T) -7 NIL NIL) (-969 2366181 2366216 2366311 "RFFACT" 2366412 NIL RFFACT (NIL T) -7 NIL NIL) (-968 2364311 2364675 2365055 "RFDIST" 2365821 T RFDIST (NIL) -7 NIL NIL) (-967 2363769 2363861 2364021 "RETSOL" 2364213 NIL RETSOL (NIL T T) -7 NIL NIL) (-966 2363362 2363442 2363483 "RETRACT" 2363673 NIL RETRACT (NIL T) -9 NIL NIL) (-965 2363214 2363239 2363323 "RETRACT-" 2363328 NIL RETRACT- (NIL T T) -8 NIL NIL) (-964 2356072 2362871 2362996 "RESULT" 2363109 T RESULT (NIL) -8 NIL NIL) (-963 2354657 2355346 2355543 "RESRING" 2355975 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-962 2354297 2354346 2354442 "RESLATC" 2354594 NIL RESLATC (NIL T) -7 NIL NIL) (-961 2354006 2354040 2354145 "REPSQ" 2354256 NIL REPSQ (NIL T) -7 NIL NIL) (-960 2351437 2352017 2352617 "REP" 2353426 T REP (NIL) -7 NIL NIL) (-959 2351138 2351172 2351281 "REPDB" 2351396 NIL REPDB (NIL T) -7 NIL NIL) (-958 2345083 2346462 2347682 "REP2" 2349950 NIL REP2 (NIL T) -7 NIL NIL) (-957 2341489 2342170 2342975 "REP1" 2344310 NIL REP1 (NIL T) -7 NIL NIL) (-956 2334235 2339650 2340102 "REGSET" 2341120 NIL REGSET (NIL T T T T) -8 NIL NIL) (-955 2333056 2333391 2333639 "REF" 2334020 NIL REF (NIL T) -8 NIL NIL) (-954 2332437 2332540 2332705 "REDORDER" 2332940 NIL REDORDER (NIL T T) -7 NIL NIL) (-953 2328406 2331671 2331892 "RECLOS" 2332268 NIL RECLOS (NIL T) -8 NIL NIL) (-952 2327463 2327644 2327857 "REALSOLV" 2328213 T REALSOLV (NIL) -7 NIL NIL) (-951 2327311 2327352 2327380 "REAL" 2327385 T REAL (NIL) -9 NIL 2327420) (-950 2323802 2324604 2325486 "REAL0Q" 2326476 NIL REAL0Q (NIL T) -7 NIL NIL) (-949 2319413 2320401 2321460 "REAL0" 2322783 NIL REAL0 (NIL T) -7 NIL NIL) (-948 2318821 2318893 2319098 "RDIV" 2319335 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-947 2317894 2318068 2318279 "RDIST" 2318643 NIL RDIST (NIL T) -7 NIL NIL) (-946 2316498 2316785 2317154 "RDETRS" 2317602 NIL RDETRS (NIL T T) -7 NIL NIL) (-945 2314319 2314773 2315308 "RDETR" 2316040 NIL RDETR (NIL T T) -7 NIL NIL) (-944 2312935 2313213 2313614 "RDEEFS" 2314035 NIL RDEEFS (NIL T T) -7 NIL NIL) (-943 2311435 2311741 2312170 "RDEEF" 2312623 NIL RDEEF (NIL T T) -7 NIL NIL) (-942 2305720 2308652 2308680 "RCFIELD" 2309957 T RCFIELD (NIL) -9 NIL 2310687) (-941 2303789 2304293 2304986 "RCFIELD-" 2305059 NIL RCFIELD- (NIL T) -8 NIL NIL) (-940 2300121 2301906 2301947 "RCAGG" 2303018 NIL RCAGG (NIL T) -9 NIL 2303483) (-939 2299752 2299846 2300006 "RCAGG-" 2300011 NIL RCAGG- (NIL T T) -8 NIL NIL) (-938 2299096 2299208 2299370 "RATRET" 2299636 NIL RATRET (NIL T) -7 NIL NIL) (-937 2298653 2298720 2298839 "RATFACT" 2299024 NIL RATFACT (NIL T) -7 NIL NIL) (-936 2297968 2298088 2298238 "RANDSRC" 2298523 T RANDSRC (NIL) -7 NIL NIL) (-935 2297705 2297749 2297820 "RADUTIL" 2297917 T RADUTIL (NIL) -7 NIL NIL) (-934 2290712 2296448 2296765 "RADIX" 2297420 NIL RADIX (NIL NIL) -8 NIL NIL) (-933 2282282 2290556 2290684 "RADFF" 2290689 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-932 2281934 2282009 2282037 "RADCAT" 2282194 T RADCAT (NIL) -9 NIL NIL) (-931 2281719 2281767 2281864 "RADCAT-" 2281869 NIL RADCAT- (NIL T) -8 NIL NIL) (-930 2279870 2281494 2281583 "QUEUE" 2281663 NIL QUEUE (NIL T) -8 NIL NIL) (-929 2276367 2279807 2279852 "QUAT" 2279857 NIL QUAT (NIL T) -8 NIL NIL) (-928 2276005 2276048 2276175 "QUATCT2" 2276318 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-927 2269799 2273179 2273219 "QUATCAT" 2273998 NIL QUATCAT (NIL T) -9 NIL 2274763) (-926 2265943 2266980 2268367 "QUATCAT-" 2268461 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-925 2263464 2265028 2265069 "QUAGG" 2265444 NIL QUAGG (NIL T) -9 NIL 2265619) (-924 2262389 2262862 2263034 "QFORM" 2263336 NIL QFORM (NIL NIL T) -8 NIL NIL) (-923 2253686 2258944 2258984 "QFCAT" 2259642 NIL QFCAT (NIL T) -9 NIL 2260635) (-922 2249258 2250459 2252050 "QFCAT-" 2252144 NIL QFCAT- (NIL T T) -8 NIL NIL) (-921 2248896 2248939 2249066 "QFCAT2" 2249209 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-920 2248356 2248466 2248596 "QEQUAT" 2248786 T QEQUAT (NIL) -8 NIL NIL) (-919 2241542 2242613 2243795 "QCMPACK" 2247289 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-918 2239118 2239539 2239967 "QALGSET" 2241197 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-917 2238363 2238537 2238769 "QALGSET2" 2238938 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-916 2237054 2237277 2237594 "PWFFINTB" 2238136 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-915 2235242 2235410 2235763 "PUSHVAR" 2236868 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-914 2231160 2232214 2232255 "PTRANFN" 2234139 NIL PTRANFN (NIL T) -9 NIL NIL) (-913 2229572 2229863 2230184 "PTPACK" 2230871 NIL PTPACK (NIL T) -7 NIL NIL) (-912 2229208 2229265 2229372 "PTFUNC2" 2229509 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-911 2223685 2228026 2228066 "PTCAT" 2228434 NIL PTCAT (NIL T) -9 NIL 2228596) (-910 2223343 2223378 2223502 "PSQFR" 2223644 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-909 2221938 2222236 2222570 "PSEUDLIN" 2223041 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-908 2208746 2211110 2213433 "PSETPK" 2219698 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-907 2201833 2204547 2204641 "PSETCAT" 2207622 NIL PSETCAT (NIL T T T T) -9 NIL 2208436) (-906 2199671 2200305 2201124 "PSETCAT-" 2201129 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-905 2199020 2199185 2199213 "PSCURVE" 2199481 T PSCURVE (NIL) -9 NIL 2199648) (-904 2195472 2196998 2197062 "PSCAT" 2197898 NIL PSCAT (NIL T T T) -9 NIL 2198138) (-903 2194536 2194752 2195151 "PSCAT-" 2195156 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-902 2193188 2193821 2194035 "PRTITION" 2194342 T PRTITION (NIL) -8 NIL NIL) (-901 2182286 2184492 2186680 "PRS" 2191050 NIL PRS (NIL T T) -7 NIL NIL) (-900 2180145 2181637 2181677 "PRQAGG" 2181860 NIL PRQAGG (NIL T) -9 NIL 2181962) (-899 2179716 2179818 2179846 "PROPLOG" 2180031 T PROPLOG (NIL) -9 NIL NIL) (-898 2176839 2177404 2177931 "PROPFRML" 2179221 NIL PROPFRML (NIL T) -8 NIL NIL) (-897 2176299 2176409 2176539 "PROPERTY" 2176729 T PROPERTY (NIL) -8 NIL NIL) (-896 2170073 2174465 2175285 "PRODUCT" 2175525 NIL PRODUCT (NIL T T) -8 NIL NIL) (-895 2167349 2169533 2169766 "PR" 2169884 NIL PR (NIL T T) -8 NIL NIL) (-894 2167145 2167177 2167236 "PRINT" 2167310 T PRINT (NIL) -7 NIL NIL) (-893 2166485 2166602 2166754 "PRIMES" 2167025 NIL PRIMES (NIL T) -7 NIL NIL) (-892 2164550 2164951 2165417 "PRIMELT" 2166064 NIL PRIMELT (NIL T) -7 NIL NIL) (-891 2164279 2164328 2164356 "PRIMCAT" 2164480 T PRIMCAT (NIL) -9 NIL NIL) (-890 2160440 2164217 2164262 "PRIMARR" 2164267 NIL PRIMARR (NIL T) -8 NIL NIL) (-889 2159447 2159625 2159853 "PRIMARR2" 2160258 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-888 2159090 2159146 2159257 "PREASSOC" 2159385 NIL PREASSOC (NIL T T) -7 NIL NIL) (-887 2158565 2158698 2158726 "PPCURVE" 2158931 T PPCURVE (NIL) -9 NIL 2159067) (-886 2155924 2156323 2156915 "POLYROOT" 2158146 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-885 2149830 2155530 2155689 "POLY" 2155797 NIL POLY (NIL T) -8 NIL NIL) (-884 2149215 2149273 2149506 "POLYLIFT" 2149766 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-883 2145500 2145949 2146577 "POLYCATQ" 2148760 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-882 2132541 2137938 2138002 "POLYCAT" 2141487 NIL POLYCAT (NIL T T T) -9 NIL 2143414) (-881 2125992 2127853 2130236 "POLYCAT-" 2130241 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-880 2125581 2125649 2125768 "POLY2UP" 2125918 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-879 2125217 2125274 2125381 "POLY2" 2125518 NIL POLY2 (NIL T T) -7 NIL NIL) (-878 2123902 2124141 2124417 "POLUTIL" 2124991 NIL POLUTIL (NIL T T) -7 NIL NIL) (-877 2122264 2122541 2122871 "POLTOPOL" 2123624 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-876 2117787 2122201 2122246 "POINT" 2122251 NIL POINT (NIL T) -8 NIL NIL) (-875 2115974 2116331 2116706 "PNTHEORY" 2117432 T PNTHEORY (NIL) -7 NIL NIL) (-874 2114402 2114699 2115108 "PMTOOLS" 2115672 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-873 2113995 2114073 2114190 "PMSYM" 2114318 NIL PMSYM (NIL T) -7 NIL NIL) (-872 2113505 2113574 2113748 "PMQFCAT" 2113920 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-871 2112860 2112970 2113126 "PMPRED" 2113382 NIL PMPRED (NIL T) -7 NIL NIL) (-870 2112256 2112342 2112503 "PMPREDFS" 2112761 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-869 2110902 2111110 2111494 "PMPLCAT" 2112018 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-868 2110434 2110513 2110665 "PMLSAGG" 2110817 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-867 2109911 2109987 2110167 "PMKERNEL" 2110352 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-866 2109528 2109603 2109716 "PMINS" 2109830 NIL PMINS (NIL T) -7 NIL NIL) (-865 2108958 2109027 2109242 "PMFS" 2109453 NIL PMFS (NIL T T T) -7 NIL NIL) (-864 2108189 2108307 2108511 "PMDOWN" 2108835 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-863 2107352 2107511 2107693 "PMASS" 2108027 T PMASS (NIL) -7 NIL NIL) (-862 2106626 2106737 2106900 "PMASSFS" 2107238 NIL PMASSFS (NIL T T) -7 NIL NIL) (-861 2106281 2106349 2106443 "PLOTTOOL" 2106552 T PLOTTOOL (NIL) -7 NIL NIL) (-860 2100903 2102092 2103240 "PLOT" 2105153 T PLOT (NIL) -8 NIL NIL) (-859 2096717 2097751 2098672 "PLOT3D" 2100002 T PLOT3D (NIL) -8 NIL NIL) (-858 2095629 2095806 2096041 "PLOT1" 2096521 NIL PLOT1 (NIL T) -7 NIL NIL) (-857 2071023 2075695 2080546 "PLEQN" 2090895 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-856 2070341 2070463 2070643 "PINTERP" 2070888 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-855 2070034 2070081 2070184 "PINTERPA" 2070288 NIL PINTERPA (NIL T T) -7 NIL NIL) (-854 2069261 2069828 2069921 "PI" 2069961 T PI (NIL) -8 NIL NIL) (-853 2067653 2068638 2068666 "PID" 2068848 T PID (NIL) -9 NIL 2068982) (-852 2067378 2067415 2067503 "PICOERCE" 2067610 NIL PICOERCE (NIL T) -7 NIL NIL) (-851 2066698 2066837 2067013 "PGROEB" 2067234 NIL PGROEB (NIL T) -7 NIL NIL) (-850 2062285 2063099 2064004 "PGE" 2065813 T PGE (NIL) -7 NIL NIL) (-849 2060409 2060655 2061021 "PGCD" 2062002 NIL PGCD (NIL T T T T) -7 NIL NIL) (-848 2059747 2059850 2060011 "PFRPAC" 2060293 NIL PFRPAC (NIL T) -7 NIL NIL) (-847 2056362 2058295 2058648 "PFR" 2059426 NIL PFR (NIL T) -8 NIL NIL) (-846 2054751 2054995 2055320 "PFOTOOLS" 2056109 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-845 2053284 2053523 2053874 "PFOQ" 2054508 NIL PFOQ (NIL T T T) -7 NIL NIL) (-844 2051761 2051973 2052335 "PFO" 2053068 NIL PFO (NIL T T T T T) -7 NIL NIL) (-843 2048284 2051650 2051719 "PF" 2051724 NIL PF (NIL NIL) -8 NIL NIL) (-842 2045713 2046994 2047022 "PFECAT" 2047607 T PFECAT (NIL) -9 NIL 2047991) (-841 2045158 2045312 2045526 "PFECAT-" 2045531 NIL PFECAT- (NIL T) -8 NIL NIL) (-840 2043762 2044013 2044314 "PFBRU" 2044907 NIL PFBRU (NIL T T) -7 NIL NIL) (-839 2041629 2041980 2042412 "PFBR" 2043413 NIL PFBR (NIL T T T T) -7 NIL NIL) (-838 2037481 2039005 2039681 "PERM" 2040986 NIL PERM (NIL T) -8 NIL NIL) (-837 2032746 2033688 2034558 "PERMGRP" 2036644 NIL PERMGRP (NIL T) -8 NIL NIL) (-836 2030817 2031810 2031851 "PERMCAT" 2032297 NIL PERMCAT (NIL T) -9 NIL 2032602) (-835 2030472 2030513 2030636 "PERMAN" 2030770 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-834 2027912 2030041 2030172 "PENDTREE" 2030374 NIL PENDTREE (NIL T) -8 NIL NIL) (-833 2025985 2026763 2026804 "PDRING" 2027461 NIL PDRING (NIL T) -9 NIL 2027746) (-832 2025088 2025306 2025668 "PDRING-" 2025673 NIL PDRING- (NIL T T) -8 NIL NIL) (-831 2022229 2022980 2023671 "PDEPROB" 2024417 T PDEPROB (NIL) -8 NIL NIL) (-830 2019800 2020296 2020845 "PDEPACK" 2021700 T PDEPACK (NIL) -7 NIL NIL) (-829 2018712 2018902 2019153 "PDECOMP" 2019599 NIL PDECOMP (NIL T T) -7 NIL NIL) (-828 2016324 2017139 2017167 "PDECAT" 2017952 T PDECAT (NIL) -9 NIL 2018663) (-827 2016077 2016110 2016199 "PCOMP" 2016285 NIL PCOMP (NIL T T) -7 NIL NIL) (-826 2014284 2014880 2015176 "PBWLB" 2015807 NIL PBWLB (NIL T) -8 NIL NIL) (-825 2006792 2008361 2009697 "PATTERN" 2012969 NIL PATTERN (NIL T) -8 NIL NIL) (-824 2006424 2006481 2006590 "PATTERN2" 2006729 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-823 2004181 2004569 2005026 "PATTERN1" 2006013 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-822 2001576 2002130 2002611 "PATRES" 2003746 NIL PATRES (NIL T T) -8 NIL NIL) (-821 2001140 2001207 2001339 "PATRES2" 2001503 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-820 1999037 1999437 1999842 "PATMATCH" 2000809 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-819 1998574 1998757 1998798 "PATMAB" 1998905 NIL PATMAB (NIL T) -9 NIL 1998988) (-818 1997119 1997428 1997686 "PATLRES" 1998379 NIL PATLRES (NIL T T T) -8 NIL NIL) (-817 1996665 1996788 1996829 "PATAB" 1996834 NIL PATAB (NIL T) -9 NIL 1997006) (-816 1994146 1994678 1995251 "PARTPERM" 1996112 T PARTPERM (NIL) -7 NIL NIL) (-815 1993767 1993830 1993932 "PARSURF" 1994077 NIL PARSURF (NIL T) -8 NIL NIL) (-814 1993399 1993456 1993565 "PARSU2" 1993704 NIL PARSU2 (NIL T T) -7 NIL NIL) (-813 1993163 1993203 1993270 "PARSER" 1993352 T PARSER (NIL) -7 NIL NIL) (-812 1992784 1992847 1992949 "PARSCURV" 1993094 NIL PARSCURV (NIL T) -8 NIL NIL) (-811 1992416 1992473 1992582 "PARSC2" 1992721 NIL PARSC2 (NIL T T) -7 NIL NIL) (-810 1992055 1992113 1992210 "PARPCURV" 1992352 NIL PARPCURV (NIL T) -8 NIL NIL) (-809 1991687 1991744 1991853 "PARPC2" 1991992 NIL PARPC2 (NIL T T) -7 NIL NIL) (-808 1991207 1991293 1991412 "PAN2EXPR" 1991588 T PAN2EXPR (NIL) -7 NIL NIL) (-807 1990013 1990328 1990556 "PALETTE" 1990999 T PALETTE (NIL) -8 NIL NIL) (-806 1988481 1989018 1989378 "PAIR" 1989699 NIL PAIR (NIL T T) -8 NIL NIL) (-805 1982331 1987740 1987934 "PADICRC" 1988336 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-804 1975539 1981677 1981861 "PADICRAT" 1982179 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-803 1973843 1975476 1975521 "PADIC" 1975526 NIL PADIC (NIL NIL) -8 NIL NIL) (-802 1971048 1972622 1972662 "PADICCT" 1973243 NIL PADICCT (NIL NIL) -9 NIL 1973525) (-801 1970005 1970205 1970473 "PADEPAC" 1970835 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-800 1969217 1969350 1969556 "PADE" 1969867 NIL PADE (NIL T T T) -7 NIL NIL) (-799 1967228 1968060 1968375 "OWP" 1968985 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-798 1966337 1966833 1967005 "OVAR" 1967096 NIL OVAR (NIL NIL) -8 NIL NIL) (-797 1965601 1965722 1965883 "OUT" 1966196 T OUT (NIL) -7 NIL NIL) (-796 1954655 1956826 1958996 "OUTFORM" 1963451 T OUTFORM (NIL) -8 NIL NIL) (-795 1954063 1954384 1954473 "OSI" 1954586 T OSI (NIL) -8 NIL NIL) (-794 1952808 1953035 1953320 "ORTHPOL" 1953810 NIL ORTHPOL (NIL T) -7 NIL NIL) (-793 1950179 1952469 1952607 "OREUP" 1952751 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-792 1947575 1949872 1949998 "ORESUP" 1950121 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-791 1945110 1945610 1946170 "OREPCTO" 1947064 NIL OREPCTO (NIL T T) -7 NIL NIL) (-790 1939020 1941226 1941266 "OREPCAT" 1943587 NIL OREPCAT (NIL T) -9 NIL 1944690) (-789 1936168 1936950 1938007 "OREPCAT-" 1938012 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-788 1935346 1935618 1935646 "ORDSET" 1935955 T ORDSET (NIL) -9 NIL 1936119) (-787 1934865 1934987 1935180 "ORDSET-" 1935185 NIL ORDSET- (NIL T) -8 NIL NIL) (-786 1933479 1934280 1934308 "ORDRING" 1934510 T ORDRING (NIL) -9 NIL 1934634) (-785 1933124 1933218 1933362 "ORDRING-" 1933367 NIL ORDRING- (NIL T) -8 NIL NIL) (-784 1932500 1932981 1933009 "ORDMON" 1933014 T ORDMON (NIL) -9 NIL 1933035) (-783 1931662 1931809 1932004 "ORDFUNS" 1932349 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-782 1931174 1931533 1931561 "ORDFIN" 1931566 T ORDFIN (NIL) -9 NIL 1931587) (-781 1927686 1929760 1930169 "ORDCOMP" 1930798 NIL ORDCOMP (NIL T) -8 NIL NIL) (-780 1926952 1927079 1927265 "ORDCOMP2" 1927546 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-779 1923459 1924342 1925179 "OPTPROB" 1926135 T OPTPROB (NIL) -8 NIL NIL) (-778 1920301 1920930 1921624 "OPTPACK" 1922785 T OPTPACK (NIL) -7 NIL NIL) (-777 1918027 1918763 1918791 "OPTCAT" 1919606 T OPTCAT (NIL) -9 NIL 1920252) (-776 1917795 1917834 1917900 "OPQUERY" 1917981 T OPQUERY (NIL) -7 NIL NIL) (-775 1914931 1916122 1916622 "OP" 1917327 NIL OP (NIL T) -8 NIL NIL) (-774 1911696 1913728 1914097 "ONECOMP" 1914595 NIL ONECOMP (NIL T) -8 NIL NIL) (-773 1911001 1911116 1911290 "ONECOMP2" 1911568 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-772 1910420 1910526 1910656 "OMSERVER" 1910891 T OMSERVER (NIL) -7 NIL NIL) (-771 1907309 1909861 1909901 "OMSAGG" 1909962 NIL OMSAGG (NIL T) -9 NIL 1910026) (-770 1905932 1906195 1906477 "OMPKG" 1907047 T OMPKG (NIL) -7 NIL NIL) (-769 1905362 1905465 1905493 "OM" 1905792 T OM (NIL) -9 NIL NIL) (-768 1903901 1904914 1905082 "OMLO" 1905243 NIL OMLO (NIL T T) -8 NIL NIL) (-767 1902831 1902978 1903204 "OMEXPR" 1903727 NIL OMEXPR (NIL T) -7 NIL NIL) (-766 1902149 1902377 1902513 "OMERR" 1902715 T OMERR (NIL) -8 NIL NIL) (-765 1901327 1901570 1901730 "OMERRK" 1902009 T OMERRK (NIL) -8 NIL NIL) (-764 1900805 1901004 1901112 "OMENC" 1901239 T OMENC (NIL) -8 NIL NIL) (-763 1894700 1895885 1897056 "OMDEV" 1899654 T OMDEV (NIL) -8 NIL NIL) (-762 1893769 1893940 1894134 "OMCONN" 1894526 T OMCONN (NIL) -8 NIL NIL) (-761 1892385 1893371 1893399 "OINTDOM" 1893404 T OINTDOM (NIL) -9 NIL 1893425) (-760 1888147 1889377 1890092 "OFMONOID" 1891702 NIL OFMONOID (NIL T) -8 NIL NIL) (-759 1887585 1888084 1888129 "ODVAR" 1888134 NIL ODVAR (NIL T) -8 NIL NIL) (-758 1884710 1887082 1887267 "ODR" 1887460 NIL ODR (NIL T T NIL) -8 NIL NIL) (-757 1877016 1884489 1884613 "ODPOL" 1884618 NIL ODPOL (NIL T) -8 NIL NIL) (-756 1870839 1876888 1876993 "ODP" 1876998 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-755 1869605 1869820 1870095 "ODETOOLS" 1870613 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-754 1866574 1867230 1867946 "ODESYS" 1868938 NIL ODESYS (NIL T T) -7 NIL NIL) (-753 1861478 1862386 1863409 "ODERTRIC" 1865649 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-752 1860904 1860986 1861180 "ODERED" 1861390 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-751 1857806 1858354 1859029 "ODERAT" 1860327 NIL ODERAT (NIL T T) -7 NIL NIL) (-750 1854774 1855238 1855834 "ODEPRRIC" 1857335 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-749 1852643 1853212 1853721 "ODEPROB" 1854285 T ODEPROB (NIL) -8 NIL NIL) (-748 1849175 1849658 1850304 "ODEPRIM" 1852122 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-747 1848428 1848530 1848788 "ODEPAL" 1849067 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-746 1844630 1845411 1846265 "ODEPACK" 1847594 T ODEPACK (NIL) -7 NIL NIL) (-745 1843667 1843774 1844002 "ODEINT" 1844519 NIL ODEINT (NIL T T) -7 NIL NIL) (-744 1837768 1839193 1840640 "ODEIFTBL" 1842240 T ODEIFTBL (NIL) -8 NIL NIL) (-743 1833112 1833898 1834856 "ODEEF" 1836927 NIL ODEEF (NIL T T) -7 NIL NIL) (-742 1832449 1832538 1832767 "ODECONST" 1833017 NIL ODECONST (NIL T T T) -7 NIL NIL) (-741 1830607 1831240 1831268 "ODECAT" 1831871 T ODECAT (NIL) -9 NIL 1832400) (-740 1827479 1830319 1830438 "OCT" 1830520 NIL OCT (NIL T) -8 NIL NIL) (-739 1827117 1827160 1827287 "OCTCT2" 1827430 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-738 1821951 1824389 1824429 "OC" 1825525 NIL OC (NIL T) -9 NIL 1826382) (-737 1819178 1819926 1820916 "OC-" 1821010 NIL OC- (NIL T T) -8 NIL NIL) (-736 1818557 1818999 1819027 "OCAMON" 1819032 T OCAMON (NIL) -9 NIL 1819053) (-735 1818011 1818418 1818446 "OASGP" 1818451 T OASGP (NIL) -9 NIL 1818471) (-734 1817299 1817762 1817790 "OAMONS" 1817830 T OAMONS (NIL) -9 NIL 1817873) (-733 1816740 1817147 1817175 "OAMON" 1817180 T OAMON (NIL) -9 NIL 1817200) (-732 1816045 1816537 1816565 "OAGROUP" 1816570 T OAGROUP (NIL) -9 NIL 1816590) (-731 1815735 1815785 1815873 "NUMTUBE" 1815989 NIL NUMTUBE (NIL T) -7 NIL NIL) (-730 1809308 1810826 1812362 "NUMQUAD" 1814219 T NUMQUAD (NIL) -7 NIL NIL) (-729 1805064 1806052 1807077 "NUMODE" 1808303 T NUMODE (NIL) -7 NIL NIL) (-728 1802468 1803314 1803342 "NUMINT" 1804259 T NUMINT (NIL) -9 NIL 1805015) (-727 1801416 1801613 1801831 "NUMFMT" 1802270 T NUMFMT (NIL) -7 NIL NIL) (-726 1787798 1790732 1793262 "NUMERIC" 1798925 NIL NUMERIC (NIL T) -7 NIL NIL) (-725 1782199 1787251 1787345 "NTSCAT" 1787350 NIL NTSCAT (NIL T T T T) -9 NIL 1787388) (-724 1781393 1781558 1781751 "NTPOLFN" 1782038 NIL NTPOLFN (NIL T) -7 NIL NIL) (-723 1769209 1778235 1779045 "NSUP" 1780615 NIL NSUP (NIL T) -8 NIL NIL) (-722 1768845 1768902 1769009 "NSUP2" 1769146 NIL NSUP2 (NIL T T) -7 NIL NIL) (-721 1758807 1768624 1768754 "NSMP" 1768759 NIL NSMP (NIL T T) -8 NIL NIL) (-720 1757239 1757540 1757897 "NREP" 1758495 NIL NREP (NIL T) -7 NIL NIL) (-719 1755830 1756082 1756440 "NPCOEF" 1756982 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-718 1754896 1755011 1755227 "NORMRETR" 1755711 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-717 1752949 1753239 1753646 "NORMPK" 1754604 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-716 1752634 1752662 1752786 "NORMMA" 1752915 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-715 1752461 1752591 1752620 "NONE" 1752625 T NONE (NIL) -8 NIL NIL) (-714 1752250 1752279 1752348 "NONE1" 1752425 NIL NONE1 (NIL T) -7 NIL NIL) (-713 1751735 1751797 1751982 "NODE1" 1752182 NIL NODE1 (NIL T T) -7 NIL NIL) (-712 1750028 1750898 1751153 "NNI" 1751500 T NNI (NIL) -8 NIL NIL) (-711 1748448 1748761 1749125 "NLINSOL" 1749696 NIL NLINSOL (NIL T) -7 NIL NIL) (-710 1744615 1745583 1746505 "NIPROB" 1747546 T NIPROB (NIL) -8 NIL NIL) (-709 1743372 1743606 1743908 "NFINTBAS" 1744377 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-708 1742080 1742311 1742592 "NCODIV" 1743140 NIL NCODIV (NIL T T) -7 NIL NIL) (-707 1741842 1741879 1741954 "NCNTFRAC" 1742037 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-706 1740022 1740386 1740806 "NCEP" 1741467 NIL NCEP (NIL T) -7 NIL NIL) (-705 1738934 1739673 1739701 "NASRING" 1739811 T NASRING (NIL) -9 NIL 1739885) (-704 1738729 1738773 1738867 "NASRING-" 1738872 NIL NASRING- (NIL T) -8 NIL NIL) (-703 1737883 1738382 1738410 "NARNG" 1738527 T NARNG (NIL) -9 NIL 1738618) (-702 1737575 1737642 1737776 "NARNG-" 1737781 NIL NARNG- (NIL T) -8 NIL NIL) (-701 1736454 1736661 1736896 "NAGSP" 1737360 T NAGSP (NIL) -7 NIL NIL) (-700 1727878 1729524 1731159 "NAGS" 1734839 T NAGS (NIL) -7 NIL NIL) (-699 1726442 1726746 1727073 "NAGF07" 1727571 T NAGF07 (NIL) -7 NIL NIL) (-698 1721024 1722304 1723600 "NAGF04" 1725166 T NAGF04 (NIL) -7 NIL NIL) (-697 1714056 1715654 1717271 "NAGF02" 1719427 T NAGF02 (NIL) -7 NIL NIL) (-696 1709320 1710410 1711517 "NAGF01" 1712969 T NAGF01 (NIL) -7 NIL NIL) (-695 1702980 1704538 1706115 "NAGE04" 1707763 T NAGE04 (NIL) -7 NIL NIL) (-694 1694221 1696324 1698436 "NAGE02" 1700888 T NAGE02 (NIL) -7 NIL NIL) (-693 1690214 1691151 1692105 "NAGE01" 1693287 T NAGE01 (NIL) -7 NIL NIL) (-692 1688021 1688552 1689107 "NAGD03" 1689679 T NAGD03 (NIL) -7 NIL NIL) (-691 1679807 1681726 1683671 "NAGD02" 1686096 T NAGD02 (NIL) -7 NIL NIL) (-690 1673666 1675079 1676507 "NAGD01" 1678399 T NAGD01 (NIL) -7 NIL NIL) (-689 1669923 1670733 1671558 "NAGC06" 1672861 T NAGC06 (NIL) -7 NIL NIL) (-688 1668400 1668729 1669082 "NAGC05" 1669590 T NAGC05 (NIL) -7 NIL NIL) (-687 1667784 1667901 1668043 "NAGC02" 1668278 T NAGC02 (NIL) -7 NIL NIL) (-686 1666846 1667403 1667443 "NAALG" 1667522 NIL NAALG (NIL T) -9 NIL 1667583) (-685 1666681 1666710 1666800 "NAALG-" 1666805 NIL NAALG- (NIL T T) -8 NIL NIL) (-684 1660631 1661739 1662926 "MULTSQFR" 1665577 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-683 1659950 1660025 1660209 "MULTFACT" 1660543 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-682 1653144 1657055 1657107 "MTSCAT" 1658167 NIL MTSCAT (NIL T T) -9 NIL 1658681) (-681 1652856 1652910 1653002 "MTHING" 1653084 NIL MTHING (NIL T) -7 NIL NIL) (-680 1652648 1652681 1652741 "MSYSCMD" 1652816 T MSYSCMD (NIL) -7 NIL NIL) (-679 1648760 1651403 1651723 "MSET" 1652361 NIL MSET (NIL T) -8 NIL NIL) (-678 1645856 1648322 1648363 "MSETAGG" 1648368 NIL MSETAGG (NIL T) -9 NIL 1648402) (-677 1641712 1643254 1643995 "MRING" 1645159 NIL MRING (NIL T T) -8 NIL NIL) (-676 1641282 1641349 1641478 "MRF2" 1641639 NIL MRF2 (NIL T T T) -7 NIL NIL) (-675 1640900 1640935 1641079 "MRATFAC" 1641241 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-674 1638512 1638807 1639238 "MPRFF" 1640605 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-673 1632532 1638367 1638463 "MPOLY" 1638468 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-672 1632022 1632057 1632265 "MPCPF" 1632491 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-671 1631538 1631581 1631764 "MPC3" 1631973 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-670 1630739 1630820 1631039 "MPC2" 1631453 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-669 1629040 1629377 1629767 "MONOTOOL" 1630399 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-668 1628165 1628500 1628528 "MONOID" 1628805 T MONOID (NIL) -9 NIL 1628977) (-667 1627543 1627706 1627949 "MONOID-" 1627954 NIL MONOID- (NIL T) -8 NIL NIL) (-666 1618524 1624510 1624569 "MONOGEN" 1625243 NIL MONOGEN (NIL T T) -9 NIL 1625699) (-665 1615742 1616477 1617477 "MONOGEN-" 1617596 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-664 1614602 1615022 1615050 "MONADWU" 1615442 T MONADWU (NIL) -9 NIL 1615680) (-663 1613974 1614133 1614381 "MONADWU-" 1614386 NIL MONADWU- (NIL T) -8 NIL NIL) (-662 1613360 1613578 1613606 "MONAD" 1613813 T MONAD (NIL) -9 NIL 1613925) (-661 1613045 1613123 1613255 "MONAD-" 1613260 NIL MONAD- (NIL T) -8 NIL NIL) (-660 1611296 1611958 1612237 "MOEBIUS" 1612798 NIL MOEBIUS (NIL T) -8 NIL NIL) (-659 1610690 1611068 1611108 "MODULE" 1611113 NIL MODULE (NIL T) -9 NIL 1611139) (-658 1610258 1610354 1610544 "MODULE-" 1610549 NIL MODULE- (NIL T T) -8 NIL NIL) (-657 1607929 1608624 1608950 "MODRING" 1610083 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-656 1604885 1606050 1606567 "MODOP" 1607461 NIL MODOP (NIL T T) -8 NIL NIL) (-655 1603072 1603524 1603865 "MODMONOM" 1604684 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-654 1592751 1601276 1601698 "MODMON" 1602700 NIL MODMON (NIL T T) -8 NIL NIL) (-653 1589877 1591595 1591871 "MODFIELD" 1592626 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-652 1588881 1589158 1589348 "MMLFORM" 1589707 T MMLFORM (NIL) -8 NIL NIL) (-651 1588407 1588450 1588629 "MMAP" 1588832 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-650 1586644 1587421 1587461 "MLO" 1587878 NIL MLO (NIL T) -9 NIL 1588119) (-649 1584011 1584526 1585128 "MLIFT" 1586125 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-648 1583402 1583486 1583640 "MKUCFUNC" 1583922 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-647 1583001 1583071 1583194 "MKRECORD" 1583325 NIL MKRECORD (NIL T T) -7 NIL NIL) (-646 1582049 1582210 1582438 "MKFUNC" 1582812 NIL MKFUNC (NIL T) -7 NIL NIL) (-645 1581437 1581541 1581697 "MKFLCFN" 1581932 NIL MKFLCFN (NIL T) -7 NIL NIL) (-644 1580863 1581230 1581319 "MKCHSET" 1581381 NIL MKCHSET (NIL T) -8 NIL NIL) (-643 1580140 1580242 1580427 "MKBCFUNC" 1580756 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-642 1576824 1579694 1579830 "MINT" 1580024 T MINT (NIL) -8 NIL NIL) (-641 1575636 1575879 1576156 "MHROWRED" 1576579 NIL MHROWRED (NIL T) -7 NIL NIL) (-640 1570907 1574081 1574505 "MFLOAT" 1575232 T MFLOAT (NIL) -8 NIL NIL) (-639 1570264 1570340 1570511 "MFINFACT" 1570819 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-638 1566579 1567427 1568311 "MESH" 1569400 T MESH (NIL) -7 NIL NIL) (-637 1564969 1565281 1565634 "MDDFACT" 1566266 NIL MDDFACT (NIL T) -7 NIL NIL) (-636 1561812 1564129 1564170 "MDAGG" 1564425 NIL MDAGG (NIL T) -9 NIL 1564568) (-635 1551510 1561105 1561312 "MCMPLX" 1561625 T MCMPLX (NIL) -8 NIL NIL) (-634 1550651 1550797 1550997 "MCDEN" 1551359 NIL MCDEN (NIL T T) -7 NIL NIL) (-633 1548541 1548811 1549191 "MCALCFN" 1550381 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-632 1546163 1546686 1547247 "MATSTOR" 1548012 NIL MATSTOR (NIL T) -7 NIL NIL) (-631 1542172 1545538 1545785 "MATRIX" 1545948 NIL MATRIX (NIL T) -8 NIL NIL) (-630 1537941 1538645 1539381 "MATLIN" 1541529 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-629 1528139 1531277 1531353 "MATCAT" 1536191 NIL MATCAT (NIL T T T) -9 NIL 1537608) (-628 1524504 1525517 1526872 "MATCAT-" 1526877 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-627 1523106 1523259 1523590 "MATCAT2" 1524339 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-626 1521218 1521542 1521926 "MAPPKG3" 1522781 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-625 1520199 1520372 1520594 "MAPPKG2" 1521042 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-624 1518698 1518982 1519309 "MAPPKG1" 1519905 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-623 1518309 1518367 1518490 "MAPHACK3" 1518634 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-622 1517901 1517962 1518076 "MAPHACK2" 1518241 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-621 1517339 1517442 1517584 "MAPHACK1" 1517792 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-620 1515447 1516041 1516344 "MAGMA" 1517068 NIL MAGMA (NIL T) -8 NIL NIL) (-619 1511921 1513691 1514151 "M3D" 1515020 NIL M3D (NIL T) -8 NIL NIL) (-618 1506077 1510292 1510333 "LZSTAGG" 1511115 NIL LZSTAGG (NIL T) -9 NIL 1511410) (-617 1502050 1503208 1504665 "LZSTAGG-" 1504670 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-616 1499166 1499943 1500429 "LWORD" 1501596 NIL LWORD (NIL T) -8 NIL NIL) (-615 1492326 1498937 1499071 "LSQM" 1499076 NIL LSQM (NIL NIL T) -8 NIL NIL) (-614 1491550 1491689 1491917 "LSPP" 1492181 NIL LSPP (NIL T T T T) -7 NIL NIL) (-613 1489362 1489663 1490119 "LSMP" 1491239 NIL LSMP (NIL T T T T) -7 NIL NIL) (-612 1486141 1486815 1487545 "LSMP1" 1488664 NIL LSMP1 (NIL T) -7 NIL NIL) (-611 1480068 1485310 1485351 "LSAGG" 1485413 NIL LSAGG (NIL T) -9 NIL 1485491) (-610 1476763 1477687 1478900 "LSAGG-" 1478905 NIL LSAGG- (NIL T T) -8 NIL NIL) (-609 1474389 1475907 1476156 "LPOLY" 1476558 NIL LPOLY (NIL T T) -8 NIL NIL) (-608 1473971 1474056 1474179 "LPEFRAC" 1474298 NIL LPEFRAC (NIL T) -7 NIL NIL) (-607 1472318 1473065 1473318 "LO" 1473803 NIL LO (NIL T T T) -8 NIL NIL) (-606 1471972 1472084 1472112 "LOGIC" 1472223 T LOGIC (NIL) -9 NIL 1472303) (-605 1471834 1471857 1471928 "LOGIC-" 1471933 NIL LOGIC- (NIL T) -8 NIL NIL) (-604 1471027 1471167 1471360 "LODOOPS" 1471690 NIL LODOOPS (NIL T T) -7 NIL NIL) (-603 1468445 1470944 1471009 "LODO" 1471014 NIL LODO (NIL T NIL) -8 NIL NIL) (-602 1466991 1467226 1467577 "LODOF" 1468192 NIL LODOF (NIL T T) -7 NIL NIL) (-601 1463411 1465847 1465887 "LODOCAT" 1466319 NIL LODOCAT (NIL T) -9 NIL 1466530) (-600 1463145 1463203 1463329 "LODOCAT-" 1463334 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-599 1460459 1462986 1463104 "LODO2" 1463109 NIL LODO2 (NIL T T) -8 NIL NIL) (-598 1457888 1460396 1460441 "LODO1" 1460446 NIL LODO1 (NIL T) -8 NIL NIL) (-597 1456751 1456916 1457227 "LODEEF" 1457711 NIL LODEEF (NIL T T T) -7 NIL NIL) (-596 1452038 1454882 1454923 "LNAGG" 1455870 NIL LNAGG (NIL T) -9 NIL 1456314) (-595 1451185 1451399 1451741 "LNAGG-" 1451746 NIL LNAGG- (NIL T T) -8 NIL NIL) (-594 1447350 1448112 1448750 "LMOPS" 1450601 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-593 1446748 1447110 1447150 "LMODULE" 1447210 NIL LMODULE (NIL T) -9 NIL 1447252) (-592 1443994 1446393 1446516 "LMDICT" 1446658 NIL LMDICT (NIL T) -8 NIL NIL) (-591 1437221 1442940 1443238 "LIST" 1443729 NIL LIST (NIL T) -8 NIL NIL) (-590 1436746 1436820 1436959 "LIST3" 1437141 NIL LIST3 (NIL T T T) -7 NIL NIL) (-589 1435753 1435931 1436159 "LIST2" 1436564 NIL LIST2 (NIL T T) -7 NIL NIL) (-588 1433887 1434199 1434598 "LIST2MAP" 1435400 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-587 1432600 1433280 1433320 "LINEXP" 1433573 NIL LINEXP (NIL T) -9 NIL 1433721) (-586 1431247 1431507 1431804 "LINDEP" 1432352 NIL LINDEP (NIL T T) -7 NIL NIL) (-585 1428014 1428733 1429510 "LIMITRF" 1430502 NIL LIMITRF (NIL T) -7 NIL NIL) (-584 1426294 1426589 1427004 "LIMITPS" 1427709 NIL LIMITPS (NIL T T) -7 NIL NIL) (-583 1420749 1425805 1426033 "LIE" 1426115 NIL LIE (NIL T T) -8 NIL NIL) (-582 1419800 1420243 1420283 "LIECAT" 1420423 NIL LIECAT (NIL T) -9 NIL 1420574) (-581 1419641 1419668 1419756 "LIECAT-" 1419761 NIL LIECAT- (NIL T T) -8 NIL NIL) (-580 1412253 1419090 1419255 "LIB" 1419496 T LIB (NIL) -8 NIL NIL) (-579 1407890 1408771 1409706 "LGROBP" 1411370 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-578 1405756 1406030 1406392 "LF" 1407611 NIL LF (NIL T T) -7 NIL NIL) (-577 1404596 1405288 1405316 "LFCAT" 1405523 T LFCAT (NIL) -9 NIL 1405662) (-576 1401508 1402134 1402820 "LEXTRIPK" 1403962 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-575 1398214 1399078 1399581 "LEXP" 1401088 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-574 1396612 1396925 1397326 "LEADCDET" 1397896 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-573 1395808 1395882 1396109 "LAZM3PK" 1396533 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-572 1390725 1393887 1394424 "LAUPOL" 1395321 NIL LAUPOL (NIL T T) -8 NIL NIL) (-571 1390292 1390336 1390503 "LAPLACE" 1390675 NIL LAPLACE (NIL T T) -7 NIL NIL) (-570 1388220 1389393 1389644 "LA" 1390125 NIL LA (NIL T T T) -8 NIL NIL) (-569 1387283 1387877 1387917 "LALG" 1387978 NIL LALG (NIL T) -9 NIL 1388036) (-568 1386998 1387057 1387192 "LALG-" 1387197 NIL LALG- (NIL T T) -8 NIL NIL) (-567 1385908 1386095 1386392 "KOVACIC" 1386798 NIL KOVACIC (NIL T T) -7 NIL NIL) (-566 1385743 1385767 1385808 "KONVERT" 1385870 NIL KONVERT (NIL T) -9 NIL NIL) (-565 1385578 1385602 1385643 "KOERCE" 1385705 NIL KOERCE (NIL T) -9 NIL NIL) (-564 1383312 1384072 1384465 "KERNEL" 1385217 NIL KERNEL (NIL T) -8 NIL NIL) (-563 1382814 1382895 1383025 "KERNEL2" 1383226 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-562 1376666 1381354 1381408 "KDAGG" 1381785 NIL KDAGG (NIL T T) -9 NIL 1381991) (-561 1376195 1376319 1376524 "KDAGG-" 1376529 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-560 1369370 1375856 1376011 "KAFILE" 1376073 NIL KAFILE (NIL T) -8 NIL NIL) (-559 1363825 1368881 1369109 "JORDAN" 1369191 NIL JORDAN (NIL T T) -8 NIL NIL) (-558 1360125 1362031 1362085 "IXAGG" 1363014 NIL IXAGG (NIL T T) -9 NIL 1363473) (-557 1359044 1359350 1359769 "IXAGG-" 1359774 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-556 1354629 1358966 1359025 "IVECTOR" 1359030 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-555 1353395 1353632 1353898 "ITUPLE" 1354396 NIL ITUPLE (NIL T) -8 NIL NIL) (-554 1351831 1352008 1352314 "ITRIGMNP" 1353217 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-553 1350576 1350780 1351063 "ITFUN3" 1351607 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-552 1350208 1350265 1350374 "ITFUN2" 1350513 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-551 1348010 1349081 1349378 "ITAYLOR" 1349943 NIL ITAYLOR (NIL T) -8 NIL NIL) (-550 1336998 1342196 1343355 "ISUPS" 1346883 NIL ISUPS (NIL T) -8 NIL NIL) (-549 1336102 1336242 1336478 "ISUMP" 1336845 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-548 1331366 1335903 1335982 "ISTRING" 1336055 NIL ISTRING (NIL NIL) -8 NIL NIL) (-547 1330579 1330660 1330875 "IRURPK" 1331280 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-546 1329515 1329716 1329956 "IRSN" 1330359 T IRSN (NIL) -7 NIL NIL) (-545 1327550 1327905 1328340 "IRRF2F" 1329153 NIL IRRF2F (NIL T) -7 NIL NIL) (-544 1327297 1327335 1327411 "IRREDFFX" 1327506 NIL IRREDFFX (NIL T) -7 NIL NIL) (-543 1325912 1326171 1326470 "IROOT" 1327030 NIL IROOT (NIL T) -7 NIL NIL) (-542 1322550 1323601 1324291 "IR" 1325254 NIL IR (NIL T) -8 NIL NIL) (-541 1320163 1320658 1321224 "IR2" 1322028 NIL IR2 (NIL T T) -7 NIL NIL) (-540 1319239 1319352 1319572 "IR2F" 1320046 NIL IR2F (NIL T T) -7 NIL NIL) (-539 1319030 1319064 1319124 "IPRNTPK" 1319199 T IPRNTPK (NIL) -7 NIL NIL) (-538 1315584 1318919 1318988 "IPF" 1318993 NIL IPF (NIL NIL) -8 NIL NIL) (-537 1313901 1315509 1315566 "IPADIC" 1315571 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-536 1313400 1313458 1313647 "INVLAPLA" 1313837 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-535 1303049 1305402 1307788 "INTTR" 1311064 NIL INTTR (NIL T T) -7 NIL NIL) (-534 1299397 1300138 1301001 "INTTOOLS" 1302235 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-533 1298983 1299074 1299191 "INTSLPE" 1299300 T INTSLPE (NIL) -7 NIL NIL) (-532 1296933 1298906 1298965 "INTRVL" 1298970 NIL INTRVL (NIL T) -8 NIL NIL) (-531 1294540 1295052 1295626 "INTRF" 1296418 NIL INTRF (NIL T) -7 NIL NIL) (-530 1293955 1294052 1294193 "INTRET" 1294438 NIL INTRET (NIL T) -7 NIL NIL) (-529 1291957 1292346 1292815 "INTRAT" 1293563 NIL INTRAT (NIL T T) -7 NIL NIL) (-528 1289190 1289773 1290398 "INTPM" 1291442 NIL INTPM (NIL T T) -7 NIL NIL) (-527 1285899 1286498 1287242 "INTPAF" 1288576 NIL INTPAF (NIL T T T) -7 NIL NIL) (-526 1281142 1282088 1283123 "INTPACK" 1284884 T INTPACK (NIL) -7 NIL NIL) (-525 1277996 1280871 1280998 "INT" 1281035 T INT (NIL) -8 NIL NIL) (-524 1277248 1277400 1277608 "INTHERTR" 1277838 NIL INTHERTR (NIL T T) -7 NIL NIL) (-523 1276687 1276767 1276955 "INTHERAL" 1277162 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-522 1274533 1274976 1275433 "INTHEORY" 1276250 T INTHEORY (NIL) -7 NIL NIL) (-521 1265855 1267476 1269254 "INTG0" 1272885 NIL INTG0 (NIL T T T) -7 NIL NIL) (-520 1246428 1251218 1256028 "INTFTBL" 1261065 T INTFTBL (NIL) -8 NIL NIL) (-519 1245677 1245815 1245988 "INTFACT" 1246287 NIL INTFACT (NIL T) -7 NIL NIL) (-518 1243068 1243514 1244077 "INTEF" 1245231 NIL INTEF (NIL T T) -7 NIL NIL) (-517 1241530 1242279 1242307 "INTDOM" 1242608 T INTDOM (NIL) -9 NIL 1242815) (-516 1240899 1241073 1241315 "INTDOM-" 1241320 NIL INTDOM- (NIL T) -8 NIL NIL) (-515 1237392 1239324 1239378 "INTCAT" 1240177 NIL INTCAT (NIL T) -9 NIL 1240496) (-514 1236865 1236967 1237095 "INTBIT" 1237284 T INTBIT (NIL) -7 NIL NIL) (-513 1235540 1235694 1236007 "INTALG" 1236710 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-512 1234997 1235087 1235257 "INTAF" 1235444 NIL INTAF (NIL T T) -7 NIL NIL) (-511 1228451 1234807 1234947 "INTABL" 1234952 NIL INTABL (NIL T T T) -8 NIL NIL) (-510 1223402 1226131 1226159 "INS" 1227127 T INS (NIL) -9 NIL 1227808) (-509 1220642 1221413 1222387 "INS-" 1222460 NIL INS- (NIL T) -8 NIL NIL) (-508 1219421 1219648 1219945 "INPSIGN" 1220395 NIL INPSIGN (NIL T T) -7 NIL NIL) (-507 1218539 1218656 1218853 "INPRODPF" 1219301 NIL INPRODPF (NIL T T) -7 NIL NIL) (-506 1217433 1217550 1217787 "INPRODFF" 1218419 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-505 1216433 1216585 1216845 "INNMFACT" 1217269 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-504 1215630 1215727 1215915 "INMODGCD" 1216332 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-503 1214139 1214383 1214707 "INFSP" 1215375 NIL INFSP (NIL T T T) -7 NIL NIL) (-502 1213323 1213440 1213623 "INFPROD0" 1214019 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-501 1210333 1211492 1211983 "INFORM" 1212840 T INFORM (NIL) -8 NIL NIL) (-500 1209943 1210003 1210101 "INFORM1" 1210268 NIL INFORM1 (NIL T) -7 NIL NIL) (-499 1209466 1209555 1209669 "INFINITY" 1209849 T INFINITY (NIL) -7 NIL NIL) (-498 1208083 1208332 1208653 "INEP" 1209214 NIL INEP (NIL T T T) -7 NIL NIL) (-497 1207359 1207980 1208045 "INDE" 1208050 NIL INDE (NIL T) -8 NIL NIL) (-496 1206923 1206991 1207108 "INCRMAPS" 1207286 NIL INCRMAPS (NIL T) -7 NIL NIL) (-495 1202234 1203159 1204103 "INBFF" 1206011 NIL INBFF (NIL T) -7 NIL NIL) (-494 1198729 1202079 1202182 "IMATRIX" 1202187 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-493 1197441 1197564 1197879 "IMATQF" 1198585 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-492 1195661 1195888 1196225 "IMATLIN" 1197197 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-491 1190287 1195585 1195643 "ILIST" 1195648 NIL ILIST (NIL T NIL) -8 NIL NIL) (-490 1188240 1190147 1190260 "IIARRAY2" 1190265 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-489 1183608 1188151 1188215 "IFF" 1188220 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-488 1178651 1182900 1183088 "IFARRAY" 1183465 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-487 1177858 1178555 1178628 "IFAMON" 1178633 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-486 1177442 1177507 1177561 "IEVALAB" 1177768 NIL IEVALAB (NIL T T) -9 NIL NIL) (-485 1177117 1177185 1177345 "IEVALAB-" 1177350 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-484 1176775 1177031 1177094 "IDPO" 1177099 NIL IDPO (NIL T T) -8 NIL NIL) (-483 1176052 1176664 1176739 "IDPOAMS" 1176744 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-482 1175386 1175941 1176016 "IDPOAM" 1176021 NIL IDPOAM (NIL T T) -8 NIL NIL) (-481 1174472 1174722 1174775 "IDPC" 1175188 NIL IDPC (NIL T T) -9 NIL 1175337) (-480 1173968 1174364 1174437 "IDPAM" 1174442 NIL IDPAM (NIL T T) -8 NIL NIL) (-479 1173371 1173860 1173933 "IDPAG" 1173938 NIL IDPAG (NIL T T) -8 NIL NIL) (-478 1169626 1170474 1171369 "IDECOMP" 1172528 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-477 1162499 1163549 1164596 "IDEAL" 1168662 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-476 1161663 1161775 1161974 "ICDEN" 1162383 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-475 1160762 1161143 1161290 "ICARD" 1161536 T ICARD (NIL) -8 NIL NIL) (-474 1158834 1159147 1159550 "IBPTOOLS" 1160439 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-473 1154448 1158454 1158567 "IBITS" 1158753 NIL IBITS (NIL NIL) -8 NIL NIL) (-472 1151171 1151747 1152442 "IBATOOL" 1153865 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-471 1148951 1149412 1149945 "IBACHIN" 1150706 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-470 1146828 1148797 1148900 "IARRAY2" 1148905 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-469 1142981 1146754 1146811 "IARRAY1" 1146816 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-468 1136919 1141399 1141877 "IAN" 1142523 T IAN (NIL) -8 NIL NIL) (-467 1136430 1136487 1136660 "IALGFACT" 1136856 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-466 1135958 1136071 1136099 "HYPCAT" 1136306 T HYPCAT (NIL) -9 NIL NIL) (-465 1135496 1135613 1135799 "HYPCAT-" 1135804 NIL HYPCAT- (NIL T) -8 NIL NIL) (-464 1132176 1133507 1133548 "HOAGG" 1134529 NIL HOAGG (NIL T) -9 NIL 1135208) (-463 1130770 1131169 1131695 "HOAGG-" 1131700 NIL HOAGG- (NIL T T) -8 NIL NIL) (-462 1124600 1130211 1130377 "HEXADEC" 1130624 T HEXADEC (NIL) -8 NIL NIL) (-461 1123348 1123570 1123833 "HEUGCD" 1124377 NIL HEUGCD (NIL T) -7 NIL NIL) (-460 1122451 1123185 1123315 "HELLFDIV" 1123320 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-459 1120679 1122228 1122316 "HEAP" 1122395 NIL HEAP (NIL T) -8 NIL NIL) (-458 1114546 1120594 1120656 "HDP" 1120661 NIL HDP (NIL NIL T) -8 NIL NIL) (-457 1108258 1114183 1114334 "HDMP" 1114447 NIL HDMP (NIL NIL T) -8 NIL NIL) (-456 1107583 1107722 1107886 "HB" 1108114 T HB (NIL) -7 NIL NIL) (-455 1101080 1107429 1107533 "HASHTBL" 1107538 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-454 1098833 1100708 1100887 "HACKPI" 1100921 T HACKPI (NIL) -8 NIL NIL) (-453 1094529 1098687 1098799 "GTSET" 1098804 NIL GTSET (NIL T T T T) -8 NIL NIL) (-452 1088055 1094407 1094505 "GSTBL" 1094510 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-451 1080288 1087091 1087355 "GSERIES" 1087846 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-450 1079311 1079764 1079792 "GROUP" 1080053 T GROUP (NIL) -9 NIL 1080212) (-449 1078427 1078650 1078994 "GROUP-" 1078999 NIL GROUP- (NIL T) -8 NIL NIL) (-448 1076796 1077115 1077502 "GROEBSOL" 1078104 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-447 1075737 1075999 1076050 "GRMOD" 1076579 NIL GRMOD (NIL T T) -9 NIL 1076747) (-446 1075505 1075541 1075669 "GRMOD-" 1075674 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-445 1070831 1071859 1072859 "GRIMAGE" 1074525 T GRIMAGE (NIL) -8 NIL NIL) (-444 1069298 1069558 1069882 "GRDEF" 1070527 T GRDEF (NIL) -7 NIL NIL) (-443 1068742 1068858 1068999 "GRAY" 1069177 T GRAY (NIL) -7 NIL NIL) (-442 1067976 1068356 1068407 "GRALG" 1068560 NIL GRALG (NIL T T) -9 NIL 1068652) (-441 1067637 1067710 1067873 "GRALG-" 1067878 NIL GRALG- (NIL T T T) -8 NIL NIL) (-440 1064445 1067226 1067402 "GPOLSET" 1067544 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-439 1063801 1063858 1064115 "GOSPER" 1064382 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-438 1059560 1060239 1060765 "GMODPOL" 1063500 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-437 1058565 1058749 1058987 "GHENSEL" 1059372 NIL GHENSEL (NIL T T) -7 NIL NIL) (-436 1052631 1053474 1054500 "GENUPS" 1057649 NIL GENUPS (NIL T T) -7 NIL NIL) (-435 1052328 1052379 1052468 "GENUFACT" 1052574 NIL GENUFACT (NIL T) -7 NIL NIL) (-434 1051740 1051817 1051982 "GENPGCD" 1052246 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-433 1051214 1051249 1051462 "GENMFACT" 1051699 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-432 1049782 1050037 1050344 "GENEEZ" 1050957 NIL GENEEZ (NIL T T) -7 NIL NIL) (-431 1043656 1049395 1049556 "GDMP" 1049705 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-430 1033036 1037427 1038533 "GCNAALG" 1042639 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-429 1031458 1032330 1032358 "GCDDOM" 1032613 T GCDDOM (NIL) -9 NIL 1032770) (-428 1030928 1031055 1031270 "GCDDOM-" 1031275 NIL GCDDOM- (NIL T) -8 NIL NIL) (-427 1029600 1029785 1030089 "GB" 1030707 NIL GB (NIL T T T T) -7 NIL NIL) (-426 1018220 1020546 1022938 "GBINTERN" 1027291 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-425 1016057 1016349 1016770 "GBF" 1017895 NIL GBF (NIL T T T T) -7 NIL NIL) (-424 1014838 1015003 1015270 "GBEUCLID" 1015873 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-423 1014187 1014312 1014461 "GAUSSFAC" 1014709 T GAUSSFAC (NIL) -7 NIL NIL) (-422 1012564 1012866 1013179 "GALUTIL" 1013906 NIL GALUTIL (NIL T) -7 NIL NIL) (-421 1010881 1011155 1011478 "GALPOLYU" 1012291 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-420 1008270 1008560 1008965 "GALFACTU" 1010578 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-419 1000076 1001575 1003183 "GALFACT" 1006702 NIL GALFACT (NIL T) -7 NIL NIL) (-418 997464 998122 998150 "FVFUN" 999306 T FVFUN (NIL) -9 NIL 1000026) (-417 996730 996912 996940 "FVC" 997231 T FVC (NIL) -9 NIL 997414) (-416 996372 996527 996608 "FUNCTION" 996682 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-415 994042 994593 995082 "FT" 995903 T FT (NIL) -8 NIL NIL) (-414 992860 993343 993546 "FTEM" 993859 T FTEM (NIL) -8 NIL NIL) (-413 991125 991413 991815 "FSUPFACT" 992552 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-412 989522 989811 990143 "FST" 990813 T FST (NIL) -8 NIL NIL) (-411 988697 988803 988997 "FSRED" 989404 NIL FSRED (NIL T T) -7 NIL NIL) (-410 987376 987631 987985 "FSPRMELT" 988412 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-409 984461 984899 985398 "FSPECF" 986939 NIL FSPECF (NIL T T) -7 NIL NIL) (-408 966835 975392 975432 "FS" 979270 NIL FS (NIL T) -9 NIL 981552) (-407 955485 958475 962531 "FS-" 962828 NIL FS- (NIL T T) -8 NIL NIL) (-406 955001 955055 955231 "FSINT" 955426 NIL FSINT (NIL T T) -7 NIL NIL) (-405 953282 953994 954297 "FSERIES" 954780 NIL FSERIES (NIL T T) -8 NIL NIL) (-404 952300 952416 952646 "FSCINT" 953162 NIL FSCINT (NIL T T) -7 NIL NIL) (-403 948535 951245 951286 "FSAGG" 951656 NIL FSAGG (NIL T) -9 NIL 951915) (-402 946297 946898 947694 "FSAGG-" 947789 NIL FSAGG- (NIL T T) -8 NIL NIL) (-401 945339 945482 945709 "FSAGG2" 946150 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-400 942998 943277 943830 "FS2UPS" 945057 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-399 942584 942627 942780 "FS2" 942949 NIL FS2 (NIL T T T T) -7 NIL NIL) (-398 941444 941615 941923 "FS2EXPXP" 942409 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-397 940870 940985 941137 "FRUTIL" 941324 NIL FRUTIL (NIL T) -7 NIL NIL) (-396 932290 936369 937725 "FR" 939546 NIL FR (NIL T) -8 NIL NIL) (-395 927367 930010 930050 "FRNAALG" 931446 NIL FRNAALG (NIL T) -9 NIL 932053) (-394 923045 924116 925391 "FRNAALG-" 926141 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-393 922683 922726 922853 "FRNAAF2" 922996 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-392 921048 921540 921834 "FRMOD" 922496 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-391 918770 919439 919755 "FRIDEAL" 920839 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-390 917969 918056 918343 "FRIDEAL2" 918677 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-389 917227 917635 917676 "FRETRCT" 917681 NIL FRETRCT (NIL T) -9 NIL 917852) (-388 916339 916570 916921 "FRETRCT-" 916926 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-387 913549 914769 914828 "FRAMALG" 915710 NIL FRAMALG (NIL T T) -9 NIL 916002) (-386 911682 912138 912768 "FRAMALG-" 912991 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-385 905584 911157 911433 "FRAC" 911438 NIL FRAC (NIL T) -8 NIL NIL) (-384 905220 905277 905384 "FRAC2" 905521 NIL FRAC2 (NIL T T) -7 NIL NIL) (-383 904856 904913 905020 "FR2" 905157 NIL FR2 (NIL T T) -7 NIL NIL) (-382 899530 902443 902471 "FPS" 903590 T FPS (NIL) -9 NIL 904146) (-381 898979 899088 899252 "FPS-" 899398 NIL FPS- (NIL T) -8 NIL NIL) (-380 896428 898125 898153 "FPC" 898378 T FPC (NIL) -9 NIL 898520) (-379 896221 896261 896358 "FPC-" 896363 NIL FPC- (NIL T) -8 NIL NIL) (-378 895100 895710 895751 "FPATMAB" 895756 NIL FPATMAB (NIL T) -9 NIL 895908) (-377 892800 893276 893702 "FPARFRAC" 894737 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-376 888193 888692 889374 "FORTRAN" 892232 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-375 885909 886409 886948 "FORT" 887674 T FORT (NIL) -7 NIL NIL) (-374 883585 884147 884175 "FORTFN" 885235 T FORTFN (NIL) -9 NIL 885859) (-373 883349 883399 883427 "FORTCAT" 883486 T FORTCAT (NIL) -9 NIL 883548) (-372 881409 881892 882291 "FORMULA" 882970 T FORMULA (NIL) -8 NIL NIL) (-371 881197 881227 881296 "FORMULA1" 881373 NIL FORMULA1 (NIL T) -7 NIL NIL) (-370 880720 880772 880945 "FORDER" 881139 NIL FORDER (NIL T T T T) -7 NIL NIL) (-369 879816 879980 880173 "FOP" 880547 T FOP (NIL) -7 NIL NIL) (-368 878424 879096 879270 "FNLA" 879698 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-367 877093 877482 877510 "FNCAT" 878082 T FNCAT (NIL) -9 NIL 878375) (-366 876659 877052 877080 "FNAME" 877085 T FNAME (NIL) -8 NIL NIL) (-365 875319 876292 876320 "FMTC" 876325 T FMTC (NIL) -9 NIL 876360) (-364 871637 872844 873472 "FMONOID" 874724 NIL FMONOID (NIL T) -8 NIL NIL) (-363 870857 871380 871528 "FM" 871533 NIL FM (NIL T T) -8 NIL NIL) (-362 868281 868927 868955 "FMFUN" 870099 T FMFUN (NIL) -9 NIL 870807) (-361 867550 867731 867759 "FMC" 868049 T FMC (NIL) -9 NIL 868231) (-360 864780 865614 865667 "FMCAT" 866849 NIL FMCAT (NIL T T) -9 NIL 867343) (-359 863675 864548 864647 "FM1" 864725 NIL FM1 (NIL T T) -8 NIL NIL) (-358 861449 861865 862359 "FLOATRP" 863226 NIL FLOATRP (NIL T) -7 NIL NIL) (-357 854935 859105 859735 "FLOAT" 860839 T FLOAT (NIL) -8 NIL NIL) (-356 852373 852873 853451 "FLOATCP" 854402 NIL FLOATCP (NIL T) -7 NIL NIL) (-355 851162 852010 852050 "FLINEXP" 852055 NIL FLINEXP (NIL T) -9 NIL 852148) (-354 850317 850552 850879 "FLINEXP-" 850884 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-353 849393 849537 849761 "FLASORT" 850169 NIL FLASORT (NIL T T) -7 NIL NIL) (-352 846612 847454 847506 "FLALG" 848733 NIL FLALG (NIL T T) -9 NIL 849200) (-351 840397 844099 844140 "FLAGG" 845402 NIL FLAGG (NIL T) -9 NIL 846054) (-350 839123 839462 839952 "FLAGG-" 839957 NIL FLAGG- (NIL T T) -8 NIL NIL) (-349 838165 838308 838535 "FLAGG2" 838976 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-348 835138 836156 836215 "FINRALG" 837343 NIL FINRALG (NIL T T) -9 NIL 837851) (-347 834298 834527 834866 "FINRALG-" 834871 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-346 833705 833918 833946 "FINITE" 834142 T FINITE (NIL) -9 NIL 834249) (-345 826165 828326 828366 "FINAALG" 832033 NIL FINAALG (NIL T) -9 NIL 833486) (-344 821506 822547 823691 "FINAALG-" 825070 NIL FINAALG- (NIL T T) -8 NIL NIL) (-343 820901 821261 821364 "FILE" 821436 NIL FILE (NIL T) -8 NIL NIL) (-342 819586 819898 819952 "FILECAT" 820636 NIL FILECAT (NIL T T) -9 NIL 820852) (-341 817449 819005 819033 "FIELD" 819073 T FIELD (NIL) -9 NIL 819153) (-340 816069 816454 816965 "FIELD-" 816970 NIL FIELD- (NIL T) -8 NIL NIL) (-339 813884 814706 815052 "FGROUP" 815756 NIL FGROUP (NIL T) -8 NIL NIL) (-338 812974 813138 813358 "FGLMICPK" 813716 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-337 808776 812899 812956 "FFX" 812961 NIL FFX (NIL T NIL) -8 NIL NIL) (-336 808377 808438 808573 "FFSLPE" 808709 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-335 804370 805149 805945 "FFPOLY" 807613 NIL FFPOLY (NIL T) -7 NIL NIL) (-334 803874 803910 804119 "FFPOLY2" 804328 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-333 799695 803793 803856 "FFP" 803861 NIL FFP (NIL T NIL) -8 NIL NIL) (-332 795063 799606 799670 "FF" 799675 NIL FF (NIL NIL NIL) -8 NIL NIL) (-331 790159 794406 794596 "FFNBX" 794917 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-330 785068 789294 789552 "FFNBP" 790013 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-329 779671 784352 784563 "FFNB" 784901 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-328 778503 778701 779016 "FFINTBAS" 779468 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-327 774727 776967 776995 "FFIELDC" 777615 T FFIELDC (NIL) -9 NIL 777991) (-326 773390 773760 774257 "FFIELDC-" 774262 NIL FFIELDC- (NIL T) -8 NIL NIL) (-325 772960 773005 773129 "FFHOM" 773332 NIL FFHOM (NIL T T T) -7 NIL NIL) (-324 770658 771142 771659 "FFF" 772475 NIL FFF (NIL T) -7 NIL NIL) (-323 766246 770400 770501 "FFCGX" 770601 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-322 761848 765978 766085 "FFCGP" 766189 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-321 757001 761575 761683 "FFCG" 761784 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-320 738947 748070 748156 "FFCAT" 753321 NIL FFCAT (NIL T T T) -9 NIL 754808) (-319 734145 735192 736506 "FFCAT-" 737736 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-318 733556 733599 733834 "FFCAT2" 734096 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-317 722756 726546 727763 "FEXPR" 732411 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-316 721756 722191 722232 "FEVALAB" 722316 NIL FEVALAB (NIL T) -9 NIL 722577) (-315 720915 721125 721463 "FEVALAB-" 721468 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-314 719508 720298 720501 "FDIV" 720814 NIL FDIV (NIL T T T T) -8 NIL NIL) (-313 716575 717290 717405 "FDIVCAT" 718973 NIL FDIVCAT (NIL T T T T) -9 NIL 719410) (-312 716337 716364 716534 "FDIVCAT-" 716539 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-311 715557 715644 715921 "FDIV2" 716244 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-310 714243 714502 714791 "FCPAK1" 715288 T FCPAK1 (NIL) -7 NIL NIL) (-309 713371 713743 713884 "FCOMP" 714134 NIL FCOMP (NIL T) -8 NIL NIL) (-308 697006 700420 703981 "FC" 709830 T FC (NIL) -8 NIL NIL) (-307 689602 693648 693688 "FAXF" 695490 NIL FAXF (NIL T) -9 NIL 696181) (-306 686881 687536 688361 "FAXF-" 688826 NIL FAXF- (NIL T T) -8 NIL NIL) (-305 681981 686257 686433 "FARRAY" 686738 NIL FARRAY (NIL T) -8 NIL NIL) (-304 677372 679443 679495 "FAMR" 680507 NIL FAMR (NIL T T) -9 NIL 680967) (-303 676263 676565 676999 "FAMR-" 677004 NIL FAMR- (NIL T T T) -8 NIL NIL) (-302 675459 676185 676238 "FAMONOID" 676243 NIL FAMONOID (NIL T) -8 NIL NIL) (-301 673292 673976 674029 "FAMONC" 674970 NIL FAMONC (NIL T T) -9 NIL 675355) (-300 671984 673046 673183 "FAGROUP" 673188 NIL FAGROUP (NIL T) -8 NIL NIL) (-299 669787 670106 670508 "FACUTIL" 671665 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-298 668886 669071 669293 "FACTFUNC" 669597 NIL FACTFUNC (NIL T) -7 NIL NIL) (-297 661206 668137 668349 "EXPUPXS" 668742 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-296 658689 659229 659815 "EXPRTUBE" 660640 T EXPRTUBE (NIL) -7 NIL NIL) (-295 654883 655475 656212 "EXPRODE" 658028 NIL EXPRODE (NIL T T) -7 NIL NIL) (-294 640042 653542 653968 "EXPR" 654489 NIL EXPR (NIL T) -8 NIL NIL) (-293 634470 635057 635869 "EXPR2UPS" 639340 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-292 634106 634163 634270 "EXPR2" 634407 NIL EXPR2 (NIL T T) -7 NIL NIL) (-291 625460 633243 633538 "EXPEXPAN" 633944 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-290 625287 625417 625446 "EXIT" 625451 T EXIT (NIL) -8 NIL NIL) (-289 624914 624976 625089 "EVALCYC" 625219 NIL EVALCYC (NIL T) -7 NIL NIL) (-288 624455 624573 624614 "EVALAB" 624784 NIL EVALAB (NIL T) -9 NIL 624888) (-287 623936 624058 624279 "EVALAB-" 624284 NIL EVALAB- (NIL T T) -8 NIL NIL) (-286 621399 622711 622739 "EUCDOM" 623294 T EUCDOM (NIL) -9 NIL 623644) (-285 619804 620246 620836 "EUCDOM-" 620841 NIL EUCDOM- (NIL T) -8 NIL NIL) (-284 607382 610130 612870 "ESTOOLS" 617084 T ESTOOLS (NIL) -7 NIL NIL) (-283 607018 607075 607182 "ESTOOLS2" 607319 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-282 606769 606811 606891 "ESTOOLS1" 606970 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-281 600707 602431 602459 "ES" 605223 T ES (NIL) -9 NIL 606629) (-280 595654 596941 598758 "ES-" 598922 NIL ES- (NIL T) -8 NIL NIL) (-279 592029 592789 593569 "ESCONT" 594894 T ESCONT (NIL) -7 NIL NIL) (-278 591774 591806 591888 "ESCONT1" 591991 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-277 591449 591499 591599 "ES2" 591718 NIL ES2 (NIL T T) -7 NIL NIL) (-276 591079 591137 591246 "ES1" 591385 NIL ES1 (NIL T T) -7 NIL NIL) (-275 590295 590424 590600 "ERROR" 590923 T ERROR (NIL) -7 NIL NIL) (-274 583798 590154 590245 "EQTBL" 590250 NIL EQTBL (NIL T T) -8 NIL NIL) (-273 576235 579116 580563 "EQ" 582384 NIL -2473 (NIL T) -8 NIL NIL) (-272 575867 575924 576033 "EQ2" 576172 NIL EQ2 (NIL T T) -7 NIL NIL) (-271 571159 572205 573298 "EP" 574806 NIL EP (NIL T) -7 NIL NIL) (-270 569742 570042 570359 "ENV" 570862 T ENV (NIL) -8 NIL NIL) (-269 568902 569466 569494 "ENTIRER" 569499 T ENTIRER (NIL) -9 NIL 569544) (-268 565358 566857 567227 "EMR" 568701 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-267 564502 564687 564741 "ELTAGG" 565121 NIL ELTAGG (NIL T T) -9 NIL 565332) (-266 564221 564283 564424 "ELTAGG-" 564429 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-265 564010 564039 564093 "ELTAB" 564177 NIL ELTAB (NIL T T) -9 NIL NIL) (-264 563136 563282 563481 "ELFUTS" 563861 NIL ELFUTS (NIL T T) -7 NIL NIL) (-263 562878 562934 562962 "ELEMFUN" 563067 T ELEMFUN (NIL) -9 NIL NIL) (-262 562748 562769 562837 "ELEMFUN-" 562842 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-261 557640 560849 560890 "ELAGG" 561830 NIL ELAGG (NIL T) -9 NIL 562293) (-260 555925 556359 557022 "ELAGG-" 557027 NIL ELAGG- (NIL T T) -8 NIL NIL) (-259 554582 554862 555157 "ELABEXPR" 555650 T ELABEXPR (NIL) -8 NIL NIL) (-258 547450 549249 550076 "EFUPXS" 553858 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-257 540900 542701 543511 "EFULS" 546726 NIL EFULS (NIL T T T) -8 NIL NIL) (-256 538331 538689 539167 "EFSTRUC" 540532 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-255 527403 528968 530528 "EF" 536846 NIL EF (NIL T T) -7 NIL NIL) (-254 526504 526888 527037 "EAB" 527274 T EAB (NIL) -8 NIL NIL) (-253 525717 526463 526491 "E04UCFA" 526496 T E04UCFA (NIL) -8 NIL NIL) (-252 524930 525676 525704 "E04NAFA" 525709 T E04NAFA (NIL) -8 NIL NIL) (-251 524143 524889 524917 "E04MBFA" 524922 T E04MBFA (NIL) -8 NIL NIL) (-250 523356 524102 524130 "E04JAFA" 524135 T E04JAFA (NIL) -8 NIL NIL) (-249 522571 523315 523343 "E04GCFA" 523348 T E04GCFA (NIL) -8 NIL NIL) (-248 521786 522530 522558 "E04FDFA" 522563 T E04FDFA (NIL) -8 NIL NIL) (-247 520999 521745 521773 "E04DGFA" 521778 T E04DGFA (NIL) -8 NIL NIL) (-246 515184 516529 517891 "E04AGNT" 519657 T E04AGNT (NIL) -7 NIL NIL) (-245 513911 514391 514431 "DVARCAT" 514906 NIL DVARCAT (NIL T) -9 NIL 515104) (-244 513115 513327 513641 "DVARCAT-" 513646 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-243 505977 512917 513044 "DSMP" 513049 NIL DSMP (NIL T T T) -8 NIL NIL) (-242 500787 501922 502990 "DROPT" 504929 T DROPT (NIL) -8 NIL NIL) (-241 500452 500511 500609 "DROPT1" 500722 NIL DROPT1 (NIL T) -7 NIL NIL) (-240 495567 496693 497830 "DROPT0" 499335 T DROPT0 (NIL) -7 NIL NIL) (-239 493912 494237 494623 "DRAWPT" 495201 T DRAWPT (NIL) -7 NIL NIL) (-238 488499 489422 490501 "DRAW" 492886 NIL DRAW (NIL T) -7 NIL NIL) (-237 488132 488185 488303 "DRAWHACK" 488440 NIL DRAWHACK (NIL T) -7 NIL NIL) (-236 486863 487132 487423 "DRAWCX" 487861 T DRAWCX (NIL) -7 NIL NIL) (-235 486381 486449 486599 "DRAWCURV" 486789 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-234 476852 478811 480926 "DRAWCFUN" 484286 T DRAWCFUN (NIL) -7 NIL NIL) (-233 473666 475548 475589 "DQAGG" 476218 NIL DQAGG (NIL T) -9 NIL 476491) (-232 462173 468911 468993 "DPOLCAT" 470831 NIL DPOLCAT (NIL T T T T) -9 NIL 471375) (-231 457013 458359 460316 "DPOLCAT-" 460321 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-230 451097 456875 456972 "DPMO" 456977 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-229 445084 450878 451044 "DPMM" 451049 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-228 444597 444695 444815 "DOMAIN" 444984 T DOMAIN (NIL) -8 NIL NIL) (-227 438309 444234 444385 "DMP" 444498 NIL DMP (NIL NIL T) -8 NIL NIL) (-226 437909 437965 438109 "DLP" 438247 NIL DLP (NIL T) -7 NIL NIL) (-225 431553 437010 437237 "DLIST" 437714 NIL DLIST (NIL T) -8 NIL NIL) (-224 428400 430409 430450 "DLAGG" 431000 NIL DLAGG (NIL T) -9 NIL 431229) (-223 427110 427802 427830 "DIVRING" 427980 T DIVRING (NIL) -9 NIL 428088) (-222 426098 426351 426744 "DIVRING-" 426749 NIL DIVRING- (NIL T) -8 NIL NIL) (-221 424200 424557 424963 "DISPLAY" 425712 T DISPLAY (NIL) -7 NIL NIL) (-220 418089 424114 424177 "DIRPROD" 424182 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-219 416937 417140 417405 "DIRPROD2" 417882 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-218 406568 412573 412626 "DIRPCAT" 413034 NIL DIRPCAT (NIL NIL T) -9 NIL 413861) (-217 403894 404536 405417 "DIRPCAT-" 405754 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-216 403181 403341 403527 "DIOSP" 403728 T DIOSP (NIL) -7 NIL NIL) (-215 399884 402094 402135 "DIOPS" 402569 NIL DIOPS (NIL T) -9 NIL 402798) (-214 399433 399547 399738 "DIOPS-" 399743 NIL DIOPS- (NIL T T) -8 NIL NIL) (-213 398305 398943 398971 "DIFRING" 399158 T DIFRING (NIL) -9 NIL 399267) (-212 397951 398028 398180 "DIFRING-" 398185 NIL DIFRING- (NIL T) -8 NIL NIL) (-211 395741 397023 397063 "DIFEXT" 397422 NIL DIFEXT (NIL T) -9 NIL 397715) (-210 394027 394455 395120 "DIFEXT-" 395125 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-209 391350 393560 393601 "DIAGG" 393606 NIL DIAGG (NIL T) -9 NIL 393626) (-208 390734 390891 391143 "DIAGG-" 391148 NIL DIAGG- (NIL T T) -8 NIL NIL) (-207 386199 389693 389970 "DHMATRIX" 390503 NIL DHMATRIX (NIL T) -8 NIL NIL) (-206 381811 382720 383730 "DFSFUN" 385209 T DFSFUN (NIL) -7 NIL NIL) (-205 376597 380525 380890 "DFLOAT" 381466 T DFLOAT (NIL) -8 NIL NIL) (-204 374830 375111 375506 "DFINTTLS" 376305 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-203 371863 372865 373263 "DERHAM" 374497 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-202 369712 371638 371727 "DEQUEUE" 371807 NIL DEQUEUE (NIL T) -8 NIL NIL) (-201 368930 369063 369258 "DEGRED" 369574 NIL DEGRED (NIL T T) -7 NIL NIL) (-200 365330 366075 366927 "DEFINTRF" 368158 NIL DEFINTRF (NIL T) -7 NIL NIL) (-199 362861 363330 363928 "DEFINTEF" 364849 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-198 356691 362302 362468 "DECIMAL" 362715 T DECIMAL (NIL) -8 NIL NIL) (-197 354203 354661 355167 "DDFACT" 356235 NIL DDFACT (NIL T T) -7 NIL NIL) (-196 353799 353842 353993 "DBLRESP" 354154 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-195 351509 351843 352212 "DBASE" 353557 NIL DBASE (NIL T) -8 NIL NIL) (-194 350644 351468 351496 "D03FAFA" 351501 T D03FAFA (NIL) -8 NIL NIL) (-193 349780 350603 350631 "D03EEFA" 350636 T D03EEFA (NIL) -8 NIL NIL) (-192 347730 348196 348685 "D03AGNT" 349311 T D03AGNT (NIL) -7 NIL NIL) (-191 347048 347689 347717 "D02EJFA" 347722 T D02EJFA (NIL) -8 NIL NIL) (-190 346366 347007 347035 "D02CJFA" 347040 T D02CJFA (NIL) -8 NIL NIL) (-189 345684 346325 346353 "D02BHFA" 346358 T D02BHFA (NIL) -8 NIL NIL) (-188 345002 345643 345671 "D02BBFA" 345676 T D02BBFA (NIL) -8 NIL NIL) (-187 338200 339788 341394 "D02AGNT" 343416 T D02AGNT (NIL) -7 NIL NIL) (-186 335969 336491 337037 "D01WGTS" 337674 T D01WGTS (NIL) -7 NIL NIL) (-185 335072 335928 335956 "D01TRNS" 335961 T D01TRNS (NIL) -8 NIL NIL) (-184 334175 335031 335059 "D01GBFA" 335064 T D01GBFA (NIL) -8 NIL NIL) (-183 333278 334134 334162 "D01FCFA" 334167 T D01FCFA (NIL) -8 NIL NIL) (-182 332381 333237 333265 "D01ASFA" 333270 T D01ASFA (NIL) -8 NIL NIL) (-181 331484 332340 332368 "D01AQFA" 332373 T D01AQFA (NIL) -8 NIL NIL) (-180 330587 331443 331471 "D01APFA" 331476 T D01APFA (NIL) -8 NIL NIL) (-179 329690 330546 330574 "D01ANFA" 330579 T D01ANFA (NIL) -8 NIL NIL) (-178 328793 329649 329677 "D01AMFA" 329682 T D01AMFA (NIL) -8 NIL NIL) (-177 327896 328752 328780 "D01ALFA" 328785 T D01ALFA (NIL) -8 NIL NIL) (-176 326999 327855 327883 "D01AKFA" 327888 T D01AKFA (NIL) -8 NIL NIL) (-175 326102 326958 326986 "D01AJFA" 326991 T D01AJFA (NIL) -8 NIL NIL) (-174 319406 320955 322514 "D01AGNT" 324563 T D01AGNT (NIL) -7 NIL NIL) (-173 318743 318871 319023 "CYCLOTOM" 319274 T CYCLOTOM (NIL) -7 NIL NIL) (-172 315478 316191 316918 "CYCLES" 318036 T CYCLES (NIL) -7 NIL NIL) (-171 314790 314924 315095 "CVMP" 315339 NIL CVMP (NIL T) -7 NIL NIL) (-170 312571 312829 313204 "CTRIGMNP" 314518 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-169 312176 312259 312364 "CTORCALL" 312486 T CTORCALL (NIL) -8 NIL NIL) (-168 311550 311649 311802 "CSTTOOLS" 312073 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-167 307349 308006 308764 "CRFP" 310862 NIL CRFP (NIL T T) -7 NIL NIL) (-166 306396 306581 306809 "CRAPACK" 307153 NIL CRAPACK (NIL T) -7 NIL NIL) (-165 305780 305881 306085 "CPMATCH" 306272 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-164 305505 305533 305639 "CPIMA" 305746 NIL CPIMA (NIL T T T) -7 NIL NIL) (-163 301869 302541 303259 "COORDSYS" 304840 NIL COORDSYS (NIL T) -7 NIL NIL) (-162 301253 301382 301532 "CONTOUR" 301739 T CONTOUR (NIL) -8 NIL NIL) (-161 297114 299256 299748 "CONTFRAC" 300793 NIL CONTFRAC (NIL T) -8 NIL NIL) (-160 296268 296832 296860 "COMRING" 296865 T COMRING (NIL) -9 NIL 296916) (-159 295349 295626 295810 "COMPPROP" 296104 T COMPPROP (NIL) -8 NIL NIL) (-158 295010 295045 295173 "COMPLPAT" 295308 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-157 284991 294819 294928 "COMPLEX" 294933 NIL COMPLEX (NIL T) -8 NIL NIL) (-156 284627 284684 284791 "COMPLEX2" 284928 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-155 284345 284380 284478 "COMPFACT" 284586 NIL COMPFACT (NIL T T) -7 NIL NIL) (-154 268680 278974 279014 "COMPCAT" 280016 NIL COMPCAT (NIL T) -9 NIL 281409) (-153 258195 261119 264746 "COMPCAT-" 265102 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-152 257926 257954 258056 "COMMUPC" 258161 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-151 257721 257754 257813 "COMMONOP" 257887 T COMMONOP (NIL) -7 NIL NIL) (-150 257304 257472 257559 "COMM" 257654 T COMM (NIL) -8 NIL NIL) (-149 256553 256747 256775 "COMBOPC" 257113 T COMBOPC (NIL) -9 NIL 257288) (-148 255449 255659 255901 "COMBINAT" 256343 NIL COMBINAT (NIL T) -7 NIL NIL) (-147 251647 252220 252860 "COMBF" 254871 NIL COMBF (NIL T T) -7 NIL NIL) (-146 250433 250763 250998 "COLOR" 251432 T COLOR (NIL) -8 NIL NIL) (-145 250073 250120 250245 "CMPLXRT" 250380 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-144 245575 246603 247683 "CLIP" 249013 T CLIP (NIL) -7 NIL NIL) (-143 243913 244683 244921 "CLIF" 245403 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-142 240136 242060 242101 "CLAGG" 243030 NIL CLAGG (NIL T) -9 NIL 243566) (-141 238558 239015 239598 "CLAGG-" 239603 NIL CLAGG- (NIL T T) -8 NIL NIL) (-140 238102 238187 238327 "CINTSLPE" 238467 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-139 235603 236074 236622 "CHVAR" 237630 NIL CHVAR (NIL T T T) -7 NIL NIL) (-138 234826 235390 235418 "CHARZ" 235423 T CHARZ (NIL) -9 NIL 235437) (-137 234580 234620 234698 "CHARPOL" 234780 NIL CHARPOL (NIL T) -7 NIL NIL) (-136 233687 234284 234312 "CHARNZ" 234359 T CHARNZ (NIL) -9 NIL 234414) (-135 231712 232377 232712 "CHAR" 233372 T CHAR (NIL) -8 NIL NIL) (-134 231438 231499 231527 "CFCAT" 231638 T CFCAT (NIL) -9 NIL NIL) (-133 230683 230794 230976 "CDEN" 231322 NIL CDEN (NIL T T T) -7 NIL NIL) (-132 226675 229836 230116 "CCLASS" 230423 T CCLASS (NIL) -8 NIL NIL) (-131 226594 226620 226655 "CATEGORY" 226660 T -10 (NIL) -8 NIL NIL) (-130 221646 222623 223376 "CARTEN" 225897 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-129 220754 220902 221123 "CARTEN2" 221493 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-128 219052 219906 220162 "CARD" 220518 T CARD (NIL) -8 NIL NIL) (-127 218425 218753 218781 "CACHSET" 218913 T CACHSET (NIL) -9 NIL 218990) (-126 217922 218218 218246 "CABMON" 218296 T CABMON (NIL) -9 NIL 218352) (-125 217410 217724 217804 "BYTE" 217862 T BYTE (NIL) -8 NIL NIL) (-124 213358 217357 217391 "BYTEARY" 217396 T BYTEARY (NIL) -8 NIL NIL) (-123 210915 213050 213157 "BTREE" 213284 NIL BTREE (NIL T) -8 NIL NIL) (-122 208413 210563 210685 "BTOURN" 210825 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205832 207885 207926 "BTCAT" 207994 NIL BTCAT (NIL T) -9 NIL 208071) (-120 205499 205579 205728 "BTCAT-" 205733 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200720 204591 204619 "BTAGG" 204875 T BTAGG (NIL) -9 NIL 205054) (-118 200143 200287 200517 "BTAGG-" 200522 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197187 199421 199636 "BSTREE" 199960 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196325 196451 196635 "BRILL" 197043 NIL BRILL (NIL T) -7 NIL NIL) (-115 193027 195054 195095 "BRAGG" 195744 NIL BRAGG (NIL T) -9 NIL 196001) (-114 191556 191962 192517 "BRAGG-" 192522 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184764 190902 191086 "BPADICRT" 191404 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183068 184701 184746 "BPADIC" 184751 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182768 182798 182911 "BOUNDZRO" 183032 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178283 179374 180241 "BOP" 181921 T BOP (NIL) -8 NIL NIL) (-109 175904 176348 176868 "BOP1" 177796 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174539 175244 175462 "BOOLEAN" 175706 T BOOLEAN (NIL) -8 NIL NIL) (-107 173906 174284 174336 "BMODULE" 174341 NIL BMODULE (NIL T T) -9 NIL 174405) (-106 169716 173704 173777 "BITS" 173853 T BITS (NIL) -8 NIL NIL) (-105 168813 169248 169400 "BINFILE" 169584 T BINFILE (NIL) -8 NIL NIL) (-104 168225 168347 168489 "BINDING" 168691 T BINDING (NIL) -8 NIL NIL) (-103 162059 167669 167834 "BINARY" 168080 T BINARY (NIL) -8 NIL NIL) (-102 159887 161315 161356 "BGAGG" 161616 NIL BGAGG (NIL T) -9 NIL 161753) (-101 159718 159750 159841 "BGAGG-" 159846 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158816 159102 159307 "BFUNCT" 159533 T BFUNCT (NIL) -8 NIL NIL) (-99 157517 157695 157980 "BEZOUT" 158640 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154042 156377 156705 "BBTREE" 157220 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153780 153833 153859 "BASTYPE" 153976 T BASTYPE (NIL) -9 NIL NIL) (-96 153635 153664 153734 "BASTYPE-" 153739 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153073 153149 153299 "BALFACT" 153546 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151895 152492 152677 "AUTOMOR" 152918 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151621 151626 151652 "ATTREG" 151657 T ATTREG (NIL) -9 NIL NIL) (-92 149900 150318 150670 "ATTRBUT" 151287 T ATTRBUT (NIL) -8 NIL NIL) (-91 149436 149549 149575 "ATRIG" 149776 T ATRIG (NIL) -9 NIL NIL) (-90 149245 149286 149373 "ATRIG-" 149378 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147442 149021 149109 "ASTACK" 149188 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145947 146244 146609 "ASSOCEQ" 147124 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144979 145606 145730 "ASP9" 145854 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144743 144927 144966 "ASP8" 144971 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143612 144348 144490 "ASP80" 144632 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142511 143247 143379 "ASP7" 143511 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141465 142188 142306 "ASP78" 142424 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140434 141145 141262 "ASP77" 141379 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139346 140072 140203 "ASP74" 140334 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138246 138981 139113 "ASP73" 139245 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137201 137923 138041 "ASP6" 138159 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136149 136878 136996 "ASP55" 137114 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135099 135823 135942 "ASP50" 136061 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134187 134800 134910 "ASP4" 135020 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133275 133888 133998 "ASP49" 134108 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132060 132814 132982 "ASP42" 133164 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130837 131593 131763 "ASP41" 131947 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129787 130514 130632 "ASP35" 130750 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129552 129735 129774 "ASP34" 129779 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129289 129356 129432 "ASP33" 129507 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128184 128924 129056 "ASP31" 129188 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127949 128132 128171 "ASP30" 128176 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127684 127753 127829 "ASP29" 127904 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127449 127632 127671 "ASP28" 127676 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127214 127397 127436 "ASP27" 127441 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126298 126912 127023 "ASP24" 127134 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125214 125939 126069 "ASP20" 126199 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124302 124915 125025 "ASP1" 125135 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123246 123976 124095 "ASP19" 124214 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122983 123050 123126 "ASP12" 123201 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122582 122726 "ASP10" 122870 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-520))))) +(((*1 *2 *3) (-12 (-5 *3 (-591 *2)) (-5 *1 (-1100 *2)) (-4 *2 (-341))))) +(((*1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-1096))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-517) (-788))) + (-4 *2 (-13 (-408 (-157 *4)) (-932) (-1111))) + (-5 *1 (-554 *4 *3 *2)) (-4 *3 (-13 (-408 *4) (-932) (-1111)))))) +(((*1 *2 *1) (-12 (-4 *1 (-233 *2)) (-4 *2 (-1125))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-525)) (-4 *1 (-55 *2 *4 *5)) (-4 *2 (-1125)) (-4 *4 (-351 *2)) (-4 *5 (-351 *2)))) @@ -5780,822 +7159,958 @@ (-12 (-5 *3 "first") (|has| *1 (-6 -4251)) (-4 *1 (-1159 *2)) (-4 *2 (-1125))))) (((*1 *2 *1) - (-12 (-5 *2 (-161 (-385 (-525)))) (-5 *1 (-113 *3)) (-14 *3 (-525)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1070 *2)) (-4 *2 (-286)) (-5 *1 (-161 *2)))) - ((*1 *1 *2) (-12 (-5 *2 (-385 *3)) (-4 *3 (-286)) 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(-33))) (-5 *2 (-591 (-1054 *3 *5))) (-5 *1 (-1054 *3 *5)) (-4 *3 (-13 (-1018) (-33))))) ((*1 *2 *3) - (-12 (-5 *3 (-591 (-2 (|:| |val| *4) (|:| -3374 *5)))) + (-12 (-5 *3 (-591 (-2 (|:| |val| *4) (|:| -3585 *5)))) (-4 *4 (-13 (-1018) (-33))) (-4 *5 (-13 (-1018) (-33))) (-5 *2 (-591 (-1054 *4 *5))) (-5 *1 (-1054 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3374 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3585 *4))) (-4 *3 (-13 (-1018) (-33))) (-4 *4 (-13 (-1018) (-33))) (-5 *1 (-1054 *3 *4)))) ((*1 *1 *2 *3) @@ -6654,69 +8169,32 @@ (-4 *4 (-13 (-1018) (-33))) (-5 *1 (-1055 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1079 *2 *3)) (-4 *2 (-1018)) (-4 *3 (-1018))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-591 *6)) (-4 *6 (-989 *3 *4 *5)) (-4 *3 (-429)) + (-4 *3 (-517)) (-4 *4 (-734)) (-4 *5 (-788)) + (-5 *1 (-908 *3 *4 *5 *6))))) +(((*1 *2 *2) + (-12 (-4 *3 (-429)) (-4 *4 (-734)) (-4 *5 (-788)) + (-5 *1 (-426 *3 *4 *5 *2)) (-4 *2 (-882 *3 *4 *5))))) (((*1 *2 *3) - (-12 (-4 *4 (-286)) 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*2 (-1013 (-205))) (-5 *1 (-859)))) + ((*1 *1 *1 *2 *2) (-12 (-5 *2 (-1013 (-205))) (-5 *1 (-860)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1013 (-205))) (-5 *1 (-860)))) + ((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-357)) (-5 *2 (-1176)) (-5 *1 (-1173)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-357)) (-5 *2 (-1176)) (-5 *1 (-1173))))) +(((*1 *1 *1 *2 *2 *2 *2) + (-12 (-5 *2 (-525)) (-4 *1 (-629 *3 *4 *5)) (-4 *3 (-975)) + (-4 *4 (-351 *3)) (-4 *5 (-351 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-1070 *3)) (-5 *1 (-161 *3)) (-4 *3 (-286))))) (((*1 *1 *2) (-12 (-4 *1 (-37 *2)) (-4 *2 (-160)))) ((*1 *1 *2) (-12 (-5 *2 (-1171 *3)) (-4 *3 (-341)) (-14 *6 (-1171 (-631 *3))) @@ -6724,69 +8202,69 @@ ((*1 *1 *2) (-12 (-5 *2 (-1041 (-525) (-564 (-47)))) (-5 *1 (-47)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-50 *3)) (-4 *3 (-1125)))) ((*1 *1 *2) - (-12 (-5 *2 (-1171 (-317 (-3036 'JINT 'X 'ELAM) (-3036) (-640)))) + (-12 (-5 *2 (-1171 (-317 (-2695 'JINT 'X 'ELAM) (-2695) (-640)))) (-5 *1 (-59 *3)) (-14 *3 (-1089)))) ((*1 *1 *2) 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(-1171 (-317 (-2695 'X) (-2695 '-1389) (-640)))) (-5 *1 (-84 *3)) (-14 *3 (-1089)))) ((*1 *1 *2) - (-12 (-5 *2 (-631 (-317 (-3036 'XL 'XR 'ELAM) (-3036) (-640)))) + (-12 (-5 *2 (-631 (-317 (-2695 'XL 'XR 'ELAM) (-2695) (-640)))) (-5 *1 (-85 *3)) (-14 *3 (-1089)))) ((*1 *1 *2) - (-12 (-5 *2 (-317 (-3036 'X) (-3036 '-2424) (-640))) (-5 *1 (-87 *3)) + (-12 (-5 *2 (-317 (-2695 'X) (-2695 '-1389) (-640))) (-5 *1 (-87 *3)) (-14 *3 (-1089)))) ((*1 *2 *1) (-12 (-5 *2 (-934 2)) (-5 *1 (-103)))) ((*1 *2 *1) (-12 (-5 *2 (-385 (-525))) (-5 *1 (-103)))) @@ -6810,8 +8288,8 @@ (-12 (-5 *2 (-591 *3)) (-4 *3 (-13 (-788) - (-10 -8 (-15 -3164 ((-1072) $ (-1089))) (-15 -3551 ((-1176) $)) - (-15 -3600 ((-1176) $))))) + (-10 -8 (-15 -1881 ((-1072) $ (-1089))) (-15 -1285 ((-1176) $)) + (-15 -3829 ((-1176) $))))) (-5 *1 (-195 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-934 10)) (-5 *1 (-198)))) ((*1 *2 *1) (-12 (-5 *2 (-385 (-525))) (-5 *1 (-198)))) @@ -6852,14 +8330,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-352 *2 *3)) (-4 *2 (-788)) (-4 *3 (-160)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3380 (-591 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3145 (-591 (-308))))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-591 (-308))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 (-5 *2 (-631 (-640))) (-4 *1 (-361)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3380 (-591 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3145 (-591 (-308))))) (-4 *1 (-362)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-362)))) ((*1 *1 *2) (-12 (-5 *2 (-591 (-308))) (-4 *1 (-362)))) @@ -6869,71 +8347,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-796)) (-5 *1 (-372)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3380 (-591 (-308))))) + (-5 *2 (-2 (|:| |localSymbols| (-1093)) (|:| -3145 (-591 (-308))))) (-4 *1 (-374)))) ((*1 *1 *2) (-12 (-5 *2 (-308)) (-4 *1 (-374)))) ((*1 *1 *2) (-12 (-5 *2 (-591 (-308))) (-4 *1 (-374)))) ((*1 *1 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(-5 *3 (-710)) (-5 *2 - (-2 (|:| -2432 (-357)) (|:| -2400 (-1072)) + (-2 (|:| -2282 (-357)) (|:| -3419 (-1072)) (|:| |explanations| (-591 (-1072))) (|:| |extra| (-964)))) (-5 *1 (-526)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-710)) (-5 *4 (-987)) (-5 *2 - (-2 (|:| -2432 (-357)) (|:| -2400 (-1072)) + (-2 (|:| -2282 (-357)) (|:| -3419 (-1072)) (|:| |explanations| (-591 (-1072))) (|:| |extra| (-964)))) (-5 *1 (-526)))) ((*1 *2 *3 *4) (-12 (-4 *1 (-728)) (-5 *3 (-987)) (-5 *4 (-2 (|:| |fn| (-294 (-205))) - (|:| -1767 (-591 (-1013 (-781 (-205))))) (|:| |abserr| (-205)) + (|:| -3756 (-591 (-1013 (-781 (-205))))) (|:| |abserr| (-205)) (|:| |relerr| (-205)))) (-5 *2 - (-2 (|:| -2432 (-357)) (|:| |explanations| (-1072)) + (-2 (|:| -2282 (-357)) (|:| |explanations| (-1072)) (|:| |extra| (-964)))))) ((*1 *2 *3 *4) (-12 (-4 *1 (-728)) (-5 *3 (-987)) (-5 *4 (-2 (|:| |var| (-1089)) (|:| |fn| (-294 (-205))) - (|:| -1767 (-1013 (-781 (-205)))) (|:| |abserr| (-205)) + (|:| -3756 (-1013 (-781 (-205)))) (|:| 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(-964)) + (-5 *1 (-690))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-205)) (-5 *4 (-525)) + (-5 *5 (-3 (|:| |fn| (-366)) (|:| |fp| (-62 -1730)))) (-5 *2 (-964)) + (-5 *1 (-690))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1089)) (|:| |fn| (-294 (-205))) + (|:| -3756 (-1013 (-781 (-205)))) (|:| |abserr| (-205)) + (|:| |relerr| (-205)))) (-5 *2 - (-2 (|:| |particular| (-3 (-1171 *6) "failed")) - (|:| -4003 (-591 (-1171 *6))))) - (-5 *1 (-754 *6 *7)) (-5 *4 (-1171 *6))))) + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1070 (-205))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3756 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-520))))) +(((*1 *2 *1) (-12 (-4 *3 (-1125)) (-5 *2 (-591 *1)) (-4 *1 (-940 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-591 (-1078 *3 *4))) (-5 *1 (-1078 *3 *4)) + (-14 *3 (-854)) (-4 *4 (-975))))) +(((*1 *2 *1) + (-12 (-5 *2 (-806 (-898 *3) (-898 *3))) (-5 *1 (-898 *3)) + (-4 *3 (-899))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-796))))) (((*1 *2 *1) (-12 (-4 *3 (-975)) (-4 *4 (-734)) (-4 *5 (-788)) (-5 *2 (-591 *1)) (-4 *1 (-882 *3 *4 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-205)) (-5 *4 (-525)) (-5 *2 (-964)) (-5 *1 (-700))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-955 (-781 (-525)))) - (-5 *3 (-1070 (-2 (|:| |k| (-525)) (|:| |c| *4)))) (-4 *4 (-975)) - (-5 *1 (-550 *4))))) -(((*1 *2 *3 *4 *3 *3) - 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((*1 *1 *1 *2) (-12 (-4 *1 (-261 *2)) (-4 *2 (-1125)))) - ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4251)) (-4 *1 (-1159 *2)) (-4 *2 (-1125)))) - ((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4251)) (-4 *1 (-1159 *2)) (-4 *2 (-1125))))) + (-12 (-5 *3 (-1171 (-1171 *4))) (-4 *4 (-975)) (-5 *2 (-631 *4)) + (-5 *1 (-958 *4))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-525)) (-4 *1 (-55 *4 *3 *5)) (-4 *4 (-1125)) + (-4 *3 (-351 *4)) (-4 *5 (-351 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-46 *2 *3)) (-4 *3 (-733)) (-4 *2 (-975)))) ((*1 *2 *1) (-12 (-4 *2 (-975)) (-5 *1 (-49 *2 *3)) (-14 *3 (-591 (-1089))))) @@ -13738,10 +14854,10 @@ (-4 *3 (-13 (-975) (-788))) (-14 *4 (-591 (-1089))))) ((*1 *2 *1) (-12 (-4 *1 (-360 *2 *3)) (-4 *3 (-1018)) (-4 *2 (-975)))) ((*1 *2 *1) - (-12 (-14 *3 (-591 (-1089))) (-4 *5 (-218 (-4045 *3) (-712))) + (-12 (-14 *3 (-591 (-1089))) (-4 *5 (-218 (-2028 *3) (-712))) (-14 *6 - (-1 (-108) (-2 (|:| -2226 *4) (|:| -2008 *5)) - (-2 (|:| -2226 *4) (|:| -2008 *5)))) + (-1 (-108) (-2 (|:| -3229 *4) (|:| -3987 *5)) + (-2 (|:| -3229 *4) (|:| -3987 *5)))) (-4 *2 (-160)) (-5 *1 (-438 *3 *2 *4 *5 *6 *7)) (-4 *4 (-788)) (-4 *7 (-882 *2 *5 (-798 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-481 *2 *3)) (-4 *3 (-788)) (-4 *2 (-1018)))) @@ -13758,85 +14874,55 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-989 *3 *4 *2)) (-4 *3 (-975)) (-4 *4 (-734)) (-4 *2 (-788))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1072)) (-4 *4 (-429)) (-4 *5 (-734)) (-4 *6 (-788)) - (-4 *7 (-989 *4 *5 *6)) (-5 *2 (-1176)) - (-5 *1 (-995 *4 *5 *6 *7 *8)) (-4 *8 (-994 *4 *5 *6 *7)))) - ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-1072)) (-4 *4 (-429)) (-4 *5 (-734)) (-4 *6 (-788)) - (-4 *7 (-989 *4 *5 *6)) (-5 *2 (-1176)) - (-5 *1 (-1026 *4 *5 *6 *7 *8)) (-4 *8 (-994 *4 *5 *6 *7))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1171 *5)) (-4 *5 (-733)) (-5 *2 (-108)) - (-5 *1 (-783 *4 *5)) (-14 *4 (-712))))) -(((*1 *2 *3) - (-12 (-5 *3 (-591 *2)) (-4 *2 (-1147 *4)) (-5 *1 (-504 *4 *2 *5 *6)) - (-4 *4 (-286)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-712)))))) -(((*1 *2 *1) (-12 (-4 *1 (-367)) (-5 *2 (-108))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1021 *3 *4 *5 *6 *2)) (-4 *3 (-1018)) (-4 *4 (-1018)) + (-4 *5 (-1018)) (-4 *6 (-1018)) (-4 *2 (-1018))))) +(((*1 *1 *2) (-12 (-5 *2 (-1171 *3)) (-4 *3 (-341)) (-4 *1 (-307 *3)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1171 *3)) (-4 *3 (-1147 *4)) (-4 *4 (-1129)) + (-4 *1 (-320 *4 *3 *5)) (-4 *5 (-1147 (-385 *3))))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1171 *4)) (-5 *3 (-1171 *1)) (-4 *4 (-160)) + (-4 *1 (-345 *4)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1171 *4)) (-5 *3 (-1171 *1)) (-4 *4 (-160)) + (-4 *1 (-348 *4 *5)) (-4 *5 (-1147 *4)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1171 *3)) (-4 *3 (-160)) (-4 *1 (-387 *3 *4)) + (-4 *4 (-1147 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1171 *3)) (-4 *3 (-160)) (-4 *1 (-395 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-517)) (-4 *5 (-734)) (-4 *6 (-788)) - (-4 *7 (-989 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-591 *7)) (|:| |badPols| (-591 *7)))) - (-5 *1 (-908 *4 *5 *6 *7)) (-5 *3 (-591 *7))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-591 (-796))) (-5 *1 (-796)))) - ((*1 *2 *1) - (-12 + (-12 (-5 *3 (-1089)) (-5 *2 - (-2 (|:| -2718 (-591 (-796))) (|:| -2593 (-591 (-796))) - (|:| |presup| (-591 (-796))) (|:| -1772 (-591 (-796))) - (|:| |args| (-591 (-796))))) - (-5 *1 (-1089))))) + (-2 (|:| |zeros| (-1070 (-205))) (|:| |ones| (-1070 (-205))) + (|:| |singularities| (-1070 (-205))))) + (-5 *1 (-100))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-525)) (-5 *4 (-631 (-205))) (-5 *2 (-964)) + (-5 *1 (-697))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-631 *3)) + (-4 *3 (-13 (-286) (-10 -8 (-15 -3898 ((-396 $) $))))) + (-4 *4 (-1147 *3)) (-5 *1 (-472 *3 *4 *5)) (-4 *5 (-387 *3 *4)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-631 *3)) + (-4 *3 (-13 (-286) (-10 -8 (-15 -3898 ((-396 $) $))))) + (-4 *4 (-1147 *3)) (-5 *1 (-472 *3 *4 *5)) (-4 *5 (-387 *3 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-517)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2976 *4))) - (-5 *1 (-901 *4 *3)) (-4 *3 (-1147 *4))))) + (-12 (-4 *1 (-853)) (-5 *2 (-2 (|:| -2976 (-591 *1)) (|:| -3965 *1))) + (-5 *3 (-591 *1))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-598 *4)) (-4 *4 (-320 *5 *6 *7)) - (-4 *5 (-13 (-341) (-138) (-966 (-525)) (-966 (-385 (-525))))) - (-4 *6 (-1147 *5)) (-4 *7 (-1147 (-385 *6))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -4003 (-591 *4)))) - (-5 *1 (-747 *5 *6 *7 *4))))) -(((*1 *2 *3 *1) - (-12 (-5 *2 (-591 (-1089))) (-5 *1 (-1092)) (-5 *3 (-1089))))) -(((*1 *1 *2) (-12 (-5 *2 (-591 *1)) (-4 *1 (-281)))) - ((*1 *1 *1) (-4 *1 (-281))) - ((*1 *1 *2) (-12 (-5 *2 (-591 (-796))) (-5 *1 (-796)))) - ((*1 *1 *1) (-5 *1 (-796)))) -(((*1 *2 *3 *3 *3 *4 *3) - (-12 (-5 *3 (-525)) (-5 *4 (-631 (-157 (-205)))) (-5 *2 (-964)) - (-5 *1 (-696))))) -(((*1 *2 *3) - (-12 (-4 *4 (-327)) (-5 *2 (-108)) (-5 *1 (-197 *4 *3)) - (-4 *3 (-1147 *4))))) -(((*1 *2 *2 *2 *3 *3 *4 *2 *5) - (|partial| -12 (-5 *3 (-564 *2)) - (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1089))) (-5 *5 (-1085 *2)) - (-4 *2 (-13 (-408 *6) (-27) (-1111))) - (-4 *6 (-13 (-429) (-966 (-525)) (-788) (-138) (-587 (-525)))) - (-5 *1 (-521 *6 *2 *7)) (-4 *7 (-1018)))) - ((*1 *2 *2 *2 *3 *3 *4 *3 *2 *5) - (|partial| -12 (-5 *3 (-564 *2)) - (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1089))) - (-5 *5 (-385 (-1085 *2))) (-4 *2 (-13 (-408 *6) (-27) (-1111))) - (-4 *6 (-13 (-429) (-966 (-525)) (-788) (-138) (-587 (-525)))) - (-5 *1 (-521 *6 *2 *7)) (-4 *7 (-1018))))) -(((*1 *2 *1) (-12 (-5 *2 (-1072)) (-5 *1 (-1107))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1021 *3 *4 *5 *6 *7)) (-4 *3 (-1018)) (-4 *4 (-1018)) - (-4 *5 (-1018)) (-4 *6 (-1018)) (-4 *7 (-1018)) (-5 *2 (-108))))) -(((*1 *2 *3 *4 *5 *5 *4 *6) - (-12 (-5 *4 (-525)) (-5 *6 (-1 (-1176) (-1171 *5) (-1171 *5) (-357))) - (-5 *3 (-1171 (-357))) (-5 *5 (-357)) (-5 *2 (-1176)) - (-5 *1 (-729))))) + (-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1147 *5)) (-4 *5 (-341)) + (-5 *2 (-2 (|:| |answer| *3) (|:| |polypart| *3))) + (-5 *1 (-535 *5 *3))))) (((*1 *1 *1) (-12 (-4 *1 (-46 *2 *3)) (-4 *2 (-975)) (-4 *3 (-733)))) ((*1 *2 *1) (-12 (-4 *1 (-360 *3 *2)) (-4 *3 (-975)) (-4 *2 (-1018)))) ((*1 *2 *1) (-12 (-14 *3 (-591 (-1089))) (-4 *4 (-160)) - (-4 *6 (-218 (-4045 *3) (-712))) + (-4 *6 (-218 (-2028 *3) (-712))) (-14 *7 - (-1 (-108) (-2 (|:| -2226 *5) (|:| -2008 *6)) - (-2 (|:| -2226 *5) (|:| -2008 *6)))) + (-1 (-108) (-2 (|:| -3229 *5) (|:| -3987 *6)) + (-2 (|:| -3229 *5) (|:| -3987 *6)))) (-5 *2 (-655 *5 *6 *7)) (-5 *1 (-438 *3 *4 *5 *6 *7 *8)) (-4 *5 (-788)) (-4 *8 (-882 *4 *6 (-798 *3))))) ((*1 *2 *1) @@ -13845,182 +14931,126 @@ ((*1 *1 *1) (-12 (-4 *1 (-904 *2 *3 *4)) (-4 *2 (-975)) (-4 *3 (-733)) (-4 *4 (-788))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-108)) (-5 *1 (-1121 *3)) (-4 *3 (-905))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-591 (-525))) (-5 *1 (-1028)) (-5 *3 (-525))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-273 (-774 *3))) - (-4 *5 (-13 (-429) (-788) (-966 (-525)) (-587 (-525)))) - (-5 *2 (-774 *3)) (-5 *1 (-584 *5 *3)) - (-4 *3 (-13 (-27) (-1111) (-408 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-273 (-774 (-885 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52319) (-4005 . 52266) + (-4006 . 51820) (-4007 . 51412) (-4008 . 50807) (-4009 . 50688) + (-4010 . 50558) (-4011 . 50487) (-4012 . 50113) (-4013 . 49934) + (-4014 . 49884) (-4015 . 49801) (-4016 . 49588) (-4017 . 49488) + (-4018 . 47236) (-4019 . 47136) (-4020 . 47075) (-4021 . 46970) + (-4022 . 46781) (-4023 . 46573) (-4024 . 46500) (-4025 . 46469) + (-4026 . 46081) (-4027 . 46016) (-4028 . 45949) (-4029 . 45850) + (-4030 . 45748) (-4031 . 45621) (-4032 . 45548) (-4033 . 45361) + (-4034 . 45122) (-4035 . 44987) (-4036 . 43803) (-4037 . 43692) + (-4038 . 43636) (-4039 . 43568) (-4040 . 43465) (-4041 . 43366) + (-4042 . 43260) (-4043 . 42846) (-4044 . 42793) (-4045 . 42687) + (-4046 . 42624) (-4047 . 41446) (-4048 . 41272) (-4049 . 41056) + (-4050 . 41003) (-4051 . 40906) (-4052 . 40810) (-4053 . 40753) + (-4054 . 40533) (-4055 . 40438) (-4056 . 40212) (-4057 . 40132) + (-4058 . 39445) (-4059 . 37247) (-4060 . 37162) (-4061 . 37091) + (-4062 . 37038) (-4063 . 36738) (-4064 . 36614) 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24167) + (-4126 . 24046) (-4127 . 23802) (-4128 . 23707) (-4129 . 23453) + (-4130 . 23359) (-4131 . 23306) (-4132 . 23255) (-4133 . 23114) + (-4134 . 23062) (-4135 . 22964) (-4136 . 22778) (-4137 . 22204) + (-4138 . 21893) (-4139 . 21821) (-4140 . 21577) (-4141 . 21406) + (-4142 . 21221) (-4143 . 20968) (-4144 . 20902) (-4145 . 20380) + (-4146 . 20206) (-4147 . 20079) (-4148 . 19961) (-4149 . 19387) + (-4150 . 19292) (-4151 . 18983) (-4152 . 18888) (-4153 . 18744) + (-4154 . 18643) (-4155 . 18465) (-4156 . 18333) (-4157 . 18178) + (-4158 . 17974) (-4159 . 17910) (-4160 . 17704) (-4161 . 17621) + (-4162 . 17503) (-4163 . 16929) (-4164 . 16874) (-4165 . 16565) + (-4166 . 16509) (-4167 . 16343) (-4168 . 16248) (-4169 . 16150) + (-4170 . 16048) (-4171 . 15991) (-4172 . 15898) (-4173 . 15225) + (-4174 . 10704) (-4175 . 10565) (-4176 . 10410) (-4177 . 10304) + (-4178 . 10244) (-4179 . 9670) (-4180 . 9593) (-4181 . 9456) + (-4182 . 9074) (-4183 . 8714) (-4184 . 8545) (-4185 . 8487) + (-4186 . 8264) (-4187 . 8155) (-4188 . 6790) (-4189 . 6716) + (-4190 . 6543) (-4191 . 6339) (-4192 . 6112) (-4193 . 5538) + (-4194 . 5322) (-4195 . 5248) (-4196 . 5174) (-4197 . 5108) + (-4198 . 4717) (-4199 . 4622) (-4200 . 4549) (-4201 . 4453) + (-4202 . 4344) (-4203 . 3859) (-4204 . 3791) (-4205 . 3559) + (-4206 . 3456) (-4207 . 3283) (-4208 . 3128) (-4209 . 2962) + (-4210 . 2832) (-4211 . 2758) (-4212 . 2696) (-4213 . 2559) + (-4214 . 2431) (-4215 . 2353) (-4216 . 2301) (-4217 . 2148) + (-4218 . 2069) (-4219 . 1943) (-4220 . 1892) (-4221 . 1864) + (-4222 . 1571) (-4223 . 1513) (-4224 . 1450) (-4225 . 1258) + (-4226 . 1051) (-4227 . 907) (-4228 . 517) (-4229 . 108) (-4230 . 30))
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