diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-10-12 07:32:48 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-10-12 07:32:48 +0000 |
| commit | 8968a58f48c6d75ccdc73c086687f63d18c9fec7 (patch) | |
| tree | 806cdac98cc2a90a273e4bfade70667384a96ccb | |
| parent | 5687e549faf2a00133c91dd21b48d876e0e2c449 (diff) | |
| download | open-axiom-8968a58f48c6d75ccdc73c086687f63d18c9fec7.tar.gz | |
update databses
| -rw-r--r-- | src/share/algebra/browse.daase | 2016 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 5808 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1959 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9588 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 32605 |
5 files changed, 26990 insertions, 24986 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index dc9d5f7a..cfbaa7fa 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2267936 . 3432506631) +(2269608 . 3432784494) (-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."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . 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}."))) @@ -46,7 +46,7 @@ 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4350 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4346 . T) (-4351 . T) (-4345 . T) (-2368 . T)) +((-4350 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4346 . T) (-4351 . T) (-4345 . T) (-3526 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) @@ -56,17 +56,17 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3428) +(-32 R -3281) ((|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 -1014) (QUOTE (-538))))) +((|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (-33 S) ((|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."))) NIL ((|HasAttribute| |#1| (QUOTE -4353))) (-34) ((|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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2368 . T)) +((-3526 . T)) NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,7 +74,7 @@ NIL NIL (-36 |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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -88,14 +88,14 @@ 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 -(-40 -3428 UP UPUP -2943) +(-40 -3281 UP UPUP -1531) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4346 |has| (-402 |#2|) (-358)) (-4351 |has| (-402 |#2|) (-358)) (-4345 |has| (-402 |#2|) (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-402 |#2|) (QUOTE (-143))) (|HasCategory| (-402 |#2|) (QUOTE (-145))) (|HasCategory| (-402 |#2|) (QUOTE (-345))) (-3891 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-363))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-345))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-3891 (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358))))) -(-41 R -3428) +((|HasCategory| (-402 |#2|) (QUOTE (-143))) (|HasCategory| (-402 |#2|) (QUOTE (-145))) (|HasCategory| (-402 |#2|) (QUOTE (-344))) (-1523 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-344)))) (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-363))) (-1523 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (|HasCategory| (-402 |#2|) (QUOTE (-344)))) (-1523 (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-344))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-1523 (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358))))) +(-41 R -3281) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,24 +106,24 @@ NIL ((|HasCategory| |#1| (QUOTE (-302)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4350 |has| |#1| (-545)) (-4348 . T) (-4347 . T)) -((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) +((-4350 |has| |#1| (-544)) (-4348 . T) (-4347 . T)) +((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-45 |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."))) ((-4353 . T) (-4354 . T)) -((-3891 (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827)))) (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|))))))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-827))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-46 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-358)))) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-358)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\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| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\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| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538))))) +((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-552))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL @@ -132,19 +132,19 @@ NIL ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) ((-4350 . T)) NIL -(-51) -((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) +(-51 S) +((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) NIL NIL -(-52 S) -((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) +(-52) +((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL (-53 R M P) ((|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 -(-54 |Base| R -3428) +(-54 |Base| R -3281) ((|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 @@ -154,133 +154,133 @@ NIL NIL (-56 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"))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) 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}"))) -((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-58 A B) +(-57 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),{}...]}."))) NIL NIL +(-58 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}"))) +((-4354 . T) (-4353 . T)) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-59 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-60 -3905) -((|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 -(-61 -3905) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-60 -1288) ((|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 -(-62 -3905) +(-61 -1288) ((|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 -(-63 -3905) +(-62 -1288) ((|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 -(-64 -3905) +(-63 -1288) +((|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 +(-64 -1288) ((|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 -(-65 -3905) +(-65 -1288) ((|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 -(-66 -3905) +(-66 -1288) ((|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 -(-67 -3905) +(-67 -1288) ((|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 -(-68 -3905) +(-68 -1288) ((|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 -(-69 -3905) +(-69 -1288) ((|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 -(-70 -3905) +(-70 -1288) ((|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 -(-71 -3905) +(-71 -1288) ((|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 -(-72 -3905) +(-72 -1288) ((|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 -(-73 -3905) +(-73 -1288) ((|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 -(-74 -3905) -((|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 -(-75 |nameOne| |nameTwo| |nameThree|) +(-74 |nameOne| |nameTwo| |nameThree|) ((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 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 FCN(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=Y(2) F(2)=Y(3) F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) RETURN END SUBROUTINE JACOBF(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N,N),X,Y(N) INTEGER N F(1,1)=0.0D0 F(1,2)=1.0D0 F(1,3)=0.0D0 F(2,1)=0.0D0 F(2,2)=0.0D0 F(2,3)=1.0D0 F(3,1)=-1.0D0*Y(3) F(3,2)=4.0D0*EPS*Y(2) F(3,3)=-1.0D0*Y(1) RETURN END SUBROUTINE JACEPS(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=0.0D0 F(2)=0.0D0 F(3)=2.0D0*Y(2)**2-2.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-76 |nameOne| |nameTwo| |nameThree|) +(-75 |nameOne| |nameTwo| |nameThree|) ((|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 -(-77 -3905) +(-76 -1288) ((|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 -(-78 -3905) +(-77 -1288) +((|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 +(-78 -1288) ((|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 -(-79 -3905) +(-79 -1288) ((|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 -(-80 -3905) +(-80 -1288) ((|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 -(-81 -3905) -((|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 -(-82 -3905) +(-81 -1288) ((|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 -(-83 -3905) +(-82 -1288) ((|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 -(-84 -3905) +(-83 -1288) ((|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 -(-85 -3905) +(-84 -1288) ((|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 -(-86 -3905) -((|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}"))) +(-85 -1288) +((|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 -(-87 -3905) +(-86 -1288) ((|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 -(-88 -3905) +(-87 -1288) +((|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 +(-88 -1288) ((|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 @@ -291,7 +291,7 @@ NIL (-90 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-91 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -339,7 +339,7 @@ NIL (-102 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-103 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 @@ -354,12 +354,12 @@ NIL NIL (-106 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."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-107) ((|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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143))))) +((|HasCategory| (-552) (QUOTE (-885))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-552) (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-145))) (|HasCategory| (-552) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-998))) (|HasCategory| (-552) (QUOTE (-800))) (-1523 (|HasCategory| (-552) (QUOTE (-800))) (|HasCategory| (-552) (QUOTE (-827)))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1124))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-229))) (|HasCategory| (-552) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-552) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -304) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -281) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-302))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-552) (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (|HasCategory| (-552) (QUOTE (-143))))) (-108) ((|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -371,7 +371,7 @@ NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-112) (QUOTE (-1073))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1073))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-839))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) ((-4348 . T) (-4347 . T)) @@ -380,15 +380,15 @@ NIL ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-113) -((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-114 A) +(-113 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL ((|HasCategory| |#1| (QUOTE (-827)))) -(-115 -3428 UP) +(-114) +((|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 +(-115 -3281 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 @@ -399,14 +399,14 @@ NIL (-117 |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}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-886))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-116 |#1|) (QUOTE (-996))) (|HasCategory| (-116 |#1|) (QUOTE (-800))) (-3891 (|HasCategory| (-116 |#1|) (QUOTE (-800))) (|HasCategory| (-116 |#1|) (QUOTE (-827)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1124))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-229))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-302))) (|HasCategory| (-116 |#1|) (QUOTE (-537))) (|HasCategory| (-116 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-886)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) +((|HasCategory| (-116 |#1|) (QUOTE (-885))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-116 |#1|) (QUOTE (-998))) (|HasCategory| (-116 |#1|) (QUOTE (-800))) (-1523 (|HasCategory| (-116 |#1|) (QUOTE (-800))) (|HasCategory| (-116 |#1|) (QUOTE (-827)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-116 |#1|) (QUOTE (-1124))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| (-116 |#1|) (QUOTE (-229))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-302))) (|HasCategory| (-116 |#1|) (QUOTE (-537))) (|HasCategory| (-116 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-885)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) (-118 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4354))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-2368 . T)) +((-3526 . T)) NIL (-120 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."))) @@ -415,14 +415,14 @@ NIL (-121 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"))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,24 +430,24 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-127 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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-128) +((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) +((-4354 . T) (-4353 . T)) +((-1523 (-12 (|HasCategory| (-129) (QUOTE (-827))) (|HasCategory| (-129) (LIST (QUOTE -304) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1073))) (|HasCategory| (-129) (LIST (QUOTE -304) (QUOTE (-129)))))) (-1523 (-12 (|HasCategory| (-129) (QUOTE (-1073))) (|HasCategory| (-129) (LIST (QUOTE -304) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-129) (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| (-129) (QUOTE (-827))) (|HasCategory| (-129) (QUOTE (-1073)))) (|HasCategory| (-129) (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-129) (QUOTE (-1073))) (-12 (|HasCategory| (-129) (QUOTE (-1073))) (|HasCategory| (-129) (LIST (QUOTE -304) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -597) (QUOTE (-839))))) +(-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} views \\spad{`c'} a a byte. In particular \\spad{`c'} is supposed to have a numerical value less than 256.") (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL -(-129) -((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) -((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128)))))) (-3891 (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-128) (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-128) (QUOTE (-1074)))) (|HasCategory| (-128) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-128) (QUOTE (-1074))) (-12 (|HasCategory| (-128) (QUOTE (-1074))) (|HasCategory| (-128) (LIST (QUOTE -304) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -597) (QUOTE (-840))))) (-130) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -464,12 +464,12 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4355 "*") . T)) NIL -(-134 |minix| -2950 R) -((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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."))) +(-134 |minix| -2562 S T$) +((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -2950 S T$) -((|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}."))) +(-135 |minix| -2562 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 (-136) @@ -487,7 +487,7 @@ NIL (-139) ((|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}."))) ((-4353 . T) (-4343 . T) (-4354 . T)) -((-3891 (-12 (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-142) (QUOTE (-363))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1073))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-839))))) (-140 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 @@ -512,7 +512,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4350 . T)) NIL -(-146 -3428 UP UPUP) +(-146 -3281 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 @@ -523,10 +523,10 @@ NIL (-148 A 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|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\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| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\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.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\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}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\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| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\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."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasAttribute| |#1| (QUOTE -4353))) +((|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasAttribute| |#1| (QUOTE -4353))) (-149 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."))) -((-2368 . T)) +((-3526 . T)) NIL (-150 |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."))) @@ -552,7 +552,7 @@ 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 -(-156 R -3428) +(-156 R -3281) ((|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 @@ -565,11 +565,11 @@ NIL NIL NIL (-159) -((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) +((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) NIL NIL (-160) -((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) +((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) NIL NIL (-161) @@ -583,23 +583,23 @@ NIL (-163 S 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| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\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| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasAttribute| |#2| (QUOTE -4349)) (|HasAttribute| |#2| (QUOTE -4352)) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-827)))) +((|HasCategory| |#2| (QUOTE (-885))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasAttribute| |#2| (QUOTE -4349)) (|HasAttribute| |#2| (QUOTE -4352)) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-827)))) (-164 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})).")) 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T)) +((-4346 -1523 (|has| |#1| (-544)) (-12 (|has| |#1| (-302)) (|has| |#1| (-885)))) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4349 |has| |#1| (-6 -4349)) (-4352 |has| |#1| (-6 -4352)) (-3858 . T) (-3526 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-165 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."))) 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(QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-808))) (|HasCategory| |#1| (QUOTE (-1034))) (-12 (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-1171)))) (|HasCategory| |#1| (QUOTE (-537))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-358)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-229))) (-12 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasAttribute| |#1| (QUOTE -4349)) (|HasAttribute| |#1| (QUOTE -4352)) (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-344))))) (-168 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 @@ -635,7 +635,7 @@ NIL (-176 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-922 |#2|) (LIST (QUOTE -862) (|devaluate| |#1|)))) +((|HasCategory| (-928 |#2|) (LIST (QUOTE -862) (|devaluate| |#1|)))) (-177 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -653,18 +653,18 @@ NIL NIL NIL (-181) -((|constructor| (NIL "This domain provides implementations for constructors.")) (|arity| (((|SingleInteger|) $) "\\spad{arity(ctor)} returns the arity of the constructor `ctor'. \\indented{2}{A negative value means that the \\spad{ctor} takes a variable} \\indented{2}{length argument list,{} \\spadignore{e.g.} Mapping,{} Record,{} etc.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")) (|name| (((|Identifier|) $) "\\spad{name(ctor)} returns the name of the constructor `ctor'."))) +((|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 (-182) -((|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|) $) "\\spad{constructorName c} returns the name of the constructor"))) +((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' designates package constructors.")) (|domain| (($) "`domain' designates domain constructors")) (|category| (($) "`category' designates category constructors"))) NIL NIL (-183) -((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' designates package constructors.")) (|domain| (($) "`domain' designates domain constructors")) (|category| (($) "`category' designates category constructors"))) +((|constructor| (NIL "This domain provides implementations for constructors.")) (|arity| (((|SingleInteger|) $) "\\spad{arity(ctor)} returns the arity of the constructor `ctor'. \\indented{2}{A negative value means that the \\spad{ctor} takes a variable} \\indented{2}{length argument list,{} \\spadignore{e.g.} Mapping,{} Record,{} etc.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")) (|name| (((|Identifier|) $) "\\spad{name(ctor)} returns the name of the constructor `ctor'."))) NIL NIL -(-184 R -3428) +(-184 R -3281) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -772,28 +772,28 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -(-211 -3428 UP UPUP R) +(-211 -3281 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 -(-212 -3428 FP) +(-212 -3281 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 (-213) ((|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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143))))) +((|HasCategory| (-552) (QUOTE (-885))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-552) (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-145))) (|HasCategory| (-552) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-998))) (|HasCategory| (-552) (QUOTE (-800))) (-1523 (|HasCategory| (-552) (QUOTE (-800))) (|HasCategory| (-552) (QUOTE (-827)))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1124))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-229))) (|HasCategory| (-552) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-552) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -304) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -281) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-302))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-552) (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (|HasCategory| (-552) (QUOTE (-143))))) (-214) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-215 R -3428) -((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="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| #1#) (|:| |pole| #2#)) |#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| #1#) (|:| |pole| #2#)) |#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}."))) +(-215 R -3281) +((|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 (-216 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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}."))) +((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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 (-217 R1 R2) @@ -803,18 +803,18 @@ NIL (-218 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-219 |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}."))) ((-4350 . T)) NIL -(-220 R -3428) +(-220 R -3281) ((|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 (-221) ((|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)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\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}."))) -((-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-2874 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-222) ((|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)}.}"))) @@ -823,14 +823,14 @@ NIL (-223 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}"))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-224 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 (-225 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."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-226 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}."))) @@ -854,28 +854,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4353))) (-231 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}."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-232) ((|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 -(-233 S -2950 R) +(-233 S -2562 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 (-358))) (|HasCategory| |#3| (QUOTE (-773))) (|HasCategory| |#3| (QUOTE (-825))) (|HasAttribute| |#3| (QUOTE -4350)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-707))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (QUOTE (-1074)))) -(-234 -2950 R) +((|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (QUOTE (-773))) (|HasCategory| |#3| (QUOTE (-825))) (|HasAttribute| |#3| (QUOTE -4350)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-707))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (QUOTE (-1073)))) +(-234 -2562 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4347 |has| |#2| (-1025)) (-4348 |has| |#2| (-1025)) (-4350 |has| |#2| (-6 -4350)) ((-4355 "*") |has| |#2| (-170)) (-4353 . T) (-2368 . T)) +((-4347 |has| |#2| (-1025)) (-4348 |has| |#2| (-1025)) (-4350 |has| |#2| (-6 -4350)) ((-4355 "*") |has| |#2| (-170)) (-4353 . T) (-3526 . T)) NIL -(-235 -2950 R) -((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4347 |has| |#2| (-1025)) (-4348 |has| |#2| (-1025)) (-4350 |has| |#2| (-6 -4350)) ((-4355 "*") |has| |#2| (-170)) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-707))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-773))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-707))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-773))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))))) (|HasCategory| (-538) (QUOTE (-827))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (QUOTE (-1025)))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-1025)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4350)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) -(-236 -2950 A B) +(-235 -2562 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL +(-236 -2562 R) +((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) +((-4347 |has| |#2| (-1025)) (-4348 |has| |#2| (-1025)) (-4350 |has| |#2| (-6 -4350)) ((-4355 "*") |has| |#2| (-170)) (-4353 . 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -890,84 +890,84 @@ NIL NIL (-240 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."))) -((-2368 . T)) +((-3526 . T)) NIL (-241 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. 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|#3| (QUOTE (-1025)))) (-1523 (-12 (|HasCategory| |#3| (QUOTE (-229))) (|HasCategory| |#3| (QUOTE (-1025)))) (|HasCategory| |#3| (QUOTE (-707))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-552))))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149)))))) (-1523 (|HasCategory| |#3| (QUOTE (-1025))) (-12 (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-552)))))) (-12 (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#3| (QUOTE (-1073)))) (-1523 (|HasAttribute| |#3| (QUOTE -4350)) (-12 (|HasCategory| |#3| (QUOTE (-229))) (|HasCategory| |#3| (QUOTE (-1025)))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-552))))) (-12 (|HasCategory| |#3| (QUOTE (-1025))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-839))))) (-247 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 ((|HasCategory| |#2| (QUOTE (-229)))) (-248 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| ((|#3| $) "\\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|) $ |#2|) "\\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|)) $ |#2|) "\\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|) $ |#2|) "\\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|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\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|)) |#2|) "\\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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL (-249 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}."))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL -(-250 |Ex|) -((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} 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)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = 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)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = 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)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = 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)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = 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)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) -NIL -NIL -(-251) +(-250) ((|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."))) NIL NIL -(-252 R |Ex|) +(-251 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-253) +(-252) ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-254 R) +(-253 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL NIL +(-254 |Ex|) +((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} 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)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = 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)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = 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)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = 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)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = 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)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = 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)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) +NIL +NIL (-255) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL (-256) -((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) -NIL -NIL -(-257) ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL NIL -(-258 S) +(-257 S) ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL +(-258) +((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) +NIL +NIL (-259 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"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . 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T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#3| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#3| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#3| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#3| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-260 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 @@ -1012,11 +1012,11 @@ 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 -(-271 R -3428) +(-271 R -3281) ((|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 -(-272 R -3428) +(-272 R -3281) ((|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 @@ -1035,10 +1035,10 @@ NIL (-276 A 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|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|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!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074)))) +((|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073)))) (-277 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}."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-278 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}."))) @@ -1064,7 +1064,7 @@ 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 -(-284 S R |Mod| -2152 -3872 |exactQuo|) +(-284 S R |Mod| -3297 -3280 |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"))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL @@ -1080,58 +1080,58 @@ NIL ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-288 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."))) -((-4350 -3891 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4347 |has| |#1| (-1025)) (-4348 |has| |#1| (-1025))) -((|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025)))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-3891 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707)))) (|HasCategory| |#1| (QUOTE (-467))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-293))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467)))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707)))) (-3891 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) -(-289 S R) +(-288 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL +(-289 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."))) +((-4350 -1523 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4347 |has| |#1| (-1025)) (-4348 |has| |#1| (-1025))) +((|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707)))) (|HasCategory| |#1| (QUOTE (-467))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-1073)))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-297))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-467)))) (-1523 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707)))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) (-290 |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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-291) ((|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 -(-292 S) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) -NIL -((|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1025)))) -(-293) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) -NIL -NIL -(-294 -3428 S) +(-292 -3281 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 -(-295 E -3428) +(-293 E -3281) ((|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 -(-296) -((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) +(-294 A B) +((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) NIL NIL -(-297 A B) -((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) +(-295) +((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) NIL NIL -(-298) -((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|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{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) +(-296 S) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1025)))) +(-297) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-299 R1) +(-298 R1) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) NIL NIL -(-300 R1 R2) +(-299 R1 R2) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) NIL NIL +(-300) +((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|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{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) +NIL +NIL (-301 S) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL @@ -1148,35 +1148,35 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 -(-305 -3428) +(-305 -3281) ((|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 (-306) -((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) +((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) NIL NIL (-307) -((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) +((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL (-308 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-886))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-996))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-800))) (-3891 (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-800))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-827)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-1124))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-229))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -304) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -281) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-302))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-537))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-886)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-143))))) -(-309 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."))) -((-4350 -3891 (-3191 (|has| |#1| (-1025)) (|has| |#1| (-621 (-538)))) (-12 (|has| |#1| (-545)) (-3891 (-3191 (|has| |#1| (-1025)) (|has| |#1| (-621 (-538)))) (|has| |#1| (-1025)) (|has| |#1| (-467)))) (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) ((-4355 "*") |has| |#1| (-545)) (-4346 |has| |#1| (-545)) (-4351 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(-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -304) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (LIST (QUOTE -281) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1218) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-302))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-537))) (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-827))) (-12 (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-885))) (|HasCategory| $ (QUOTE (-143)))) (-1523 (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1218 |#1| |#2| |#3| |#4|) (QUOTE (-885))) (|HasCategory| $ (QUOTE (-143)))))) +(-309 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 NIL -(-311 R FE) +(-310 R FE) ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-312 R -3428) +(-311 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."))) +((-4350 -1523 (-3743 (|has| |#1| (-1025)) (|has| |#1| (-621 (-552)))) (-12 (|has| |#1| (-544)) (-1523 (-3743 (|has| |#1| (-1025)) (|has| |#1| (-621 (-552)))) (|has| |#1| (-1025)) (|has| |#1| (-467)))) (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) ((-4355 "*") |has| |#1| (-544)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-544)) (-4345 |has| |#1| (-544))) +((-1523 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552))))) (-1523 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1085)))) (-1523 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))))) (-1523 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1085)))) (-1523 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))))) (-1523 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#1| (QUOTE (-1025)))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-552))))) +(-312 R -3281) ((|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 @@ -1186,8 +1186,8 @@ NIL NIL (-314 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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|))))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-552)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|))))))) (-315 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 @@ -1199,7 +1199,7 @@ NIL (-317 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) ((-4348 . T) (-4347 . T)) -((|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-772)))) +((|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-772)))) (-318 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1211,20 +1211,20 @@ NIL (-320 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170)))) (-321 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-322 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."))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-323 S -3428) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-323 S -3281) ((|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 (-363)))) -(-324 -3428) +(-324 -3281) ((|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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL @@ -1240,22 +1240,22 @@ NIL ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}"))) NIL NIL -(-328 -3428 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 -(-329 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-328 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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 -(-330 S -3428 UP UPUP R) +(-329 S -3281 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 -(-331 -3428 UP UPUP R) +(-330 -3281 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 +(-331 -3281 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) +NIL +NIL (-332 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL @@ -1267,87 +1267,87 @@ NIL (-334 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-373)))) (|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538))))) -(-335 |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}."))) -((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143)))) -(-336 S -3428 UP UPUP) +((|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#3| (LIST (QUOTE -1014) (QUOTE (-374)))) (|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-552))))) +(-335 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((|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 +(-336 S -3281 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}.")) (|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 (-363))) (|HasCategory| |#2| (QUOTE (-358)))) -(-337 -3428 UP UPUP) +(-337 -3281 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}.")) (|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."))) ((-4346 |has| (-402 |#2|) (-358)) (-4351 |has| (-402 |#2|) (-358)) (-4345 |has| (-402 |#2|) (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-338 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) -((|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 -(-339 |p| |extdeg|) +(-338 |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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143)))) -(-340 GF |defpol|) +((-1523 (|HasCategory| (-886 |#1|) (QUOTE (-143))) (|HasCategory| (-886 |#1|) (QUOTE (-363)))) (|HasCategory| (-886 |#1|) (QUOTE (-145))) (|HasCategory| (-886 |#1|) (QUOTE (-363))) (|HasCategory| (-886 |#1|) (QUOTE (-143)))) +(-339 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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) -(-341 GF |extdeg|) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +(-340 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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) -(-342 GF) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +(-341 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 NIL -(-343 F1 GF F2) +(-342 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-344 S) +(-343 S) ((|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."))) NIL NIL -(-345) +(-344) ((|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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-346 R UP -3428) +(-345 R UP -3281) ((|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 -(-347 |p| |extdeg|) +(-346 |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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| (-882 |#1|) (QUOTE (-143))) (|HasCategory| (-882 |#1|) (QUOTE (-363)))) (|HasCategory| (-882 |#1|) (QUOTE (-145))) (|HasCategory| (-882 |#1|) (QUOTE (-363))) (|HasCategory| (-882 |#1|) (QUOTE (-143)))) -(-348 GF |uni|) +((-1523 (|HasCategory| (-886 |#1|) (QUOTE (-143))) (|HasCategory| (-886 |#1|) (QUOTE (-363)))) (|HasCategory| (-886 |#1|) (QUOTE (-145))) (|HasCategory| (-886 |#1|) (QUOTE (-363))) (|HasCategory| (-886 |#1|) (QUOTE (-143)))) +(-347 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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) -(-349 GF |extdeg|) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +(-348 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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +(-349 |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}."))) +((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-1523 (|HasCategory| (-886 |#1|) (QUOTE (-143))) (|HasCategory| (-886 |#1|) (QUOTE (-363)))) (|HasCategory| (-886 |#1|) (QUOTE (-145))) (|HasCategory| (-886 |#1|) (QUOTE (-363))) (|HasCategory| (-886 |#1|) (QUOTE (-143)))) (-350 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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) -(-351 GF) -((|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."))) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +(-351 -3281 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 -(-352 -3428 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{}"))) +(-352 GF) +((|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 -(-353 -3428 FP FPP) +(-353 -3281 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 (-354 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}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) +((-1523 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-143)))) (-355 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 @@ -1364,21 +1364,21 @@ NIL ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-359 S) -((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) +(-359 |Name| S) +((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL -(-360 |Name| S) -((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) +(-360 S) +((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL (-361 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-545)))) +((|HasCategory| |#2| (QUOTE (-544)))) (-362 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4350 |has| |#1| (-545)) (-4348 . T) (-4347 . T)) +((-4350 |has| |#1| (-544)) (-4348 . T) (-4347 . T)) NIL (-363) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1392,17 +1392,17 @@ NIL ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) ((-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-366 A S) -((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|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|) |#2| $) "\\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|) |#2|) $) "\\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|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) +(-366 S A R B) +((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) NIL -((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074)))) -(-367 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4353 . T) (-2368 . T)) NIL -(-368 S A R B) -((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) +(-367 A 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|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|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|) |#2| $) "\\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|) |#2|) $) "\\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|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL +((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073)))) +(-368 S) +((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) +((-4353 . T) (-3526 . T)) NIL (-369 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1415,43 +1415,43 @@ NIL (-371 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) +((|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552))))) (-372 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) ((-4350 . T)) NIL -(-373) -((|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}."))) -((-4336 . T) (-4344 . T) (-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -NIL -(-374 |Par|) +(-373 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL NIL +(-374) +((|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}."))) +((-4336 . T) (-4344 . T) (-2874 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +NIL (-375 |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}."))) NIL NIL (-376 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."))) -((-4348 . T) (-4347 . T)) -((|HasCategory| |#1| (QUOTE (-170)))) -(-377 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) ((-4348 . T) (-4347 . T)) ((|HasCategory| |#1| (QUOTE (-170)))) -(-378) -((|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}."))) -((-2368 . T)) -NIL -(-379 R |Basis|) +(-377 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) ((-4348 . T) (-4347 . T)) NIL -(-380) +(-378) +((|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}."))) +((-3526 . T)) +NIL +(-379) ((|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.}"))) -((-2368 . T)) +((-3526 . T)) NIL +(-380 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."))) +((-4348 . T) (-4347 . T)) +((|HasCategory| |#1| (QUOTE (-170)))) (-381 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL @@ -1476,41 +1476,41 @@ 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 -(-387 -3428 UP UPUP R) +(-387 -3281 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 -(-388) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) +(-388 S) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) NIL NIL -(-389 S) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) +(-389) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) NIL NIL (-390) -((|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 +((|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."))) +((-3526 . T)) NIL (-391) -((|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."))) -((-2368 . T)) +((|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.}"))) +((-3526 . T)) NIL (-392) -((|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.}"))) -((-2368 . T)) +((|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 -(-393 -3905 |returnType| -1466 |symbols|) +(-393 -1288 |returnType| -1912 |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 -(-394 -3428 UP) +(-394 -3281 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-395 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2368 . T)) +((-3526 . T)) NIL (-396 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1526,121 +1526,121 @@ NIL ((|HasAttribute| |#1| (QUOTE -4336)) (|HasAttribute| |#1| (QUOTE -4344))) (-399) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-2874 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-400 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) -((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -304) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -281) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-1190))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-996))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-446)))) -(-401 R S) +(-400 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."))) NIL NIL -(-402 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."))) -((-4340 -12 (|has| |#1| (-6 -4351)) (|has| |#1| (-446)) (|has| |#1| (-6 -4340))) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-996))) (|HasCategory| |#1| (QUOTE (-800))) (-3891 (|HasCategory| |#1| (QUOTE (-800))) (|HasCategory| |#1| (QUOTE (-827)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1124))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-801)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-537))) (-12 (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-403 A B) +(-401 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL NIL -(-404 S R UP) +(-402 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."))) +((-4340 -12 (|has| |#1| (-6 -4351)) (|has| |#1| (-446)) (|has| |#1| (-6 -4340))) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-800))) (-1523 (|HasCategory| |#1| (QUOTE (-800))) (|HasCategory| |#1| (QUOTE (-827)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1124))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808))))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-808)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-537))) (-12 (|HasAttribute| |#1| (QUOTE -4351)) (|HasAttribute| |#1| (QUOTE -4340)) (|HasCategory| |#1| (QUOTE (-446)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-403 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 NIL -(-405 R UP) +(-404 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|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{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) ((-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-406 A S) +(-405 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538))))) -(-407 S) +((|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) +(-406 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-408 R -3428 UP A) -((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4350 . T)) -NIL -(-409 R1 F1 U1 A1 R2 F2 U2 A2) +(-407 R1 F1 U1 A1 R2 F2 U2 A2) ((|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 -(-410 R -3428 UP A |ibasis|) +(-408 R -3281 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)}."))) +((-4350 . T)) +NIL +(-409 R -3281 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1014) (|devaluate| |#2|)))) -(-411 AR R AS S) +(-410 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-412 S R) +(-411 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module 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 \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL ((|HasCategory| |#2| (QUOTE (-358)))) -(-413 R) +(-412 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\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."))) -((-4350 |has| |#1| (-545)) (-4348 . T) (-4347 . T)) +((-4350 |has| |#1| (-544)) (-4348 . T) (-4347 . T)) NIL +(-413 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."))) +((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -304) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -281) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1190))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-446)))) (-414 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 NIL -(-415 S 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| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|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| |#2| (|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| |#2| (|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| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|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| ((|#2| $) "\\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}."))) +(-415 R FE |x| |cen|) +((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527))))) -(-416 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}."))) -((-4350 -3891 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) ((-4355 "*") |has| |#1| (-545)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-545)) (-4345 |has| |#1| (-545)) (-2368 . T)) NIL -(-417 R A S B) +(-416 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-418 R FE |x| |cen|) -((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) +(-417 R FE |Expon| UPS TRAN |x|) +((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) NIL NIL -(-419 R FE |Expon| UPS TRAN |x|) -((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) +(-418 S A R B) +((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\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),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-420 A S) +(-419 A 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| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\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}."))) NIL ((|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-363)))) -(-421 S) +(-420 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4353 . T) (-4343 . T) (-4354 . T) (-2368 . T)) -NIL -(-422 S A R B) -((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) -NIL +((-4353 . T) (-4343 . T) (-4354 . T) (-3526 . T)) NIL -(-423 R -3428) +(-421 R -3281) ((|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 -(-424 R E) +(-422 R E) ((|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"))) ((-4340 -12 (|has| |#1| (-6 -4340)) (|has| |#2| (-6 -4340))) (-4347 . T) (-4348 . T) (-4350 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#2| (QUOTE -4340)))) -(-425 R -3428) +(-423 R -3281) ((|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 -(-426 R -3428) +(-424 S 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| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|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| |#2| (|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| |#2| (|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| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|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| ((|#2| $) "\\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}."))) +NIL +((|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528))))) +(-425 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}."))) +((-4350 -1523 (|has| |#1| (-1025)) (|has| |#1| (-467))) (-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) ((-4355 "*") |has| |#1| (-544)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-544)) (-4345 |has| |#1| (-544)) (-3526 . T)) +NIL +(-426 R -3281) ((|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 -(-427 R -3428) +(-427 R -3281) ((|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)))) -(-428 R -3428) +(-428 R -3281) ((|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 @@ -1648,16 +1648,16 @@ 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 -(-430 R -3428 UP) +(-430 R -3281 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 -1014) (QUOTE (-48))))) (-431) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) +((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL NIL (-432) -((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) NIL NIL (-433 |f|) @@ -1666,17 +1666,17 @@ NIL NIL (-434) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|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}."))) -((-2368 . T)) +((-3526 . T)) NIL (-435) ((|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.}"))) -((-2368 . T)) +((-3526 . T)) NIL (-436 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 -(-437 R UP -3428) +(-437 R UP -3281) ((|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 @@ -1693,21 +1693,21 @@ NIL NIL NIL (-441 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) -NIL -((|HasCategory| |#1| (QUOTE (-358)))) -(-442 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL -(-443 |Dom| |Expon| |VarSet| |Dpol|) +(-442 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL NIL -(-444 |Dom| |Expon| |VarSet| |Dpol|) +(-443 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL NIL +(-444 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) +NIL +((|HasCategory| |#1| (QUOTE (-358)))) (-445 S) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL @@ -1718,12 +1718,12 @@ NIL NIL (-447 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4350 |has| (-402 (-922 |#1|)) (-545)) (-4348 . T) (-4347 . T)) -((|HasCategory| (-402 (-922 |#1|)) (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-402 (-922 |#1|)) (QUOTE (-545)))) +((-4350 |has| (-402 (-928 |#1|)) (-544)) (-4348 . T) (-4347 . T)) +((|HasCategory| (-402 (-928 |#1|)) (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-402 (-928 |#1|)) (QUOTE (-544)))) (-448 |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"))) -(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-545)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-886))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) +(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-544)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#2| (QUOTE (-885))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-358))) (-1523 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-143))))) (-449 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 @@ -1759,7 +1759,7 @@ NIL (-457 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-839))))) (-458 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1788,7 +1788,7 @@ 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 -(-465 |lv| -3428 R) +(-465 |lv| -3281 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 @@ -1802,16 +1802,16 @@ NIL NIL (-468 |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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . 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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)}"))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-839))))) (-471) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-475 |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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(|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1843,8 +1843,8 @@ NIL (-478 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-479 -3428 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-479 -3281 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 @@ -1855,14 +1855,14 @@ NIL (-481) ((|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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143))))) +((|HasCategory| (-552) (QUOTE (-885))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-552) (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-145))) (|HasCategory| (-552) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-998))) (|HasCategory| (-552) (QUOTE (-800))) (-1523 (|HasCategory| (-552) (QUOTE (-800))) (|HasCategory| (-552) (QUOTE (-827)))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1124))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-229))) (|HasCategory| (-552) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-552) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -304) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -281) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-302))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-552) (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (|HasCategory| (-552) (QUOTE (-143))))) (-482 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 -4353)) (|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) +((|HasAttribute| |#1| (QUOTE -4353)) (|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (-483 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2368 . T)) +((-3526 . T)) NIL (-484) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1876,34 +1876,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-487 -3428 UP |AlExt| |AlPol|) +(-487 -3281 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-488) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-538))))) +((|HasCategory| $ (QUOTE (-1025))) (|HasCategory| $ (LIST (QUOTE -1014) (QUOTE (-552))))) (-489 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-490 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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-491 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 -(-492 R UP -3428) +(-492 R UP -3281) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-493 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1074))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-112) (QUOTE (-1073))) (|HasCategory| (-112) (LIST (QUOTE -304) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-112) (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-112) (QUOTE (-1073))) (|HasCategory| (-112) (LIST (QUOTE -597) (QUOTE (-839))))) (-494 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1916,7 +1916,7 @@ 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 -(-497 -3428 |Expon| |VarSet| |DPoly|) +(-497 -3281 |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 -598) (QUOTE (-1149))))) @@ -1941,15 +1941,15 @@ NIL NIL NIL (-503 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL NIL (-504 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL NIL (-505 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL (-506 S A B) @@ -1967,7 +1967,7 @@ NIL (-509 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}"))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-510) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1975,15 +1975,15 @@ NIL (-511 |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}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (|HasCategory| (-567 |#1|) (QUOTE (-143))) (|HasCategory| (-567 |#1|) (QUOTE (-363)))) (|HasCategory| (-567 |#1|) (QUOTE (-145))) (|HasCategory| (-567 |#1|) (QUOTE (-363))) (|HasCategory| (-567 |#1|) (QUOTE (-143)))) +((-1523 (|HasCategory| (-567 |#1|) (QUOTE (-143))) (|HasCategory| (-567 |#1|) (QUOTE (-363)))) (|HasCategory| (-567 |#1|) (QUOTE (-145))) (|HasCategory| (-567 |#1|) (QUOTE (-363))) (|HasCategory| (-567 |#1|) (QUOTE (-143)))) (-512 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-513 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."))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-514 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 @@ -1995,7 +1995,7 @@ NIL (-516 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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-517) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2028,7 +2028,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-525 K -3428 |Par|) +(-525 K -3281 |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 @@ -2036,19 +2036,19 @@ NIL ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-527) -((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) +(-527 R) +((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-528 R) -((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) +(-528) +((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL (-529 |Coef| UTS) ((|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 -(-530 K -3428 |Par|) +(-530 K -3281 |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 @@ -2069,7 +2069,7 @@ NIL NIL NIL (-535 R UP) -((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) +((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) NIL NIL (-536 S) @@ -2080,79 +2080,79 @@ NIL ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) ((-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-538) -((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4335 . T) (-4341 . T) (-4345 . T) (-4340 . T) (-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -NIL -(-539 |Key| |Entry| |addDom|) +(-538 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) -(-540 R -3428) +((-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) +(-539 R -3281) ((|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 -(-541 R0 -3428 UP UPUP R) +(-540 R0 -3281 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 -(-542) +(-541) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-543 R) +(-542 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."))) -((-4129 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-2874 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-544 S) +(-543 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."))) NIL NIL -(-545) +(-544) ((|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."))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-546 R -3428) -((|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|)) #1="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|)) #1#) |#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."))) +(-545 R -3281) +((|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 -(-547 I) +(-546 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-548) -((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1="Continuous at the end points") (|:| |lowerSingular| #2="There is a singularity at the lower end point") (|:| |upperSingular| #3="There is a singularity at the upper end point") (|:| |bothSingular| #4="There are singularities at both end points") (|:| |notEvaluated| #5="End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6="Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| #7="The range is finite") (|:| |lowerInfinite| #8="The bottom of range is infinite") (|:| |upperInfinite| #9="The top of range is infinite") (|:| |bothInfinite| #10="Both top and bottom points are infinite") (|:| |notEvaluated| #11="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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#))))))) "\\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| #1#) (|:| |lowerSingular| #2#) (|:| |upperSingular| #3#) (|:| |bothSingular| #4#) (|:| |notEvaluated| #5#))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| #6#))) (|:| |range| (|Union| (|:| |finite| #7#) (|:| |lowerInfinite| #8#) (|:| |upperInfinite| #9#) (|:| |bothInfinite| #10#) (|:| |notEvaluated| #11#)))))))) "\\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."))) +(-547) +((|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 -(-549 R -3428 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| #1="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| #1#)) (|:| |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| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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|))))) #3="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|))))) #3#) |#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|)) #4="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|)) #4#) |#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)}."))) +(-548 R -3281 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 -638) (|devaluate| |#2|)))) -(-550) +((|HasCategory| |#3| (LIST (QUOTE -636) (|devaluate| |#2|)))) +(-549) ((|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 -(-551 -3428 UP UPUP R) +(-550 -3281 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 -(-552 -3428 UP) +(-551 -3281 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 +(-552) +((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) +((-4335 . T) (-4341 . T) (-4345 . T) (-4340 . T) (-4351 . T) (-4352 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +NIL (-553) ((|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 -(-554 R -3428 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| #1="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| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#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}."))) +(-554 R -3281 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 -638) (|devaluate| |#2|)))) -(-555 R -3428) +((|HasCategory| |#3| (LIST (QUOTE -636) (|devaluate| |#2|)))) +(-555 R -3281) ((|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 -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1112)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-612))))) -(-556 -3428 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1112)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-611))))) +(-556 -3281 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 @@ -2160,27 +2160,27 @@ 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 -(-558 -3428) +(-558 -3281) ((|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 (-559 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."))) -((-4129 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-2874 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-560) ((|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 -(-561 R -3428) +(-561 R -3281) ((|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| (QUOTE (-446))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-279))) (|HasCategory| |#2| (QUOTE (-612))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-279)))) (|HasCategory| |#1| (QUOTE (-545)))) -(-562 -3428 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|)) #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|)) #1#) |#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|)) #1#) |#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|)) #1#) |#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}."))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-279))) (|HasCategory| |#2| (QUOTE (-611))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-279)))) (|HasCategory| |#1| (QUOTE (-544)))) +(-562 -3281 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 -(-563 R -3428) +(-563 R -3281) ((|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 @@ -2204,18 +2204,18 @@ 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 -(-569 -3428) -((|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}."))) -((-4348 . T) (-4347 . T)) -((|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149))))) -(-570 E -3428) -((|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"))) +(-569 R -3281) +((|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 -(-571 R -3428) -((|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}."))) +(-570 E -3281) +((|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 +(-571 -3281) +((|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}."))) +((-4348 . T) (-4347 . T)) +((|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-1149))))) (-572 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2243,19 +2243,19 @@ NIL (-578 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (-3891 (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (-1523 (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-839)))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1073)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1073))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-839))))) (-579 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 NIL (-580 |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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-538)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-538)) (|devaluate| |#1|)))) (|HasCategory| (-538) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-538)))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-552)) (|devaluate| |#1|)))) (|HasCategory| (-552) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-552)))))) (-581 |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.}"))) -((-4348 |has| |#1| (-545)) (-4347 |has| |#1| (-545)) ((-4355 "*") |has| |#1| (-545)) (-4346 |has| |#1| (-545)) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-545)))) +((-4348 |has| |#1| (-544)) (-4347 |has| |#1| (-544)) ((-4355 "*") |has| |#1| (-544)) (-4346 |has| |#1| (-544)) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-544)))) (-582 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL @@ -2264,7 +2264,7 @@ 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 -(-584 R -3428 FG) +(-584 R -3281 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 @@ -2275,14 +2275,14 @@ NIL (-586 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-587 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 -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasAttribute| |#1| (QUOTE -4353)) (|HasCategory| |#3| (QUOTE (-1074)))) +((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-827))) (|HasAttribute| |#1| (QUOTE -4353)) (|HasCategory| |#3| (QUOTE (-1073)))) (-588 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2368 . T)) +((-3526 . T)) NIL (-589) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2294,28 +2294,28 @@ NIL NIL (-591 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)."))) -((-4350 -3891 (-3191 (|has| |#2| (-362 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-413 |#1|)) (|has| |#1| (-545)))) (-4348 . T) (-4347 . T)) -((-3891 (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) +((-4350 -1523 (-3743 (|has| |#2| (-362 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-412 |#1|)) (|has| |#1| (-544)))) (-4348 . T) (-4347 . T)) +((-1523 (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-592 |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."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| (-1131) (QUOTE (-827))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| (-1131) (QUOTE (-827))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-593 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 (-594 |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}."))) -((-4354 . T) (-2368 . T)) -NIL -(-595 S) -((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) +((-4354 . T) (-3526 . T)) NIL -((|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) -(-596 R S) +(-595 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"))) NIL NIL +(-596 S) +((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-597 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2324,7 +2324,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-599 -3428 UP) +(-599 -3281 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2332,26 +2332,26 @@ NIL ((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value"))) NIL NIL -(-601 A R S) -((|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}."))) -((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-825)))) -(-602 S R) +(-601 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-603 R) +(-602 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4350 . T)) NIL -(-604 R -3428) +(-603 A R S) +((|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}."))) +((-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-825)))) +(-604 R -3281) ((|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 (-605 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) ((-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4346 . T) (-4350 . T)) -((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) +((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (-606 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\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 \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2372,66 +2372,66 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) NIL NIL -(-611 R -3428) -((|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"))) +(-611) +((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-612) -((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) +(-612 R -3281) +((|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 -(-613 |lv| -3428) +(-613 |lv| -3281) ((|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 (-614) ((|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."))) ((-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -2191) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -304) (QUOTE (-51))))) (|HasCategory| (-1131) (QUOTE (-827))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840))))) -(-615 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)."))) -((-4350 -3891 (-3191 (|has| |#2| (-362 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-413 |#1|)) (|has| |#1| (-545)))) (-4348 . T) (-4347 . T)) -((-3891 (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) -(-616 S R) +((-12 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -4120) (QUOTE (-52))))))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-52) (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -304) (QUOTE (-52))))) (|HasCategory| (-1131) (QUOTE (-827))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839))))) +(-615 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-358)))) -(-617 R) +(-616 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) ((|JacobiIdentity| . T) (|NullSquare| . T) (-4348 . T) (-4347 . T)) NIL +(-617 R A) +((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) +((-4350 -1523 (-3743 (|has| |#2| (-362 |#1|)) (|has| |#1| (-544))) (-12 (|has| |#2| (-412 |#1|)) (|has| |#1| (-544)))) (-4348 . T) (-4347 . T)) +((-1523 (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -412) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -362) (|devaluate| |#1|)))) (-618 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|) #1="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|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) +((|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 NIL (-619 R) -((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) +((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL (-620 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 -((-3676 (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-358)))) +((-2960 (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-358)))) (-621 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4350 . T)) NIL -(-622 S) -((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-801))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-623 A B) -((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) +(-622 A B) +((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-624 A B) -((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) +(-623 A B) +((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL NIL -(-625 A B C) +(-624 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL +(-625 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."))) +((-4354 . T) (-4353 . T)) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-808))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-626 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-628 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2454,52 +2454,52 @@ NIL ((|HasAttribute| |#1| (QUOTE -4354))) (-631 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})}."))) -((-2368 . T)) +((-3526 . T)) NIL -(-632 M R S) -((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|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{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4348 . T) (-4347 . T)) -((|HasCategory| |#1| (QUOTE (-771)))) -(-633 R -3428 L) +(-632 R -3281 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 -(-634 A -2748) -((|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}}"))) -((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) -(-635 A) +(-633 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) -(-636 A M) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) +(-634 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) -(-637 S A) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) +(-635 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) NIL ((|HasCategory| |#2| (QUOTE (-358)))) -(-638 A) +(-636 A) ((|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}."))) ((-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-639 -3428 UP) +(-637 -3281 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)))) -(-640 A L) +(-638 A -3261) +((|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}}"))) +((-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) +(-639 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} 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}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} 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}. \\spad{D} is the derivation to use."))) NIL NIL -(-641 S) +(-640 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-642) +(-641) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL +(-642 M R S) +((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|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{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4348 . T) (-4347 . T)) +((|HasCategory| |#1| (QUOTE (-771)))) (-643 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([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 exists."))) NIL @@ -2514,14 +2514,14 @@ NIL NIL (-646 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}."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL -(-647 -3428 |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| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |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| #1#)) (|:| |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}."))) +(-647 -3281) +((|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 -(-648 -3428) -((|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|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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}."))) +(-648 -3281 |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 (-649 R E OV P) @@ -2531,7 +2531,7 @@ NIL (-650 |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."))) ((-4350 . T) (-4353 . T) (-4347 . T) (-4348 . T)) -((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 #1="*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-545))) (-3891 (|HasAttribute| |#2| (QUOTE (-4355 #1#))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (-1523 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-544))) (-1523 (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-170)))) (-651) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2546,12 +2546,12 @@ NIL NIL (-654 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-2368 . T)) +((-3526 . T)) NIL (-655 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 -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-656) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2588,26 +2588,26 @@ NIL ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-665 S 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| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\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|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\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.")) (* ((|#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.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|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| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\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| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\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| |#2|))) "\\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"))) +(-665 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-545)))) -(-666 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"))) -((-4353 . T) (-4354 . T) (-2368 . T)) NIL -(-667 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) -((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) +(-666 S 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| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\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|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\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.")) (* ((|#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.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|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| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\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| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\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| |#2|))) "\\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"))) NIL +((|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-544)))) +(-667 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"))) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL (-668 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."))) NIL -((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-544)))) (-669 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."))) ((-4353 . T) (-4354 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-544))) (|HasAttribute| |#1| (QUOTE (-4355 "*"))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-670 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 @@ -2616,7 +2616,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-672 S -3428 FLAF FLAS) +(-672 S -3281 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 @@ -2626,27 +2626,27 @@ NIL NIL (-674) ((|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"))) -((-4346 . T) (-4351 |has| (-679) (-358)) (-4345 |has| (-679) (-358)) (-1421 . T) (-4352 |has| (-679) (-6 -4352)) (-4349 |has| (-679) (-6 -4349)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-679) (QUOTE (-145))) (|HasCategory| (-679) (QUOTE (-143))) (|HasCategory| (-679) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-679) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-679) (QUOTE (-363))) (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-679) (QUOTE (-229))) (-3891 (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-345)))) (|HasCategory| (-679) (QUOTE (-345))) (|HasCategory| (-679) (LIST (QUOTE -281) (QUOTE (-679)) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -304) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-679) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-679) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-679) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (-3891 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-345)))) (|HasCategory| (-679) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-679) (QUOTE (-996))) (|HasCategory| (-679) (QUOTE (-1171))) (-12 (|HasCategory| (-679) (QUOTE (-978))) (|HasCategory| (-679) (QUOTE (-1171)))) (-3891 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (-12 (|HasCategory| (-679) (QUOTE (-345))) (|HasCategory| (-679) (QUOTE (-886)))) (|HasCategory| (-679) (QUOTE (-358)))) (-3891 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (-12 (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-886)))) (-12 (|HasCategory| (-679) (QUOTE (-345))) (|HasCategory| (-679) (QUOTE (-886))))) (|HasCategory| (-679) (QUOTE (-537))) (-12 (|HasCategory| (-679) (QUOTE (-1034))) (|HasCategory| (-679) (QUOTE (-1171)))) (|HasCategory| (-679) (QUOTE (-1034))) (-3891 (|HasCategory| (-679) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-679) (QUOTE (-358)))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886))) (-3891 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (|HasCategory| (-679) (QUOTE (-358)))) (-3891 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (|HasCategory| (-679) (QUOTE (-545)))) (-12 (|HasCategory| (-679) (QUOTE (-229))) (|HasCategory| (-679) (QUOTE (-358)))) (-12 (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (LIST (QUOTE -876) (QUOTE (-1149))))) (|HasCategory| (-679) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-679) (QUOTE (-827))) (|HasCategory| (-679) (QUOTE (-545))) (|HasAttribute| (-679) (QUOTE -4352)) (|HasAttribute| (-679) (QUOTE -4349)) (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (|HasCategory| (-679) (QUOTE (-143)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-886)))) (|HasCategory| (-679) (QUOTE (-345))))) +((-4346 . T) (-4351 |has| (-679) (-358)) (-4345 |has| (-679) (-358)) (-3858 . T) (-4352 |has| (-679) (-6 -4352)) (-4349 |has| (-679) (-6 -4349)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| (-679) (QUOTE (-145))) (|HasCategory| (-679) (QUOTE (-143))) (|HasCategory| (-679) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-679) (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| (-679) (QUOTE (-363))) (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-679) (QUOTE (-229))) (-1523 (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-344)))) (|HasCategory| (-679) (QUOTE (-344))) (|HasCategory| (-679) (LIST (QUOTE -281) (QUOTE (-679)) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -304) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-679)))) (|HasCategory| (-679) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-679) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-679) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-679) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (-1523 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-344)))) (|HasCategory| (-679) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-679) (QUOTE (-998))) (|HasCategory| (-679) (QUOTE (-1171))) (-12 (|HasCategory| (-679) (QUOTE (-978))) (|HasCategory| (-679) (QUOTE (-1171)))) (-1523 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (|HasCategory| (-679) (QUOTE (-358))) (-12 (|HasCategory| (-679) (QUOTE (-344))) (|HasCategory| (-679) (QUOTE (-885))))) (-1523 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (-12 (|HasCategory| (-679) (QUOTE (-358))) (|HasCategory| (-679) (QUOTE (-885)))) (-12 (|HasCategory| (-679) (QUOTE (-344))) (|HasCategory| (-679) (QUOTE (-885))))) (|HasCategory| (-679) (QUOTE (-537))) (-12 (|HasCategory| (-679) (QUOTE (-1034))) (|HasCategory| (-679) (QUOTE (-1171)))) (|HasCategory| (-679) (QUOTE (-1034))) (-1523 (|HasCategory| (-679) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-679) (QUOTE (-358)))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885))) (-1523 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (|HasCategory| (-679) (QUOTE (-358)))) (-1523 (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (|HasCategory| (-679) (QUOTE (-544)))) (-12 (|HasCategory| (-679) (QUOTE (-229))) (|HasCategory| (-679) (QUOTE (-358)))) (-12 (|HasCategory| (-679) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-679) (QUOTE (-358)))) (|HasCategory| (-679) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-679) (QUOTE (-827))) (|HasCategory| (-679) (QUOTE (-544))) (|HasAttribute| (-679) (QUOTE -4352)) (|HasAttribute| (-679) (QUOTE -4349)) (-12 (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (|HasCategory| (-679) (QUOTE (-143)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-679) (QUOTE (-302))) (|HasCategory| (-679) (QUOTE (-885)))) (|HasCategory| (-679) (QUOTE (-344))))) (-675 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-676 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}."))) NIL NIL (-677) -((|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|)) #1="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|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) +((|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 -(-678 OV E -3428 PG) +(-678 OV E -3281 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 (-679) ((|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|) (|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}"))) -((-4129 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-2874 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-680 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."))) @@ -2676,7 +2676,7 @@ 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 -(-687 S -3002 I) +(-687 S -3768 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 @@ -2696,14 +2696,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-692 R |Mod| -2152 -3872 |exactQuo|) +(-692 R |Mod| -3297 -3280 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-693 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-345))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-344))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-694 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2712,7 +2712,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T)) ((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) -(-696 R |Mod| -2152 -3872 |exactQuo|) +(-696 R |Mod| -3297 -3280 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4350 . T)) NIL @@ -2724,7 +2724,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4348 . T) (-4347 . T)) NIL -(-699 -3428) +(-699 -3281) ((|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]]}."))) ((-4350 . T)) NIL @@ -2747,7 +2747,7 @@ NIL (-704 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-345))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-363)))) (-705 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) ((-4346 |has| |#1| (-358)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) @@ -2760,7 +2760,7 @@ 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.")) (|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 -(-708 -3428 UP) +(-708 -3281 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 @@ -2778,8 +2778,8 @@ NIL NIL (-712 |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."))) -(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-545)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-886))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) +(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-544)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#2| (QUOTE (-885))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-841 |#1|) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-358))) (-1523 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-143))))) (-713 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2797,13 +2797,13 @@ NIL ((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-827)))) (-717 S) -((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) -((-4353 . T) (-4343 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-718 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4343 . T) (-4354 . T) (-2368 . T)) +((-4343 . T) (-4354 . T) (-3526 . T)) NIL +(-718 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}."))) +((-4353 . T) (-4343 . T) (-4354 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-719) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2814,7 +2814,7 @@ NIL NIL (-721 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|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}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL (-722 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2912,15 +2912,15 @@ 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 -(-746 -3428) +(-746 -3281) ((|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 -(-747 P -3428) +(-747 P -3281) ((|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 -(-748 UP -3428) +(-748 UP -3281) ((|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 @@ -2936,16 +2936,16 @@ 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."))) (((-4355 "*") . T)) NIL -(-752 R -3428) +(-752 R -3281) ((|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 -(-753) -((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) +(-753 S) +((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-754 S) -((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) +(-754) +((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL (-755 R |PolR| E |PolE|) @@ -2956,7 +2956,7 @@ 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 -(-757 -3428 |ExtF| |SUEx| |ExtP| |n|) +(-757 -3281 |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 @@ -2970,28 +2970,28 @@ NIL NIL (-760 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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149))))) (-3891 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))) (-3676 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))))) (-3891 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))) (-3676 (|HasCategory| |#1| (QUOTE (-537)))) (-3676 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))) (-3676 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-538))))) (-3676 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-1149)))) (-3676 (|HasCategory| |#1| (LIST (QUOTE -967) (QUOTE (-538))))))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-761 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)}"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . 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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 NIL +(-762 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)}"))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-763 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 -38) (LIST (QUOTE -402) (QUOTE (-538)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-764 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.}"))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-765 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}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-170)))) +((-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-170)))) (-766) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -3028,43 +3028,43 @@ NIL ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-775 S R) +(-775) +((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) +NIL +NIL +(-776 S R) ((|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| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-363)))) -(-776 R) +((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-363)))) +(-777 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-777) -((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) +(-778 -1523 R OS S) +((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-778 R) +(-779 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-3891 (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) -(-779 -3891 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 +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (-1523 (|HasCategory| (-975 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (|HasCategory| (-975 |#1|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-975 |#1|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-975 |#1|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (-780) ((|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 -(-781 R -3428 L) +(-781 R -3281 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 -(-782 R -3428) -((|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| #1="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| #1#) (|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| #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| #2#) (|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."))) +(-782 R -3281) +((|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 (-783) ((|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 -(-784 R -3428) +(-784 R -3281) ((|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 @@ -3072,11 +3072,11 @@ 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 -(-786 -3428 UP UPUP R) +(-786 -3281 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 -(-787 -3428 UP L LQ) +(-787 -3281 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 @@ -3084,38 +3084,38 @@ 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 -(-789 -3428 UP L LQ) +(-789 -3281 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 -(-790 -3428 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|) #1="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|) #1#)) (|:| |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."))) +(-790 -3281 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 -(-791 -3428 L UP A LO) +(-791 -3281 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 -(-792 -3428 UP) +(-792 -3281 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)))) -(-793 -3428 LO) +(-793 -3281 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 -(-794 -3428 LODO) +(-794 -3281 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-707))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-773))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))))) (|HasCategory| (-552) (QUOTE (-827))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (QUOTE (-1025)))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552))))) (-1523 (|HasCategory| |#2| (QUOTE (-1025))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-1073)))) (|HasAttribute| |#2| (QUOTE -4350)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (-796 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-798 (-1149)) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-798 (-1149)) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-798 (-1149)) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-798 (-1149)) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-798 (-1149)) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-797 |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."))) (((-4355 "*") |has| |#2| (-358)) (-4346 |has| |#2| (-358)) (-4351 |has| |#2| (-358)) (-4345 |has| |#2| (-358)) (-4350 . T) (-4348 . T) (-4347 . T)) @@ -3133,57 +3133,57 @@ NIL ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-801) -((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) +((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL (-802) -((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) +((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL (-803) -((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) +((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL (-804) -((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) +((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL (-805) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-806) -((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) -NIL -NIL -(-807 R) +(-806 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-808 P R) +(-807 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) ((-4347 . T) (-4348 . T) (-4350 . T)) ((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-229)))) +(-808) +((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) +NIL +NIL (-809) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL (-810 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4353 . T) (-4343 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4343 . T) (-4354 . T) (-3526 . T)) NIL (-811) ((|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."))) NIL NIL -(-812 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."))) -((-4350 |has| |#1| (-825))) -((|HasCategory| |#1| (QUOTE (-825))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-21)))) -(-813 R S) +(-812 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL +(-813 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."))) +((-4350 |has| |#1| (-825))) +((|HasCategory| |#1| (QUOTE (-825))) (-1523 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-1523 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) (-814 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4348 |has| |#1| (-170)) (-4347 |has| |#1| (-170)) (-4350 . T)) @@ -3204,19 +3204,19 @@ NIL ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-819 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."))) -((-4350 |has| |#1| (-825))) -((|HasCategory| |#1| (QUOTE (-825))) (-3891 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-21)))) -(-820 R S) +(-819 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL +(-820 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| (($) "\\spad{plusInfinity()} returns +infinity."))) +((-4350 |has| |#1| (-825))) +((|HasCategory| |#1| (QUOTE (-825))) (-1523 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-537))) (-1523 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-21)))) (-821) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-822 -2950 S) +(-822 -2562 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3243,7 +3243,7 @@ NIL (-828 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(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 right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes 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}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(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.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\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| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} 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{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(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}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170)))) (-829 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(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 right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes 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}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(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.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\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| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} 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{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(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}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) ((-4347 . T) (-4348 . T) (-4350 . T)) @@ -3251,19 +3251,19 @@ NIL (-830 R C) ((|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 (-358))) (|HasCategory| |#1| (QUOTE (-545)))) -(-831 R |sigma| -3595) +((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) +(-831 R |sigma| -4057) ((|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."))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) -(-832 |x| R |sigma| -3595) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-358)))) +(-832 |x| R |sigma| -4057) ((|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."))) ((-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-358)))) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-358)))) (-833 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-834) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL @@ -3272,24 +3272,24 @@ NIL ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-836) -((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) +(-836 S) +((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL -(-837 S) +(-837) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) NIL NIL (-838) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteArray|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) +((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL (-839) -((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) +((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL (-840) -((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) +((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL (-841 |VariableList|) @@ -3309,25 +3309,25 @@ NIL NIL NIL (-845 |p|) -((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) +((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-846 |p|) -((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) +((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-847 |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)."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-845 |#1|) (QUOTE (-886))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-845 |#1|) (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-145))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-845 |#1|) (QUOTE (-996))) (|HasCategory| (-845 |#1|) (QUOTE (-800))) (-3891 (|HasCategory| (-845 |#1|) (QUOTE (-800))) (|HasCategory| (-845 |#1|) (QUOTE (-827)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (QUOTE (-1124))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-845 |#1|) (QUOTE (-229))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -845) (|devaluate| |#1|)) (LIST (QUOTE -845) (|devaluate| |#1|)))) (|HasCategory| (-845 |#1|) (QUOTE (-302))) (|HasCategory| (-845 |#1|) (QUOTE (-537))) (|HasCategory| (-845 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-845 |#1|) (QUOTE (-886)))) (|HasCategory| (-845 |#1|) (QUOTE (-143))))) +((|HasCategory| (-846 |#1|) (QUOTE (-885))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-846 |#1|) (QUOTE (-143))) (|HasCategory| (-846 |#1|) (QUOTE (-145))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-846 |#1|) (QUOTE (-998))) (|HasCategory| (-846 |#1|) (QUOTE (-800))) (-1523 (|HasCategory| (-846 |#1|) (QUOTE (-800))) (|HasCategory| (-846 |#1|) (QUOTE (-827)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-846 |#1|) (QUOTE (-1124))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| (-846 |#1|) (QUOTE (-229))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -507) (QUOTE (-1149)) (LIST (QUOTE -846) (|devaluate| |#1|)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -846) (|devaluate| |#1|)))) (|HasCategory| (-846 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -846) (|devaluate| |#1|)) (LIST (QUOTE -846) (|devaluate| |#1|)))) (|HasCategory| (-846 |#1|) (QUOTE (-302))) (|HasCategory| (-846 |#1|) (QUOTE (-537))) (|HasCategory| (-846 |#1|) (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-846 |#1|) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-846 |#1|) (QUOTE (-885)))) (|HasCategory| (-846 |#1|) (QUOTE (-143))))) (-848 |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)}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-800))) (-3891 (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1124))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-827))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) +((|HasCategory| |#2| (QUOTE (-885))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-800))) (-1523 (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1124))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-827))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-143))))) (-849 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 (-1074))) (|HasCategory| |#2| (QUOTE (-1074)))) (-3891 (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))))) (-850) ((|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 @@ -3383,27 +3383,27 @@ NIL (-863 |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 (-3676 (|HasCategory| |#2| (QUOTE (-1025)))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (-3676 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149))))) -(-864 R S) -((|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 -(-865 R A B) +((-12 (-2960 (|HasCategory| |#2| (QUOTE (-1025)))) (-2960 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (-12 (|HasCategory| |#2| (QUOTE (-1025))) (-2960 (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149))))) +(-864 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 NIL -(-866 R) -((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) +(-865 R S) +((|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 -(-867 R -3002) +(-866 R -3768) ((|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 -(-868 R S) +(-867 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL +(-868 R) +((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) +NIL +NIL (-869 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL @@ -3416,7 +3416,7 @@ 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 -(-872 UP -3428) +(-872 UP -3281) ((|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 @@ -3439,44 +3439,44 @@ NIL (-877 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 (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-878 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."))) -((-4350 . T)) -((-3891 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827)))) -(-879 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-878 |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 NIL -(-880 S) +(-879 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not 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.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(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."))) ((-4350 . T)) NIL -(-881 S) +(-880 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-882 |p|) -((|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."))) -((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-363)))) -(-883 R E |VarSet| S) +(-881 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."))) +((-4350 . T)) +((-1523 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-827)))) +(-882 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 NIL -(-884 R S) +(-883 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\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.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\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| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\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| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\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 NIL -(-885 S) +(-884 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-143)))) -(-886) +(-885) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-887 R0 -3428 UP UPUP R) +(-886 |p|) +((|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."))) +((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-363)))) +(-887 R0 -3281 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 @@ -3504,63 +3504,63 @@ 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 -(-894 -3428) +(-894 -3281) ((|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 -(-895) -((|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}."))) -(((-4355 "*") . T)) -NIL -(-896 R) +(-895 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-897) +(-896) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-898 |xx| -3428) -((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) -NIL +(-897) +((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) +(((-4355 "*") . T)) NIL -(-899 -3428 P) +(-898 -3281 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL +(-899 |xx| -3281) +((|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 (-900 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-901) -((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) +(-901 S) +((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-902 S) -((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) +(-902) +((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL (-903) -((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) +((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL (-904) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-905) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\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.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) +(-905 R -3281) +((|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 -(-906 R -3428) -((|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."))) +(-906) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\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.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL (-907 S A B) ((|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 -(-908 S R -3428) +(-908 S R -3281) ((|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 @@ -3580,12 +3580,12 @@ 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 -862) (|devaluate| |#1|)))) -(-913 -3002) -((|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}."))) +(-913 R -3281 -3768) +((|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 -(-914 R -3428 -3002) -((|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."))) +(-914 -3768) +((|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 (-915 S R Q) @@ -3607,7 +3607,7 @@ NIL (-919 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-920 |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 @@ -3616,35 +3616,35 @@ NIL ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-825)))) -(-922 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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1149) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-923 R S) +(-922 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-924 |x| R) +(-923 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-925 S R E |VarSet|) +(-924 S R E |VarSet|) ((|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| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\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.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\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| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\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| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\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| |#4|) (|:| |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| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|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| $)) $ $ |#4|) "\\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| |#4|)) "\\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|) $ |#4|) "\\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| |#4| "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| |#2|) $) "\\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| $) $ |#4|) "\\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| |#4|) (|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)}.") (($ $ |#4| (|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| |#4|)) "\\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|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-886))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-827)))) -(-926 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-885))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#4| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#4| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-827)))) +(-925 R E |VarSet|) ((|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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL -(-927 E V R P -3428) +(-926 E V R P -3281) ((|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 -(-928 E |Vars| R P S) +(-927 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-929 E V R P -3428) +(-928 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}."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1149) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1149) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1149) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-929 E V R P -3281) ((|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 (-446)))) @@ -3656,42 +3656,42 @@ NIL ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-932 R E) -((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-130)))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351))) -(-933 R L) +(-932 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-934 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"))) -((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-935 A B) +(-933 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive 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| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive 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),{}...]}."))) NIL NIL -(-936) +(-934 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"))) +((-4354 . T) (-4353 . T)) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-935) ((|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 -(-937 -3428) +(-936 -3281) ((|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 -(-938 I) +(-937 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-939) +(-938) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL +(-939 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}"))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-130)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351))) (-940 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"))) ((-4350 -12 (|has| |#2| (-467)) (|has| |#1| (-467)))) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-827))))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-363)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707))))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-827))))) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-827))))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-363)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-467))) (|HasCategory| |#2| (QUOTE (-467)))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707)))) (-12 (|HasCategory| |#1| (QUOTE (-773))) (|HasCategory| |#2| (QUOTE (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-707)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-827))))) (-941) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3706,7 +3706,7 @@ NIL NIL (-944 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL (-945 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}}"))) @@ -3726,7 +3726,7 @@ NIL NIL (-949 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-950) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3735,10 +3735,10 @@ NIL (-951 S 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| |#5|) (|List| |#5|) $) "\\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| |#5|) (|List| |#5|) $) "\\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| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\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| |#5|) (|:| |den| |#2|)) |#5| $) "\\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| $)) $ |#4|) "\\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| (($ $ |#4|) "\\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| (($ $ |#4|) "\\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| (($ $ |#4|) "\\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|) |#4| $) "\\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| |#4|) $) "\\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| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\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| |#5|)) "\\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."))) NIL -((|HasCategory| |#2| (QUOTE (-545)))) +((|HasCategory| |#2| (QUOTE (-544)))) (-952 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."))) -((-4353 . T) (-2368 . T)) +((-4353 . T) (-3526 . T)) NIL (-953 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."))) @@ -3754,7 +3754,7 @@ NIL NIL (-956 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}."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-957 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3772,18 +3772,18 @@ 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 -(-961 K R UP -3428) +(-961 K R UP -3281) ((|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 -(-962 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) -NIL -((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-302))))) -(-963 |vl| |nv|) +(-962 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL +(-963 R |Var| |Expon| |Dpoly|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +NIL +((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-302))))) (-964 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular 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} \\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.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL @@ -3792,17 +3792,17 @@ NIL ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-966 A S) -((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\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| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) +(-966 A B R S) +((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL -((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1124)))) -(-967 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}."))) -((-2368 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-968 A B R S) -((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) +(-967 A S) +((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\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| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL +((|HasCategory| |#2| (QUOTE (-885))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-800))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-1124)))) +(-968 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}."))) +((-3526 . T) (-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-969 |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}."))) @@ -3814,28 +3814,28 @@ NIL NIL (-971 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."))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL -(-972 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.}"))) -((-4346 |has| |#1| (-285)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))))) -(-973 S R) +(-972 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}."))) NIL -((|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-285)))) -(-974 R) +((|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (QUOTE (-1034))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-285)))) +(-973 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| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) ((-4346 |has| |#1| (-285)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-975 QR R QS S) +(-974 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL +(-975 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.}"))) +((-4346 |has| |#1| (-285)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1149)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-1034))) (|HasCategory| |#1| (QUOTE (-537))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-358))))) (-976 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-977 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3844,14 +3844,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-979 -3428 UP UPUP |radicnd| |n|) +(-979 -3281 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4346 |has| (-402 |#2|) (-358)) (-4351 |has| (-402 |#2|) (-358)) (-4345 |has| (-402 |#2|) (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-402 |#2|) (QUOTE (-143))) (|HasCategory| (-402 |#2|) (QUOTE (-145))) (|HasCategory| (-402 |#2|) (QUOTE (-345))) (-3891 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-363))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (|HasCategory| (-402 |#2|) (QUOTE (-345)))) (-3891 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-345))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-3891 (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358))))) +((|HasCategory| (-402 |#2|) (QUOTE (-143))) (|HasCategory| (-402 |#2|) (QUOTE (-145))) (|HasCategory| (-402 |#2|) (QUOTE (-344))) (-1523 (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-344)))) (|HasCategory| (-402 |#2|) (QUOTE (-358))) (|HasCategory| (-402 |#2|) (QUOTE (-363))) (-1523 (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (|HasCategory| (-402 |#2|) (QUOTE (-344)))) (-1523 (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-344))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-1523 (|HasCategory| (-402 |#2|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-402 |#2|) (QUOTE (-358)))) (-12 (|HasCategory| (-402 |#2|) (QUOTE (-229))) (|HasCategory| (-402 |#2|) (QUOTE (-358))))) (-980 |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."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-538) (QUOTE (-886))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-538) (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-145))) (|HasCategory| (-538) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-996))) (|HasCategory| (-538) (QUOTE (-800))) (-3891 (|HasCategory| (-538) (QUOTE (-800))) (|HasCategory| (-538) (QUOTE (-827)))) (|HasCategory| (-538) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-1124))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-538) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-538) (QUOTE (-229))) (|HasCategory| (-538) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-538) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -304) (QUOTE (-538)))) (|HasCategory| (-538) (LIST (QUOTE -281) (QUOTE (-538)) (QUOTE (-538)))) (|HasCategory| (-538) (QUOTE (-302))) (|HasCategory| (-538) (QUOTE (-537))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-538) (LIST (QUOTE -621) (QUOTE (-538)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (-3891 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-538) (QUOTE (-886)))) (|HasCategory| (-538) (QUOTE (-143))))) +((|HasCategory| (-552) (QUOTE (-885))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-1149)))) (|HasCategory| (-552) (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-145))) (|HasCategory| (-552) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-998))) (|HasCategory| (-552) (QUOTE (-800))) (-1523 (|HasCategory| (-552) (QUOTE (-800))) (|HasCategory| (-552) (QUOTE (-827)))) (|HasCategory| (-552) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-1124))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| (-552) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| (-552) (QUOTE (-229))) (|HasCategory| (-552) (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| (-552) (LIST (QUOTE -507) (QUOTE (-1149)) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -304) (QUOTE (-552)))) (|HasCategory| (-552) (LIST (QUOTE -281) (QUOTE (-552)) (QUOTE (-552)))) (|HasCategory| (-552) (QUOTE (-302))) (|HasCategory| (-552) (QUOTE (-537))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-552) (LIST (QUOTE -621) (QUOTE (-552)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-552) (QUOTE (-885)))) (|HasCategory| (-552) (QUOTE (-143))))) (-981) ((|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 @@ -3871,10 +3871,10 @@ NIL (-985 A 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!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\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| |#2|) $) "\\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| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\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}."))) NIL -((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-1074)))) +((|HasAttribute| |#1| (QUOTE -4354)) (|HasCategory| |#2| (QUOTE (-1073)))) (-986 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}."))) -((-2368 . T)) +((-3526 . T)) NIL (-987 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3884,19 +3884,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4346 . T) (-4351 . T) (-4345 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4350 . T)) NIL -(-989 R -3428) +(-989 R -3281) ((|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 -(-990 R -3428) +(-990 R -3281) ((|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 -(-991 -3428 UP) +(-991 -3281 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 -(-992 -3428 UP) +(-992 -3281 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 @@ -3912,16 +3912,16 @@ NIL ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-996) -((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) +(-996 |Pol|) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL (-997 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-998 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) +(-998) +((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL (-999) @@ -3931,35 +3931,35 @@ NIL (-1000 |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"))) ((-4346 . T) (-4351 . T) (-4345 . T) (-4348 . T) (-4347 . T) ((-4355 "*") . T) (-4350 . T)) -((-3891 (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-402 (-538)) (LIST (QUOTE -1014) (QUOTE (-538))))) -(-1001 -3428 L) +((-1523 (|HasCategory| (-402 (-552)) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-402 (-552)) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-402 (-552)) (LIST (QUOTE -1014) (QUOTE (-552))))) +(-1001 -3281 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 (-1002 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1074)))) +((|HasCategory| |#1| (QUOTE (-1073)))) (-1003 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\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.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840))))) -(-1004) -((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) -NIL -NIL -(-1005 R) +((-12 (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-839))))) +(-1004 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL ((|HasAttribute| |#1| (QUOTE (-4355 "*")))) -(-1006 R) +(-1005 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-302)))) -(-1007 S) +(-1006 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL +(-1007) +((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) +NIL +NIL (-1008 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL @@ -3968,14 +3968,14 @@ 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 -(-1010 -3428 |Expon| |VarSet| |FPol| |LFPol|) +(-1010 -3281 |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"))) (((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-1011) ((|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.}"))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -2191) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -304) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-51) (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -4120) (QUOTE (-52))))))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-52) (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -304) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-52) (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839))))) (-1012) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -3992,22 +3992,22 @@ NIL ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1016 R) -((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\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| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) -NIL -NIL -(-1017) +(-1016) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1018 UP) +(-1017 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1019 R) +(-1018 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL +(-1019 R) +((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\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| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) +NIL +NIL (-1020 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL @@ -4019,7 +4019,7 @@ NIL (-1022 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1074))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -760) (|devaluate| |#1|) (LIST (QUOTE -841) (|devaluate| |#2|)))))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-841 |#2|) (QUOTE (-363))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1073))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -760) (|devaluate| |#1|) (LIST (QUOTE -841) (|devaluate| |#2|)))))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-760 |#1| (-841 |#2|)) (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| (-841 |#2|) (QUOTE (-363))) (|HasCategory| (-760 |#1| (-841 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-1023) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL @@ -4032,22 +4032,22 @@ 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."))) ((-4350 . T)) NIL -(-1026 |xx| -3428) +(-1026 |xx| -3281) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL (-1027 S |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| |#6|) $) "\\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|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\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| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|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| ((|#5| $ (|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| ((|#4| $ (|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| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\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.") ((|#4| $ (|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| |#4|)) $) "\\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| |#4|))) "\\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"))) NIL -((|HasCategory| |#4| (QUOTE (-302))) (|HasCategory| |#4| (QUOTE (-358))) (|HasCategory| |#4| (QUOTE (-545))) (|HasCategory| |#4| (QUOTE (-170)))) +((|HasCategory| |#4| (QUOTE (-302))) (|HasCategory| |#4| (QUOTE (-358))) (|HasCategory| |#4| (QUOTE (-544))) (|HasCategory| |#4| (QUOTE (-170)))) (-1028 |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"))) -((-4353 . T) (-2368 . T) (-4348 . T) (-4347 . T)) +((-4353 . T) (-3526 . T) (-4348 . T) (-4347 . T)) NIL (-1029 |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}."))) ((-4353 . T) (-4348 . T) (-4347 . T)) -((-3891 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-358)))) (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (QUOTE (-302))) (|HasCategory| |#3| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-840)))) (-12 (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))))) +((-1523 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-358)))) (|HasCategory| |#3| (QUOTE (-358))) (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (QUOTE (-302))) (|HasCategory| |#3| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -597) (QUOTE (-839)))) (-12 (|HasCategory| |#3| (QUOTE (-1073))) (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))))) (-1030 |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 @@ -4079,14 +4079,14 @@ NIL (-1037) ((|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}"))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -2191) (QUOTE (-51)))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| (-51) (QUOTE (-1074))) (|HasCategory| (-51) (LIST (QUOTE -304) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (QUOTE (-1074))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-51) (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-51) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1149)) (|:| -2191 (-51))) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (QUOTE (-1149))) (LIST (QUOTE |:|) (QUOTE -4120) (QUOTE (-52))))))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-52) (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| (-52) (QUOTE (-1073))) (|HasCategory| (-52) (LIST (QUOTE -304) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (QUOTE (-1073))) (|HasCategory| (-1149) (QUOTE (-827))) (|HasCategory| (-52) (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-52) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 (-1149)) (|:| -4120 (-52))) (LIST (QUOTE -597) (QUOTE (-839))))) (-1038 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -967) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-1149))))) +((|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-537))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -968) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-1149))))) (-1039 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|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| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| |#1|)) "\\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| $)) $ $ |#3|) "\\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| $)) $ $ |#3|) "\\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| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\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}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\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.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\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}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\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|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\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| (($ $ |#3|) "\\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| ((|#3| $) "\\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}}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL (-1040) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4110,7 +4110,7 @@ NIL NIL (-1045 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}."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-1046 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."))) @@ -4120,15 +4120,15 @@ NIL ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1048 |Base| R -3428) -((|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}."))) +(-1048 |f|) +((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1049 |f|) -((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) +(-1049 |Base| R -3281) +((|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 -(-1050 |Base| R -3428) +(-1050 |Base| R -3281) ((|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 @@ -4136,14 +4136,14 @@ NIL ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1052 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."))) -((-4346 |has| |#1| (-358)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-345))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-345)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-345)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-345))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358))))) -(-1053 UP SAE UPA) +(-1052 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL +(-1053 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."))) +((-4346 |has| |#1| (-358)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-344))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-363))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-344)))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149))))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (QUOTE (-358))))) (-1054 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 @@ -4170,74 +4170,74 @@ NIL NIL (-1060 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"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1061 (-1149)) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1061 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 NIL -(-1062 S) -((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) -NIL -((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1074)))) -(-1063 R S) +(-1062 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-825)))) -(-1064) +(-1063) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL +(-1064 R S) +((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) +NIL +NIL (-1065 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1074)))) -(-1066 R S) -((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) -NIL +((|HasCategory| |#1| (QUOTE (-1073)))) +(-1066 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."))) +((-3526 . T)) NIL (-1067 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."))) -((-2368 . T)) +((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL +((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1073)))) (-1068 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]}."))) -((-2368 . T)) +((-3526 . T)) NIL (-1069) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1070 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)}}"))) -((-4353 . T) (-4343 . T) (-4354 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-1071 A S) +(-1070 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.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1072 S) +(-1071 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4343 . T) (-2368 . T)) +((-4343 . T) (-3526 . T)) NIL -(-1073 S) +(-1072 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}."))) NIL NIL -(-1074) +(-1073) ((|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}."))) NIL NIL -(-1075 |m| |n|) -((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) +(-1074 |m| |n|) +((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1076) -((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) +(-1075 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)}}"))) +((-4353 . T) (-4343 . T) (-4354 . T)) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-827))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-1076 |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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1077 |Str| |Sym| |Int| |Flt| |Expr|) -((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|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."))) +(-1077) +((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL (-1078 |Str| |Sym| |Int| |Flt| |Expr|) @@ -4258,7 +4258,7 @@ NIL NIL (-1082 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.}"))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-1083) ((|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."))) @@ -4275,25 +4275,25 @@ NIL (-1086 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4347 |has| |#3| (-1025)) (-4348 |has| |#3| (-1025)) (-4350 |has| |#3| (-6 -4350)) ((-4355 "*") |has| |#3| (-170)) (-4353 . 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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 (-446)))) (-1088) -((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) +((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1089) -((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) +(-1089 R -3281) +((|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 -(-1090 R -3428) -((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) |#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|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1090 R) +((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1091 R) -((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) +(-1091) +((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL (-1092) @@ -4306,7 +4306,7 @@ NIL NIL (-1094 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4353 . T) (-4354 . T) (-2368 . T)) +((-4353 . T) (-4354 . T) (-3526 . T)) NIL (-1095 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4314,7 +4314,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-358))) (|HasAttribute| |#3| (QUOTE (-4355 "*"))) (|HasCategory| |#3| (QUOTE (-170)))) (-1096 |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."))) -((-2368 . T) (-4353 . T) (-4347 . T) (-4348 . T) (-4350 . T)) +((-3526 . T) (-4353 . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-1097 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}."))) @@ -4322,17 +4322,17 @@ NIL NIL (-1098 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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-886))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1099 |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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-358)))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-358)))) (-1100 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}"))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL -(-1101 UP -3428) +(-1101 UP -3281) ((|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 @@ -4370,7 +4370,7 @@ NIL NIL (-1110) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) -((-2368 . T)) +((-3526 . T)) NIL (-1111) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) @@ -4387,18 +4387,18 @@ NIL (-1114 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074))) (-3891 (-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1074)))) (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1073)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1073))) (-1523 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-839)))) (-12 (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1113) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1113 |#1| |#2|) (QUOTE (-1073))))) (|HasCategory| (-1113 |#1| |#2|) (LIST (QUOTE -597) (QUOTE (-839))))) (-1115 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4350 . T) (-4342 |has| |#2| (-6 (-4355 "*"))) (-4353 . T) (-4347 . T) (-4348 . T)) -((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-358))) (-3891 (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-170)))) +((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (-1523 (-12 (|HasCategory| |#2| (QUOTE (-229))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-358))) (-1523 (|HasAttribute| |#2| (QUOTE (-4355 "*"))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasCategory| |#2| (QUOTE (-229)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-170)))) (-1116 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1117) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-1118 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.}"))) @@ -4407,23 +4407,23 @@ NIL (-1119 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\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.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-839))))) (-1120 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}."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-1121 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 (-1122 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})}."))) -((-2368 . T)) +((-3526 . T)) NIL (-1123 |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."))) ((-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-827))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-827))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-1124) ((|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 @@ -4433,43 +4433,43 @@ NIL NIL NIL (-1126 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."))) -((-4354 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-1127 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1128 A B) +(-1127 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1129 A B C) +(-1128 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL +(-1129 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."))) +((-4354 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-1130) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL (-1131) NIL ((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1074))) (-12 (|HasCategory| (-142) (QUOTE (-1074))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-840))))) +((-1523 (-12 (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| (-142) (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| (-142) (QUOTE (-1073))) (-12 (|HasCategory| (-142) (QUOTE (-1073))) (|HasCategory| (-142) (LIST (QUOTE -304) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -597) (QUOTE (-839))))) (-1132 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (QUOTE (-1074))) (|HasCategory| (-1131) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 (-1131)) (|:| -2191 |#1|)) (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (QUOTE (-1131))) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#1|)))))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (QUOTE (-1073))) (|HasCategory| (-1131) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 (-1131)) (|:| -4120 |#1|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-1133 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 -((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538)))))) +((|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1134 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL (-1135 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL (-1136 R UP) @@ -4490,9 +4490,9 @@ NIL NIL (-1140 |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."))) -(((-4355 "*") -3891 (-3191 (|has| |#1| (-358)) (|has| (-1147 |#1| |#2| |#3|) (-800))) (|has| |#1| (-170)) (-3191 (|has| |#1| (-358)) (|has| (-1147 |#1| |#2| |#3|) (-886)))) (-4346 -3891 (-3191 (|has| |#1| (-358)) (|has| (-1147 |#1| |#2| |#3|) (-800))) (|has| |#1| (-545)) (-3191 (|has| |#1| (-358)) (|has| (-1147 |#1| |#2| |#3|) (-886)))) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-800)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-886)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -598) (QUOTE (-527))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -281) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -304) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| 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T)) -((|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-886)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-886)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-1144 R S) +(-1143 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| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1145 E OV R P) +(-1144 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL +(-1145 R) +((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasCategory| |#1| (QUOTE (-229))) (|HasAttribute| |#1| (QUOTE -4351)) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1146 |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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|))))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-552)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|))))))) (-1147 |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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|))))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|))))))) (-1148) ((|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 @@ -4534,10 +4534,10 @@ NIL NIL (-1151 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-6 -4351)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| (-947) (QUOTE (-130)))) (-3891 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasAttribute| |#1| (QUOTE -4351))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-6 -4351)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-446))) (-12 (|HasCategory| (-947) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasAttribute| |#1| (QUOTE -4351))) (-1152) -((|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| #1="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| #1#))) "\\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| #1#))) "\\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| #1#)) $) "\\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."))) +((|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 NIL (-1153) @@ -4560,14 +4560,14 @@ NIL ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1158 |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}"))) -((-4353 . T) (-4354 . T)) -((-12 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4220) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2191) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -598) (QUOTE (-527)))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1074))) (-3891 (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-840)))) (|HasCategory| (-2 (|:| -4220 |#1|) (|:| -2191 |#2|)) (LIST (QUOTE -597) (QUOTE (-840))))) -(-1159 S) +(-1158 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL +(-1159 |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}"))) +((-4353 . T) (-4354 . T)) +((-12 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2971) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4120) (|devaluate| |#2|)))))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1073)))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -598) (QUOTE (-528)))) (-12 (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#2| (QUOTE (-1073))) (-1523 (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#2| (LIST (QUOTE -597) (QUOTE (-839)))) (|HasCategory| (-2 (|:| -2971 |#1|) (|:| -4120 |#2|)) (LIST (QUOTE -597) (QUOTE (-839))))) (-1160 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 @@ -4578,7 +4578,7 @@ NIL NIL (-1162 |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})}."))) -((-4354 . T) (-2368 . T)) +((-4354 . T) (-3526 . T)) NIL (-1163 |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."))) @@ -4588,12 +4588,12 @@ NIL ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1165) -((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) +(-1165 S) +((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1166 S) -((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) +(-1166) +((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL (-1167) @@ -4619,7 +4619,7 @@ NIL (-1172 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1074))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1073))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-1173 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4628,7 +4628,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1175 R -3428) +(-1175 R -3281) ((|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 @@ -4636,22 +4636,22 @@ 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 -(-1177 R -3428) +(-1177 R -3281) ((|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 -598) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -862) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -862) (|devaluate| |#1|))))) -(-1178 |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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-358)))) -(-1179 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -598) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -862) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -862) (|devaluate| |#1|))))) +(-1178 S 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| (($ $ |#5|) "\\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") $ |#5|) "\\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| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\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| |#4|) $) "\\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| |#5| "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| |#5| "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| |#5|)))) (|List| |#5|)) "\\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| |#5|)) "\\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| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\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| ((|#5| |#5| $) "\\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| ((|#5| |#5| $) "\\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| ((|#5| |#5| $) "\\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| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\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| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\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|) |#5| (|List| |#5|))) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\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|) |#5| $) "\\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| |#5|)) (|:| |open| (|List| |#5|))) $) "\\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| |#5|) $) "\\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| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\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| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\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."))) NIL ((|HasCategory| |#4| (QUOTE (-363)))) -(-1180 R E V P) +(-1179 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL +(-1180 |Coef|) +((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-358)))) (-1181 |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 @@ -4663,19 +4663,19 @@ NIL (-1183 S) ((|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 (-1074))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-1184 -3428) +((|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) +(-1184 -3281) ((|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 (-1185) -((|constructor| (NIL "The fundamental Type."))) -((-2368 . T)) -NIL -(-1186) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL +(-1186) +((|constructor| (NIL "The fundamental Type."))) +((-3526 . T)) +NIL (-1187 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}.}"))) NIL @@ -4692,153 +4692,153 @@ NIL ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) ((-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-1191 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4355 "*") -3891 (-3191 (|has| |#1| (-358)) (|has| (-1221 |#1| |#2| |#3|) (-800))) (|has| |#1| (-170)) (-3191 (|has| |#1| (-358)) (|has| (-1221 |#1| |#2| |#3|) (-886)))) (-4346 -3891 (-3191 (|has| |#1| (-358)) (|has| (-1221 |#1| |#2| |#3|) (-800))) (|has| |#1| (-545)) (-3191 (|has| |#1| (-358)) (|has| (-1221 |#1| |#2| |#3|) (-886)))) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . 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|Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1193 |Coef|) +(-1192 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent 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 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") 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T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-1194 S |Coef| UTS) +(-1193 S |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| |#3| "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| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\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| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-358)))) -(-1195 |Coef| UTS) +(-1194 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) 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(LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (-12 (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-800))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-170)))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-358)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-885))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3|) (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1197 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1198 S) -((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) -NIL -((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1074)))) -(-1199 R S) +(-1198 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-825)))) -(-1200 |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."))) -(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-545)) (-4349 |has| |#2| (-358)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-373)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-373))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-538)))) (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-538))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-373)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538))))) (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -866) (QUOTE (-538)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-527))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (-3891 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-886)))) (-3891 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-886)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-1124))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (-3891 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (-3891 (-12 (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| $ (QUOTE (-143)))) (|HasCategory| |#2| (QUOTE (-143))))) -(-1201 |x| R |y| S) +(-1199 S) +((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) +NIL +((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1073)))) +(-1200 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\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| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1202 R Q UP) +(-1201 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1203 R UP) +(-1202 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1204 R UP) +(-1203 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1205 R U) +(-1204 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1206 S R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(-1205 |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."))) +(((-4355 "*") |has| |#2| (-170)) (-4346 |has| |#2| (-544)) (-4349 |has| |#2| (-358)) (-4351 |has| |#2| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#2| (QUOTE (-885))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-544)))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-374)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-374))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -862) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -862) (QUOTE (-552))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-374)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -598) (LIST (QUOTE -868) (QUOTE (-552)))))) (-12 (|HasCategory| (-1055) (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#2| (LIST (QUOTE -598) (QUOTE (-528))))) (|HasCategory| |#2| (QUOTE (-827))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (-1523 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-1124))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (-1523 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasCategory| |#2| (QUOTE (-229))) (|HasAttribute| |#2| (QUOTE -4351)) (|HasCategory| |#2| (QUOTE (-446))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (-1523 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-143))))) +(-1206 R PR S PS) +((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1124)))) -(-1207 R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL -(-1208 R PR S PS) -((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) +(-1207 S R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1124)))) +(-1208 R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4349 |has| |#1| (-358)) (-4351 |has| |#1| (-6 -4351)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL (-1209 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 -876) (QUOTE (-1149)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1085))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4317) (LIST (|devaluate| |#2|) (QUOTE (-1149)))))) +((|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1085))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1683) (LIST (|devaluate| |#2|) (QUOTE (-1149)))))) (-1210 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL (-1211 RC P) -((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) +((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1212 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|))))))) -(-1213 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1212 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1214 |Coef|) +(-1213 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux 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),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and 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 and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-1215 S |Coef| ULS) +(-1214 S |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1216 |Coef| ULS) +(-1215 |Coef| ULS) ((|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)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-1217 |Coef| ULS) +(-1216 |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)}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-170))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-538)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-3891 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-538)))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538)))))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . 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T)) +((|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-552)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) +(-1217 |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."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4351 |has| |#1| (-358)) (-4345 |has| |#1| (-358)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-170))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552))) (|devaluate| |#1|)))) (|HasCategory| (-402 (-552)) (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-1523 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-544)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -402) (QUOTE (-552)))))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|))))))) (-1218 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))}."))) -(((-4355 "*") |has| (-1212 |#2| |#3| |#4|) (-170)) (-4346 |has| (-1212 |#2| |#3| |#4|) (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (QUOTE (-538)))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-358))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-446))) (-3891 (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-538)))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-545)))) +(((-4355 "*") |has| (-1217 |#2| |#3| |#4|) (-170)) (-4346 |has| (-1217 |#2| |#3| |#4|) (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| (-1217 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1217 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-1217 |#2| |#3| |#4|) (LIST (QUOTE -1014) (QUOTE (-552)))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-358))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-446))) (-1523 (|HasCategory| (-1217 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| (-1217 |#2| |#3| |#4|) (LIST (QUOTE -1014) (LIST (QUOTE -402) (QUOTE (-552)))))) (|HasCategory| (-1217 |#2| |#3| |#4|) (QUOTE (-544)))) (-1219 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4354))) (-1220 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2368 . T)) +((-3526 . T)) NIL -(-1221 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-545))) (-3891 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -4317) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-936))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasSignature| |#1| (LIST (QUOTE -4172) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#1|))))))) -(-1222 |Coef1| |Coef2| UTS1 UTS2) +(-1221 |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)}.}"))) NIL NIL -(-1223 S |Coef|) +(-1222 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 (-538)))) (|HasCategory| |#2| (QUOTE (-936))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasSignature| |#2| (LIST (QUOTE -3417) (LIST (LIST (QUOTE -622) (QUOTE (-1149))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4172) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1149))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasCategory| |#2| (QUOTE (-358)))) -(-1224 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-1171))) (|HasSignature| |#2| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2481) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1149))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#2| (QUOTE (-358)))) +(-1223 |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."))) -(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-545)) (-4347 . T) (-4348 . T) (-4350 . T)) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) NIL +(-1224 |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}."))) +(((-4355 "*") |has| |#1| (-170)) (-4346 |has| |#1| (-544)) (-4347 . T) (-4348 . T) (-4350 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasCategory| |#1| (QUOTE (-544))) (-1523 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-1149)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-751)) (|devaluate| |#1|)))) (|HasCategory| (-751) (QUOTE (-1085))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasSignature| |#1| (LIST (QUOTE -1683) (LIST (|devaluate| |#1|) (QUOTE (-1149)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-358))) (-1523 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-552)))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-1171))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasSignature| |#1| (LIST (QUOTE -2481) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1149))))) (|HasSignature| |#1| (LIST (QUOTE -3982) (LIST (LIST (QUOTE -625) (QUOTE (-1149))) (|devaluate| |#1|))))))) (-1225 |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 -(-1226 -3428 UP L UTS) +(-1226 -3281 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 (-545)))) +((|HasCategory| |#1| (QUOTE (-544)))) (-1227) ((|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."))) -((-2368 . T)) +((-3526 . T)) NIL (-1228 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4850,30 +4850,30 @@ NIL ((|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-707))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1230 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4354 . T) (-4353 . T) (-2368 . T)) +((-4354 . T) (-4353 . T) (-3526 . T)) NIL -(-1231 R) -((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4354 . T) (-4353 . T)) -((-3891 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-3891 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-527)))) (-3891 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-538) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-840))))) -(-1232 A B) +(-1231 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}."))) NIL NIL +(-1232 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."))) +((-4354 . T) (-4353 . T)) +((-1523 (-12 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))))) (-1523 (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (|HasCategory| |#1| (LIST (QUOTE -598) (QUOTE (-528)))) (-1523 (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-827))) (|HasCategory| (-552) (QUOTE (-827))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-707))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1025)))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -597) (QUOTE (-839))))) (-1233) -((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) +((|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 NIL (-1234) -((|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."))) +((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file 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 three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} 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{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL (-1235) -((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file 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 three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} 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{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) +((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL (-1236) -((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) +((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL (-1237) @@ -4892,7 +4892,7 @@ 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 -(-1241 K R UP -3428) +(-1241 K R UP -3281) ((|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 @@ -4911,7 +4911,7 @@ NIL (-1245 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. 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. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) ((-4354 . T) (-4353 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-527)))) (|HasCategory| |#4| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-840))))) +((-12 (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -598) (QUOTE (-528)))) (|HasCategory| |#4| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -597) (QUOTE (-839))))) (-1246 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) ((-4347 . T) (-4348 . T) (-4350 . T)) @@ -4924,30 +4924,30 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1249 S -3428) +(-1249 |vl| R) +((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) +((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) +NIL +(-1250 S -3281) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145)))) -(-1250 -3428) +(-1251 -3281) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4345 . T) (-4351 . T) (-4346 . T) ((-4355 "*") . T) (-4347 . T) (-4348 . T) (-4350 . T)) NIL -(-1251 |vl| R) -((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) -NIL (-1252 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) ((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -698) (LIST (QUOTE -402) (QUOTE (-538))))) (|HasAttribute| |#2| (QUOTE -4346))) -(-1253 R) -((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4346 |has| |#1| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) -((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4346))) -(-1254 |vl| R) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -698) (LIST (QUOTE -402) (QUOTE (-552))))) (|HasAttribute| |#2| (QUOTE -4346))) +(-1253 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) ((-4346 |has| |#2| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) NIL +(-1254 R) +((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) +((-4346 |has| |#1| (-6 -4346)) (-4348 . T) (-4347 . T) (-4350 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4346))) (-1255 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) ((-4350 . T) (-4351 |has| |#1| (-6 -4351)) (-4346 |has| |#1| (-6 -4346)) (-4348 . T) (-4347 . T)) @@ -4988,4 +4988,4 @@ NIL NIL NIL NIL -((-3 NIL 2267916 2267921 2267926 2267931) (-2 NIL 2267896 2267901 2267906 2267911) (-1 NIL 2267876 2267881 2267886 2267891) (0 NIL 2267856 2267861 2267866 2267871) (-1260 "ZMOD.spad" 2267665 2267678 2267794 2267851) (-1259 "ZLINDEP.spad" 2266709 2266720 2267655 2267660) (-1258 "ZDSOLVE.spad" 2256558 2256580 2266699 2266704) (-1257 "YSTREAM.spad" 2256051 2256062 2256548 2256553) (-1256 "XRPOLY.spad" 2255271 2255291 2255907 2255976) (-1255 "XPR.spad" 2253000 2253013 2254989 2255088) (-1254 "XPOLYC.spad" 2252317 2252333 2252926 2252995) (-1253 "XPOLY.spad" 2251872 2251883 2252173 2252242) (-1252 "XPBWPOLY.spad" 2250309 2250329 2251652 2251721) (-1251 "XFALG.spad" 2247333 2247349 2250235 2250304) (-1250 "XF.spad" 2245794 2245809 2247235 2247328) (-1249 "XF.spad" 2244235 2244252 2245678 2245683) (-1248 "XEXPPKG.spad" 2243486 2243512 2244225 2244230) (-1247 "XDPOLY.spad" 2243100 2243116 2243342 2243411) (-1246 "XALG.spad" 2242698 2242709 2243056 2243095) (-1245 "WUTSET.spad" 2238537 2238554 2242344 2242371) (-1244 "WP.spad" 2237551 2237595 2238395 2238462) (-1243 "WHILEAST.spad" 2237349 2237358 2237541 2237546) (-1242 "WHEREAST.spad" 2237020 2237029 2237339 2237344) (-1241 "WFFINTBS.spad" 2234583 2234605 2237010 2237015) (-1240 "WEIER.spad" 2232797 2232808 2234573 2234578) (-1239 "VSPACE.spad" 2232470 2232481 2232765 2232792) (-1238 "VSPACE.spad" 2232163 2232176 2232460 2232465) (-1237 "VOID.spad" 2231753 2231762 2232153 2232158) (-1236 "VIEWDEF.spad" 2226950 2226959 2231743 2231748) (-1235 "VIEW3D.spad" 2210785 2210794 2226940 2226945) (-1234 "VIEW2D.spad" 2198522 2198531 2210775 2210780) (-1233 "VIEW.spad" 2196144 2196153 2198512 2198517) (-1232 "VECTOR2.spad" 2194771 2194784 2196134 2196139) (-1231 "VECTOR.spad" 2193446 2193457 2193697 2193724) (-1230 "VECTCAT.spad" 2191334 2191345 2193402 2193441) (-1229 "VECTCAT.spad" 2189042 2189055 2191112 2191117) (-1228 "VARIABLE.spad" 2188822 2188837 2189032 2189037) (-1227 "UTYPE.spad" 2188456 2188465 2188802 2188817) (-1226 "UTSODETL.spad" 2187749 2187773 2188412 2188417) (-1225 "UTSODE.spad" 2185937 2185957 2187739 2187744) (-1224 "UTSCAT.spad" 2183388 2183404 2185835 2185932) (-1223 "UTSCAT.spad" 2180483 2180501 2182932 2182937) (-1222 "UTS2.spad" 2180076 2180111 2180473 2180478) (-1221 "UTS.spad" 2174865 2174893 2178543 2178640) (-1220 "URAGG.spad" 2169487 2169498 2174845 2174860) (-1219 "URAGG.spad" 2164083 2164096 2169443 2169448) (-1218 "UPXSSING.spad" 2161726 2161752 2163164 2163297) (-1217 "UPXSCONS.spad" 2159483 2159503 2159858 2160007) (-1216 "UPXSCCA.spad" 2157941 2157961 2159329 2159478) (-1215 "UPXSCCA.spad" 2156541 2156563 2157931 2157936) (-1214 "UPXSCAT.spad" 2155122 2155138 2156387 2156536) (-1213 "UPXS2.spad" 2154663 2154716 2155112 2155117) (-1212 "UPXS.spad" 2151690 2151718 2152795 2152944) (-1211 "UPSQFREE.spad" 2150103 2150117 2151680 2151685) (-1210 "UPSCAT.spad" 2147696 2147720 2150001 2150098) (-1209 "UPSCAT.spad" 2144995 2145021 2147302 2147307) (-1208 "UPOLYC2.spad" 2144464 2144483 2144985 2144990) (-1207 "UPOLYC.spad" 2139442 2139453 2144306 2144459) (-1206 "UPOLYC.spad" 2134312 2134325 2139178 2139183) (-1205 "UPMP.spad" 2133202 2133215 2134302 2134307) (-1204 "UPDIVP.spad" 2132765 2132779 2133192 2133197) (-1203 "UPDECOMP.spad" 2131002 2131016 2132755 2132760) (-1202 "UPCDEN.spad" 2130209 2130225 2130992 2130997) (-1201 "UP2.spad" 2129571 2129592 2130199 2130204) (-1200 "UP.spad" 2126613 2126628 2127121 2127274) (-1199 "UNISEG2.spad" 2126106 2126119 2126569 2126574) (-1198 "UNISEG.spad" 2125459 2125470 2126025 2126030) (-1197 "UNIFACT.spad" 2124560 2124572 2125449 2125454) (-1196 "ULSCONS.spad" 2118599 2118619 2118971 2119120) (-1195 "ULSCCAT.spad" 2116196 2116216 2118419 2118594) (-1194 "ULSCCAT.spad" 2113927 2113949 2116152 2116157) (-1193 "ULSCAT.spad" 2112143 2112159 2113773 2113922) (-1192 "ULS2.spad" 2111655 2111708 2112133 2112138) (-1191 "ULS.spad" 2102209 2102237 2103302 2103731) (-1190 "UFD.spad" 2101274 2101283 2102135 2102204) (-1189 "UFD.spad" 2100401 2100412 2101264 2101269) (-1188 "UDVO.spad" 2099248 2099257 2100391 2100396) (-1187 "UDPO.spad" 2096675 2096686 2099204 2099209) (-1186 "TYPEAST.spad" 2096594 2096603 2096665 2096670) (-1185 "TYPE.spad" 2096516 2096525 2096574 2096589) (-1184 "TWOFACT.spad" 2095166 2095181 2096506 2096511) (-1183 "TUPLE.spad" 2094552 2094563 2095065 2095070) (-1182 "TUBETOOL.spad" 2091389 2091398 2094542 2094547) (-1181 "TUBE.spad" 2090030 2090047 2091379 2091384) (-1180 "TSETCAT.spad" 2077145 2077162 2089986 2090025) (-1179 "TSETCAT.spad" 2064258 2064277 2077101 2077106) (-1178 "TS.spad" 2062847 2062863 2063823 2063920) (-1177 "TRMANIP.spad" 2057213 2057230 2062553 2062558) (-1176 "TRIMAT.spad" 2056172 2056197 2057203 2057208) (-1175 "TRIGMNIP.spad" 2054689 2054706 2056162 2056167) (-1174 "TRIGCAT.spad" 2054201 2054210 2054679 2054684) (-1173 "TRIGCAT.spad" 2053711 2053722 2054191 2054196) (-1172 "TREE.spad" 2052282 2052293 2053318 2053345) (-1171 "TRANFUN.spad" 2052113 2052122 2052272 2052277) (-1170 "TRANFUN.spad" 2051942 2051953 2052103 2052108) (-1169 "TOPSP.spad" 2051616 2051625 2051932 2051937) (-1168 "TOOLSIGN.spad" 2051279 2051290 2051606 2051611) (-1167 "TEXTFILE.spad" 2049836 2049845 2051269 2051274) (-1166 "TEX1.spad" 2049392 2049403 2049826 2049831) (-1165 "TEX.spad" 2046409 2046418 2049382 2049387) (-1164 "TEMUTL.spad" 2045964 2045973 2046399 2046404) (-1163 "TBCMPPK.spad" 2044057 2044080 2045954 2045959) (-1162 "TBAGG.spad" 2043081 2043104 2044025 2044052) (-1161 "TBAGG.spad" 2042125 2042150 2043071 2043076) (-1160 "TANEXP.spad" 2041501 2041512 2042115 2042120) (-1159 "TABLEAU.spad" 2040982 2040993 2041491 2041496) (-1158 "TABLE.spad" 2039393 2039416 2039663 2039690) (-1157 "TABLBUMP.spad" 2036176 2036187 2039383 2039388) (-1156 "SYSTEM.spad" 2035450 2035459 2036166 2036171) (-1155 "SYSSOLP.spad" 2032923 2032934 2035440 2035445) (-1154 "SYNTAX.spad" 2029115 2029124 2032913 2032918) (-1153 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1984660 1984665) (-1134 "STTF.spad" 1977237 1977253 1981128 1981133) (-1133 "STTAYLOR.spad" 1969635 1969646 1977118 1977123) (-1132 "STRTBL.spad" 1968140 1968157 1968289 1968316) (-1131 "STRING.spad" 1967549 1967558 1967563 1967590) (-1130 "STRICAT.spad" 1967325 1967334 1967505 1967544) (-1129 "STREAM3.spad" 1966870 1966885 1967315 1967320) (-1128 "STREAM2.spad" 1965938 1965951 1966860 1966865) (-1127 "STREAM1.spad" 1965642 1965653 1965928 1965933) (-1126 "STREAM.spad" 1962410 1962421 1965167 1965182) (-1125 "STINPROD.spad" 1961316 1961332 1962400 1962405) (-1124 "STEP.spad" 1960517 1960526 1961306 1961311) (-1123 "STBL.spad" 1959043 1959071 1959210 1959225) (-1122 "STAGG.spad" 1958108 1958119 1959023 1959038) (-1121 "STAGG.spad" 1957181 1957194 1958098 1958103) (-1120 "STACK.spad" 1956532 1956543 1956788 1956815) (-1119 "SREGSET.spad" 1954236 1954253 1956178 1956205) (-1118 "SRDCMPK.spad" 1952781 1952801 1954226 1954231) (-1117 "SRAGG.spad" 1947866 1947875 1952737 1952776) (-1116 "SRAGG.spad" 1942983 1942994 1947856 1947861) (-1115 "SQMATRIX.spad" 1940599 1940617 1941515 1941602) (-1114 "SPLTREE.spad" 1935151 1935164 1940035 1940062) (-1113 "SPLNODE.spad" 1931739 1931752 1935141 1935146) (-1112 "SPFCAT.spad" 1930516 1930525 1931729 1931734) (-1111 "SPECOUT.spad" 1929066 1929075 1930506 1930511) (-1110 "SPADXPT.spad" 1921195 1921204 1929046 1929061) (-1109 "spad-parser.spad" 1920660 1920669 1921185 1921190) (-1108 "SPADAST.spad" 1920361 1920370 1920650 1920655) (-1107 "SPACEC.spad" 1904374 1904385 1920351 1920356) (-1106 "SPACE3.spad" 1904150 1904161 1904364 1904369) (-1105 "SORTPAK.spad" 1903695 1903708 1904106 1904111) (-1104 "SOLVETRA.spad" 1901452 1901463 1903685 1903690) (-1103 "SOLVESER.spad" 1899972 1899983 1901442 1901447) (-1102 "SOLVERAD.spad" 1895982 1895993 1899962 1899967) (-1101 "SOLVEFOR.spad" 1894402 1894420 1895972 1895977) (-1100 "SNTSCAT.spad" 1893990 1894007 1894358 1894397) (-1099 "SMTS.spad" 1892250 1892276 1893555 1893652) (-1098 "SMP.spad" 1889689 1889709 1890079 1890206) (-1097 "SMITH.spad" 1888532 1888557 1889679 1889684) (-1096 "SMATCAT.spad" 1886630 1886660 1888464 1888527) (-1095 "SMATCAT.spad" 1884672 1884704 1886508 1886513) (-1094 "SKAGG.spad" 1883621 1883632 1884628 1884667) (-1093 "SINT.spad" 1881929 1881938 1883487 1883616) (-1092 "SIMPAN.spad" 1881657 1881666 1881919 1881924) (-1091 "SIGNRF.spad" 1880772 1880783 1881647 1881652) (-1090 "SIGNEF.spad" 1880048 1880065 1880762 1880767) (-1089 "SIGAST.spad" 1879429 1879438 1880038 1880043) (-1088 "SIG.spad" 1878757 1878766 1879419 1879424) (-1087 "SHP.spad" 1876675 1876690 1878713 1878718) (-1086 "SHDP.spad" 1867660 1867687 1868169 1868300) (-1085 "SGROUP.spad" 1867268 1867277 1867650 1867655) (-1084 "SGROUP.spad" 1866874 1866885 1867258 1867263) (-1083 "SGCF.spad" 1859755 1859764 1866864 1866869) (-1082 "SFRTCAT.spad" 1858671 1858688 1859711 1859750) (-1081 "SFRGCD.spad" 1857734 1857754 1858661 1858666) (-1080 "SFQCMPK.spad" 1852371 1852391 1857724 1857729) (-1079 "SFORT.spad" 1851806 1851820 1852361 1852366) (-1078 "SEXOF.spad" 1851649 1851689 1851796 1851801) (-1077 "SEXCAT.spad" 1848753 1848793 1851639 1851644) (-1076 "SEX.spad" 1848645 1848654 1848743 1848748) (-1075 "SETMN.spad" 1847081 1847098 1848635 1848640) (-1074 "SETCAT.spad" 1846566 1846575 1847071 1847076) (-1073 "SETCAT.spad" 1846049 1846060 1846556 1846561) (-1072 "SETAGG.spad" 1842558 1842569 1846017 1846044) (-1071 "SETAGG.spad" 1839087 1839100 1842548 1842553) (-1070 "SET.spad" 1837387 1837398 1838508 1838547) (-1069 "SEQAST.spad" 1837090 1837099 1837377 1837382) (-1068 "SEGXCAT.spad" 1836202 1836215 1837070 1837085) (-1067 "SEGCAT.spad" 1835021 1835032 1836182 1836197) (-1066 "SEGBIND2.spad" 1834717 1834730 1835011 1835016) (-1065 "SEGBIND.spad" 1833789 1833800 1834672 1834677) (-1064 "SEGAST.spad" 1833503 1833512 1833779 1833784) (-1063 "SEG2.spad" 1832928 1832941 1833459 1833464) (-1062 "SEG.spad" 1832741 1832752 1832847 1832852) (-1061 "SDVAR.spad" 1832017 1832028 1832731 1832736) (-1060 "SDPOL.spad" 1829407 1829418 1829698 1829825) (-1059 "SCPKG.spad" 1827486 1827497 1829397 1829402) (-1058 "SCOPE.spad" 1826631 1826640 1827476 1827481) (-1057 "SCACHE.spad" 1825313 1825324 1826621 1826626) (-1056 "SASTCAT.spad" 1825222 1825231 1825303 1825308) (-1055 "SAOS.spad" 1825094 1825103 1825212 1825217) (-1054 "SAERFFC.spad" 1824807 1824827 1825084 1825089) (-1053 "SAEFACT.spad" 1824508 1824528 1824797 1824802) (-1052 "SAE.spad" 1822683 1822699 1823294 1823429) (-1051 "RURPK.spad" 1820324 1820340 1822673 1822678) (-1050 "RULESET.spad" 1819765 1819789 1820314 1820319) (-1049 "RULECOLD.spad" 1819617 1819630 1819755 1819760) (-1048 "RULE.spad" 1817821 1817845 1819607 1819612) (-1047 "RSTRCAST.spad" 1817538 1817547 1817811 1817816) (-1046 "RSETGCD.spad" 1813916 1813936 1817528 1817533) (-1045 "RSETCAT.spad" 1803688 1803705 1813872 1813911) (-1044 "RSETCAT.spad" 1793492 1793511 1803678 1803683) (-1043 "RSDCMPK.spad" 1791944 1791964 1793482 1793487) (-1042 "RRCC.spad" 1790328 1790358 1791934 1791939) (-1041 "RRCC.spad" 1788710 1788742 1790318 1790323) (-1040 "RPTAST.spad" 1788412 1788421 1788700 1788705) (-1039 "RPOLCAT.spad" 1767772 1767787 1788280 1788407) (-1038 "RPOLCAT.spad" 1746846 1746863 1767356 1767361) (-1037 "ROUTINE.spad" 1742709 1742718 1745493 1745520) (-1036 "ROMAN.spad" 1741941 1741950 1742575 1742704) (-1035 "ROIRC.spad" 1741021 1741053 1741931 1741936) (-1034 "RNS.spad" 1739924 1739933 1740923 1741016) (-1033 "RNS.spad" 1738913 1738924 1739914 1739919) (-1032 "RNG.spad" 1738648 1738657 1738903 1738908) (-1031 "RMODULE.spad" 1738286 1738297 1738638 1738643) (-1030 "RMCAT2.spad" 1737694 1737751 1738276 1738281) (-1029 "RMATRIX.spad" 1736373 1736392 1736861 1736900) (-1028 "RMATCAT.spad" 1731894 1731925 1736317 1736368) (-1027 "RMATCAT.spad" 1727317 1727350 1731742 1731747) (-1026 "RINTERP.spad" 1727205 1727225 1727307 1727312) (-1025 "RING.spad" 1726562 1726571 1727185 1727200) (-1024 "RING.spad" 1725927 1725938 1726552 1726557) (-1023 "RIDIST.spad" 1725311 1725320 1725917 1725922) (-1022 "RGCHAIN.spad" 1723890 1723906 1724796 1724823) (-1021 "RGBCSPC.spad" 1723671 1723683 1723880 1723885) (-1020 "RGBCMDL.spad" 1723201 1723213 1723661 1723666) (-1019 "RFFACTOR.spad" 1722663 1722674 1723191 1723196) (-1018 "RFFACT.spad" 1722398 1722410 1722653 1722658) (-1017 "RFDIST.spad" 1721386 1721395 1722388 1722393) (-1016 "RF.spad" 1719000 1719011 1721376 1721381) (-1015 "RETSOL.spad" 1718417 1718430 1718990 1718995) (-1014 "RETRACT.spad" 1717766 1717777 1718407 1718412) (-1013 "RETRACT.spad" 1717113 1717126 1717756 1717761) (-1012 "RETAST.spad" 1716925 1716934 1717103 1717108) (-1011 "RESULT.spad" 1714985 1714994 1715572 1715599) (-1010 "RESRING.spad" 1714332 1714379 1714923 1714980) (-1009 "RESLATC.spad" 1713656 1713667 1714322 1714327) (-1008 "REPSQ.spad" 1713385 1713396 1713646 1713651) (-1007 "REPDB.spad" 1713090 1713101 1713375 1713380) (-1006 "REP2.spad" 1702662 1702673 1712932 1712937) (-1005 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(-986 "RCAGG.spad" 1668684 1668694 1670761 1670776) (-985 "RCAGG.spad" 1666524 1666536 1668603 1668608) (-984 "RATRET.spad" 1665885 1665895 1666514 1666519) (-983 "RATFACT.spad" 1665578 1665589 1665875 1665880) (-982 "RANDSRC.spad" 1664898 1664906 1665568 1665573) (-981 "RADUTIL.spad" 1664653 1664661 1664888 1664893) (-980 "RADIX.spad" 1661444 1661457 1663121 1663214) (-979 "RADFF.spad" 1659858 1659894 1659976 1660132) (-978 "RADCAT.spad" 1659452 1659460 1659848 1659853) (-977 "RADCAT.spad" 1659044 1659054 1659442 1659447) (-976 "QUEUE.spad" 1658387 1658397 1658651 1658678) (-975 "QUATCT2.spad" 1658006 1658024 1658377 1658382) (-974 "QUATCAT.spad" 1656171 1656181 1657936 1658001) (-973 "QUATCAT.spad" 1654087 1654099 1655854 1655859) (-972 "QUAT.spad" 1652669 1652679 1653011 1653076) (-971 "QUAGG.spad" 1651483 1651493 1652625 1652664) (-970 "QQUTAST.spad" 1651252 1651260 1651473 1651478) (-969 "QFORM.spad" 1650715 1650729 1651242 1651247) (-968 "QFCAT2.spad" 1650406 1650422 1650705 1650710) (-967 "QFCAT.spad" 1649097 1649107 1650296 1650401) (-966 "QFCAT.spad" 1647392 1647404 1648593 1648598) (-965 "QEQUAT.spad" 1646949 1646957 1647382 1647387) (-964 "QCMPACK.spad" 1641696 1641715 1646939 1646944) (-963 "QALGSET2.spad" 1639692 1639710 1641686 1641691) (-962 "QALGSET.spad" 1635769 1635801 1639606 1639611) (-961 "PWFFINTB.spad" 1633079 1633100 1635759 1635764) (-960 "PUSHVAR.spad" 1632408 1632427 1633069 1633074) (-959 "PTRANFN.spad" 1628534 1628544 1632398 1632403) (-958 "PTPACK.spad" 1625622 1625632 1628524 1628529) (-957 "PTFUNC2.spad" 1625443 1625457 1625612 1625617) (-956 "PTCAT.spad" 1624525 1624535 1625399 1625438) (-955 "PSQFR.spad" 1623832 1623856 1624515 1624520) (-954 "PSEUDLIN.spad" 1622690 1622700 1623822 1623827) (-953 "PSETPK.spad" 1608123 1608139 1622568 1622573) (-952 "PSETCAT.spad" 1602031 1602054 1608091 1608118) (-951 "PSETCAT.spad" 1595925 1595950 1601987 1601992) (-950 "PSCURVE.spad" 1594908 1594916 1595915 1595920) (-949 "PSCAT.spad" 1593675 1593704 1594806 1594903) (-948 "PSCAT.spad" 1592532 1592563 1593665 1593670) (-947 "PRTITION.spad" 1591375 1591383 1592522 1592527) (-946 "PRTDAST.spad" 1591094 1591102 1591365 1591370) (-945 "PRS.spad" 1580656 1580673 1591050 1591055) (-944 "PRQAGG.spad" 1580075 1580085 1580612 1580651) (-943 "PROPLOG.spad" 1579478 1579486 1580065 1580070) (-942 "PROPFRML.spad" 1577396 1577407 1579468 1579473) (-941 "PROPERTY.spad" 1576890 1576898 1577386 1577391) (-940 "PRODUCT.spad" 1574570 1574582 1574856 1574911) (-939 "PRINT.spad" 1574322 1574330 1574560 1574565) (-938 "PRIMES.spad" 1572573 1572583 1574312 1574317) (-937 "PRIMELT.spad" 1570554 1570568 1572563 1572568) (-936 "PRIMCAT.spad" 1570177 1570185 1570544 1570549) (-935 "PRIMARR2.spad" 1568900 1568912 1570167 1570172) (-934 "PRIMARR.spad" 1567905 1567915 1568083 1568110) (-933 "PREASSOC.spad" 1567277 1567289 1567895 1567900) (-932 "PR.spad" 1565663 1565675 1566368 1566495) (-931 "PPCURVE.spad" 1564800 1564808 1565653 1565658) (-930 "PORTNUM.spad" 1564575 1564583 1564790 1564795) (-929 "POLYROOT.spad" 1563347 1563369 1564531 1564536) (-928 "POLYLIFT.spad" 1562608 1562631 1563337 1563342) (-927 "POLYCATQ.spad" 1560710 1560732 1562598 1562603) (-926 "POLYCAT.spad" 1554116 1554137 1560578 1560705) (-925 "POLYCAT.spad" 1546824 1546847 1553288 1553293) (-924 "POLY2UP.spad" 1546272 1546286 1546814 1546819) (-923 "POLY2.spad" 1545867 1545879 1546262 1546267) (-922 "POLY.spad" 1543164 1543174 1543681 1543808) (-921 "POLUTIL.spad" 1542105 1542134 1543120 1543125) (-920 "POLTOPOL.spad" 1540853 1540868 1542095 1542100) (-919 "POINT.spad" 1539692 1539702 1539779 1539806) (-918 "PNTHEORY.spad" 1536358 1536366 1539682 1539687) (-917 "PMTOOLS.spad" 1535115 1535129 1536348 1536353) (-916 "PMSYM.spad" 1534660 1534670 1535105 1535110) (-915 "PMQFCAT.spad" 1534247 1534261 1534650 1534655) (-914 "PMPREDFS.spad" 1533691 1533713 1534237 1534242) (-913 "PMPRED.spad" 1533160 1533174 1533681 1533686) (-912 "PMPLCAT.spad" 1532230 1532248 1533092 1533097) (-911 "PMLSAGG.spad" 1531811 1531825 1532220 1532225) (-910 "PMKERNEL.spad" 1531378 1531390 1531801 1531806) (-909 "PMINS.spad" 1530954 1530964 1531368 1531373) (-908 "PMFS.spad" 1530527 1530545 1530944 1530949) (-907 "PMDOWN.spad" 1529813 1529827 1530517 1530522) (-906 "PMASSFS.spad" 1528782 1528798 1529803 1529808) (-905 "PMASS.spad" 1527794 1527802 1528772 1528777) (-904 "PLOTTOOL.spad" 1527574 1527582 1527784 1527789) (-903 "PLOT3D.spad" 1523994 1524002 1527564 1527569) (-902 "PLOT1.spad" 1523135 1523145 1523984 1523989) (-901 "PLOT.spad" 1517966 1517974 1523125 1523130) (-900 "PLEQN.spad" 1505182 1505209 1517956 1517961) (-899 "PINTERPA.spad" 1504964 1504980 1505172 1505177) (-898 "PINTERP.spad" 1504580 1504599 1504954 1504959) (-897 "PID.spad" 1503536 1503544 1504506 1504575) (-896 "PICOERCE.spad" 1503193 1503203 1503526 1503531) (-895 "PI.spad" 1502800 1502808 1503167 1503188) (-894 "PGROEB.spad" 1501397 1501411 1502790 1502795) (-893 "PGE.spad" 1492650 1492658 1501387 1501392) (-892 "PGCD.spad" 1491532 1491549 1492640 1492645) (-891 "PFRPAC.spad" 1490675 1490685 1491522 1491527) (-890 "PFR.spad" 1487332 1487342 1490577 1490670) (-889 "PFOTOOLS.spad" 1486590 1486606 1487322 1487327) (-888 "PFOQ.spad" 1485960 1485978 1486580 1486585) (-887 "PFO.spad" 1485379 1485406 1485950 1485955) (-886 "PFECAT.spad" 1483045 1483053 1485305 1485374) (-885 "PFECAT.spad" 1480739 1480749 1483001 1483006) (-884 "PFBRU.spad" 1478609 1478621 1480729 1480734) (-883 "PFBR.spad" 1476147 1476170 1478599 1478604) (-882 "PF.spad" 1475721 1475733 1475952 1476045) (-881 "PERMGRP.spad" 1470457 1470467 1475711 1475716) (-880 "PERMCAT.spad" 1469009 1469019 1470437 1470452) (-879 "PERMAN.spad" 1467541 1467555 1468999 1469004) (-878 "PERM.spad" 1463222 1463232 1467371 1467386) (-877 "PENDTREE.spad" 1462495 1462505 1462851 1462856) (-876 "PDRING.spad" 1460986 1460996 1462475 1462490) (-875 "PDRING.spad" 1459485 1459497 1460976 1460981) (-874 "PDEPROB.spad" 1458442 1458450 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(-282 "ELTAGG.spad" 398981 399002 400733 400738) (-281 "ELTAB.spad" 398428 398446 398971 398976) (-280 "ELFUTS.spad" 397807 397826 398418 398423) (-279 "ELEMFUN.spad" 397496 397504 397797 397802) (-278 "ELEMFUN.spad" 397183 397193 397486 397491) (-277 "ELAGG.spad" 395114 395124 397151 397178) (-276 "ELAGG.spad" 392994 393006 395033 395038) (-275 "ELABEXPR.spad" 391925 391933 392984 392989) (-274 "EFUPXS.spad" 388701 388731 391881 391886) (-273 "EFULS.spad" 385537 385560 388657 388662) (-272 "EFSTRUC.spad" 383492 383508 385527 385532) (-271 "EF.spad" 378258 378274 383482 383487) (-270 "EAB.spad" 376534 376542 378248 378253) (-269 "E04UCFA.spad" 376070 376078 376524 376529) (-268 "E04NAFA.spad" 375647 375655 376060 376065) (-267 "E04MBFA.spad" 375227 375235 375637 375642) (-266 "E04JAFA.spad" 374763 374771 375217 375222) (-265 "E04GCFA.spad" 374299 374307 374753 374758) (-264 "E04FDFA.spad" 373835 373843 374289 374294) (-263 "E04DGFA.spad" 373371 373379 373825 373830) (-262 "E04AGNT.spad" 369213 369221 373361 373366) (-261 "DVARCAT.spad" 365898 365908 369203 369208) (-260 "DVARCAT.spad" 362581 362593 365888 365893) (-259 "DSMP.spad" 360012 360026 360317 360444) (-258 "DROPT1.spad" 359675 359685 360002 360007) (-257 "DROPT0.spad" 354502 354510 359665 359670) (-256 "DROPT.spad" 348447 348455 354492 354497) (-255 "DRAWPT.spad" 346602 346610 348437 348442) (-254 "DRAWHACK.spad" 345910 345920 346592 346597) (-253 "DRAWCX.spad" 343352 343360 345900 345905) (-252 "DRAWCURV.spad" 342889 342904 343342 343347) (-251 "DRAWCFUN.spad" 332061 332069 342879 342884) (-250 "DRAW.spad" 324661 324674 332051 332056) (-249 "DQAGG.spad" 322817 322827 324617 324656) (-248 "DPOLCAT.spad" 318158 318174 322685 322812) (-247 "DPOLCAT.spad" 313585 313603 318114 318119) (-246 "DPMO.spad" 306888 306904 307026 307327) (-245 "DPMM.spad" 300204 300222 300329 300630) (-244 "DOMAIN.spad" 299475 299483 300194 300199) (-243 "DMP.spad" 296697 296712 297269 297396) (-242 "DLP.spad" 296045 296055 296687 296692) (-241 "DLIST.spad" 294457 294467 295228 295255) (-240 "DLAGG.spad" 292858 292868 294437 294452) (-239 "DIVRING.spad" 292400 292408 292802 292853) (-238 "DIVRING.spad" 291986 291996 292390 292395) (-237 "DISPLAY.spad" 290166 290174 291976 291981) (-236 "DIRPROD2.spad" 288974 288992 290156 290161) (-235 "DIRPROD.spad" 279828 279844 280468 280599) (-234 "DIRPCAT.spad" 278758 278774 279680 279823) (-233 "DIRPCAT.spad" 277429 277447 278353 278358) (-232 "DIOSP.spad" 276254 276262 277419 277424) (-231 "DIOPS.spad" 275226 275236 276222 276249) (-230 "DIOPS.spad" 274184 274196 275182 275187) (-229 "DIFRING.spad" 273476 273484 274164 274179) (-228 "DIFRING.spad" 272776 272786 273466 273471) (-227 "DIFEXT.spad" 271935 271945 272756 272771) (-226 "DIFEXT.spad" 271011 271023 271834 271839) (-225 "DIAGG.spad" 270629 270639 270979 271006) (-224 "DIAGG.spad" 270267 270279 270619 270624) (-223 "DHMATRIX.spad" 268571 268581 269724 269751) (-222 "DFSFUN.spad" 261979 261987 268561 268566) (-221 "DFLOAT.spad" 258700 258708 261869 261974) (-220 "DFINTTLS.spad" 256909 256925 258690 258695) (-219 "DERHAM.spad" 254819 254851 256889 256904) (-218 "DEQUEUE.spad" 254137 254147 254426 254453) (-217 "DEGRED.spad" 253752 253766 254127 254132) (-216 "DEFINTRF.spad" 251322 251332 253742 253747) (-215 "DEFINTEF.spad" 249846 249862 251312 251317) (-214 "DEFAST.spad" 249214 249222 249836 249841) (-213 "DECIMAL.spad" 247096 247104 247682 247775) (-212 "DDFACT.spad" 244895 244912 247086 247091) (-211 "DBLRESP.spad" 244493 244517 244885 244890) (-210 "DBASE.spad" 243065 243075 244483 244488) (-209 "DATABUF.spad" 242553 242566 243055 243060) (-208 "D03FAFA.spad" 242381 242389 242543 242548) (-207 "D03EEFA.spad" 242201 242209 242371 242376) (-206 "D03AGNT.spad" 241281 241289 242191 242196) (-205 "D02EJFA.spad" 240743 240751 241271 241276) (-204 "D02CJFA.spad" 240221 240229 240733 240738) (-203 "D02BHFA.spad" 239711 239719 240211 240216) (-202 "D02BBFA.spad" 239201 239209 239701 239706) (-201 "D02AGNT.spad" 234005 234013 239191 239196) (-200 "D01WGTS.spad" 232324 232332 233995 234000) (-199 "D01TRNS.spad" 232301 232309 232314 232319) (-198 "D01GBFA.spad" 231823 231831 232291 232296) (-197 "D01FCFA.spad" 231345 231353 231813 231818) (-196 "D01ASFA.spad" 230813 230821 231335 231340) (-195 "D01AQFA.spad" 230259 230267 230803 230808) (-194 "D01APFA.spad" 229683 229691 230249 230254) (-193 "D01ANFA.spad" 229177 229185 229673 229678) (-192 "D01AMFA.spad" 228687 228695 229167 229172) (-191 "D01ALFA.spad" 228227 228235 228677 228682) (-190 "D01AKFA.spad" 227753 227761 228217 228222) (-189 "D01AJFA.spad" 227276 227284 227743 227748) (-188 "D01AGNT.spad" 223335 223343 227266 227271) (-187 "CYCLOTOM.spad" 222841 222849 223325 223330) (-186 "CYCLES.spad" 219673 219681 222831 222836) (-185 "CVMP.spad" 219090 219100 219663 219668) (-184 "CTRIGMNP.spad" 217580 217596 219080 219085) (-183 "CTORKIND.spad" 217195 217203 217570 217575) (-182 "CTORCALL.spad" 216783 216791 217185 217190) (-181 "CTOR.spad" 216226 216234 216773 216778) (-180 "CSTTOOLS.spad" 215469 215482 216216 216221) (-179 "CRFP.spad" 209173 209186 215459 215464) (-178 "CRCEAST.spad" 208893 208901 209163 209168) (-177 "CRAPACK.spad" 207936 207946 208883 208888) (-176 "CPMATCH.spad" 207436 207451 207861 207866) (-175 "CPIMA.spad" 207141 207160 207426 207431) (-174 "COORDSYS.spad" 202034 202044 207131 207136) (-173 "CONTOUR.spad" 201436 201444 202024 202029) (-172 "CONTFRAC.spad" 197048 197058 201338 201431) (-171 "CONDUIT.spad" 196806 196814 197038 197043) (-170 "COMRING.spad" 196480 196488 196744 196801) (-169 "COMPPROP.spad" 195994 196002 196470 196475) (-168 "COMPLPAT.spad" 195761 195776 195984 195989) (-167 "COMPLEX2.spad" 195474 195486 195751 195756) (-166 "COMPLEX.spad" 189500 189510 189744 190005) (-165 "COMPFACT.spad" 189102 189116 189490 189495) (-164 "COMPCAT.spad" 187158 187168 188824 189097) (-163 "COMPCAT.spad" 184920 184932 186588 186593) (-162 "COMMUPC.spad" 184666 184684 184910 184915) (-161 "COMMONOP.spad" 184199 184207 184656 184661) (-160 "COMMAAST.spad" 183962 183970 184189 184194) (-159 "COMM.spad" 183771 183779 183952 183957) (-158 "COMBOPC.spad" 182676 182684 183761 183766) (-157 "COMBINAT.spad" 181421 181431 182666 182671) (-156 "COMBF.spad" 178789 178805 181411 181416) (-155 "COLOR.spad" 177626 177634 178779 178784) (-154 "COLONAST.spad" 177292 177300 177616 177621) (-153 "CMPLXRT.spad" 177001 177018 177282 177287) (-152 "CLLCTAST.spad" 176663 176671 176991 176996) (-151 "CLIP.spad" 172755 172763 176653 176658) (-150 "CLIF.spad" 171394 171410 172711 172750) (-149 "CLAGG.spad" 167869 167879 171374 171389) (-148 "CLAGG.spad" 164225 164237 167732 167737) (-147 "CINTSLPE.spad" 163550 163563 164215 164220) (-146 "CHVAR.spad" 161628 161650 163540 163545) (-145 "CHARZ.spad" 161543 161551 161608 161623) (-144 "CHARPOL.spad" 161051 161061 161533 161538) (-143 "CHARNZ.spad" 160804 160812 161031 161046) (-142 "CHAR.spad" 158672 158680 160794 160799) (-141 "CFCAT.spad" 157988 157996 158662 158667) (-140 "CDEN.spad" 157146 157160 157978 157983) (-139 "CCLASS.spad" 155295 155303 156557 156596) (-138 "CATEGORY.spad" 155074 155082 155285 155290) (-137 "CATAST.spad" 154701 154709 155064 155069) (-136 "CASEAST.spad" 154415 154423 154691 154696) (-135 "CARTEN2.spad" 153801 153828 154405 154410) (-134 "CARTEN.spad" 148904 148928 153791 153796) (-133 "CARD.spad" 146193 146201 148878 148899) (-132 "CAPSLAST.spad" 145967 145975 146183 146188) (-131 "CACHSET.spad" 145589 145597 145957 145962) (-130 "CABMON.spad" 145142 145150 145579 145584) (-129 "BYTEARY.spad" 144217 144225 144311 144338) (-128 "BYTE.spad" 143391 143399 144207 144212) (-127 "BTREE.spad" 142460 142470 142998 143025) (-126 "BTOURN.spad" 141463 141473 142067 142094) (-125 "BTCAT.spad" 140839 140849 141419 141458) (-124 "BTCAT.spad" 140247 140259 140829 140834) (-123 "BTAGG.spad" 139357 139365 140203 140242) (-122 "BTAGG.spad" 138499 138509 139347 139352) (-121 "BSTREE.spad" 137234 137244 138106 138133) (-120 "BRILL.spad" 135429 135440 137224 137229) (-119 "BRAGG.spad" 134343 134353 135409 135424) (-118 "BRAGG.spad" 133231 133243 134299 134304) (-117 "BPADICRT.spad" 131213 131225 131468 131561) (-116 "BPADIC.spad" 130877 130889 131139 131208) (-115 "BOUNDZRO.spad" 130533 130550 130867 130872) (-114 "BOP1.spad" 127919 127929 130489 130494) (-113 "BOP.spad" 123383 123391 127909 127914) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP80.spad" 98366 98379 99034 99039) (-86 "ASP8.spad" 97409 97422 98356 98361) (-85 "ASP78.spad" 96860 96873 97399 97404) (-84 "ASP77.spad" 96229 96242 96850 96855) (-83 "ASP74.spad" 95321 95334 96219 96224) (-82 "ASP73.spad" 94592 94605 95311 95316) (-81 "ASP7.spad" 93752 93765 94582 94587) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP49.spad" 87709 87722 88700 88705) (-76 "ASP42.spad" 86116 86155 87699 87704) (-75 "ASP41.spad" 84695 84734 86106 86111) (-74 "ASP4.spad" 83990 84003 84685 84690) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP19.spad" 62496 62509 67800 67805) (-62 "ASP12.spad" 61910 61923 62486 62491) (-61 "ASP10.spad" 61181 61194 61900 61905) (-60 "ASP1.spad" 60562 60575 61171 61176) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY12.spad" 58591 58602 59912 59917) (-57 "ARRAY1.spad" 57426 57435 57774 57801) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY1.spad" 46688 46697 47607 47612) (-51 "ANY.spad" 45030 45037 46678 46683) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-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 2269588 2269593 2269598 2269603) (-2 NIL 2269568 2269573 2269578 2269583) (-1 NIL 2269548 2269553 2269558 2269563) (0 NIL 2269528 2269533 2269538 2269543) (-1260 "ZMOD.spad" 2269337 2269350 2269466 2269523) (-1259 "ZLINDEP.spad" 2268381 2268392 2269327 2269332) (-1258 "ZDSOLVE.spad" 2258230 2258252 2268371 2268376) (-1257 "YSTREAM.spad" 2257723 2257734 2258220 2258225) (-1256 "XRPOLY.spad" 2256943 2256963 2257579 2257648) (-1255 "XPR.spad" 2254672 2254685 2256661 2256760) (-1254 "XPOLY.spad" 2254227 2254238 2254528 2254597) (-1253 "XPOLYC.spad" 2253544 2253560 2254153 2254222) (-1252 "XPBWPOLY.spad" 2251981 2252001 2253324 2253393) (-1251 "XF.spad" 2250442 2250457 2251883 2251976) (-1250 "XF.spad" 2248883 2248900 2250326 2250331) (-1249 "XFALG.spad" 2245907 2245923 2248809 2248878) (-1248 "XEXPPKG.spad" 2245158 2245184 2245897 2245902) (-1247 "XDPOLY.spad" 2244772 2244788 2245014 2245083) (-1246 "XALG.spad" 2244370 2244381 2244728 2244767) (-1245 "WUTSET.spad" 2240209 2240226 2244016 2244043) (-1244 "WP.spad" 2239223 2239267 2240067 2240134) (-1243 "WHILEAST.spad" 2239021 2239030 2239213 2239218) (-1242 "WHEREAST.spad" 2238692 2238701 2239011 2239016) (-1241 "WFFINTBS.spad" 2236255 2236277 2238682 2238687) (-1240 "WEIER.spad" 2234469 2234480 2236245 2236250) (-1239 "VSPACE.spad" 2234142 2234153 2234437 2234464) (-1238 "VSPACE.spad" 2233835 2233848 2234132 2234137) (-1237 "VOID.spad" 2233425 2233434 2233825 2233830) (-1236 "VIEW.spad" 2231047 2231056 2233415 2233420) (-1235 "VIEWDEF.spad" 2226244 2226253 2231037 2231042) (-1234 "VIEW3D.spad" 2210079 2210088 2226234 2226239) (-1233 "VIEW2D.spad" 2197816 2197825 2210069 2210074) (-1232 "VECTOR.spad" 2196491 2196502 2196742 2196769) (-1231 "VECTOR2.spad" 2195118 2195131 2196481 2196486) (-1230 "VECTCAT.spad" 2193006 2193017 2195074 2195113) (-1229 "VECTCAT.spad" 2190714 2190727 2192784 2192789) (-1228 "VARIABLE.spad" 2190494 2190509 2190704 2190709) (-1227 "UTYPE.spad" 2190128 2190137 2190474 2190489) (-1226 "UTSODETL.spad" 2189421 2189445 2190084 2190089) (-1225 "UTSODE.spad" 2187609 2187629 2189411 2189416) (-1224 "UTS.spad" 2182398 2182426 2186076 2186173) (-1223 "UTSCAT.spad" 2179849 2179865 2182296 2182393) (-1222 "UTSCAT.spad" 2176944 2176962 2179393 2179398) (-1221 "UTS2.spad" 2176537 2176572 2176934 2176939) (-1220 "URAGG.spad" 2171159 2171170 2176517 2176532) (-1219 "URAGG.spad" 2165755 2165768 2171115 2171120) (-1218 "UPXSSING.spad" 2163398 2163424 2164836 2164969) (-1217 "UPXS.spad" 2160425 2160453 2161530 2161679) (-1216 "UPXSCONS.spad" 2158182 2158202 2158557 2158706) (-1215 "UPXSCCA.spad" 2156640 2156660 2158028 2158177) (-1214 "UPXSCCA.spad" 2155240 2155262 2156630 2156635) (-1213 "UPXSCAT.spad" 2153821 2153837 2155086 2155235) (-1212 "UPXS2.spad" 2153362 2153415 2153811 2153816) (-1211 "UPSQFREE.spad" 2151774 2151788 2153352 2153357) (-1210 "UPSCAT.spad" 2149367 2149391 2151672 2151769) (-1209 "UPSCAT.spad" 2146666 2146692 2148973 2148978) (-1208 "UPOLYC.spad" 2141644 2141655 2146508 2146661) (-1207 "UPOLYC.spad" 2136514 2136527 2141380 2141385) (-1206 "UPOLYC2.spad" 2135983 2136002 2136504 2136509) (-1205 "UP.spad" 2133025 2133040 2133533 2133686) (-1204 "UPMP.spad" 2131915 2131928 2133015 2133020) (-1203 "UPDIVP.spad" 2131478 2131492 2131905 2131910) (-1202 "UPDECOMP.spad" 2129715 2129729 2131468 2131473) (-1201 "UPCDEN.spad" 2128922 2128938 2129705 2129710) (-1200 "UP2.spad" 2128284 2128305 2128912 2128917) (-1199 "UNISEG.spad" 2127637 2127648 2128203 2128208) (-1198 "UNISEG2.spad" 2127130 2127143 2127593 2127598) (-1197 "UNIFACT.spad" 2126231 2126243 2127120 2127125) (-1196 "ULS.spad" 2116785 2116813 2117878 2118307) (-1195 "ULSCONS.spad" 2110824 2110844 2111196 2111345) (-1194 "ULSCCAT.spad" 2108421 2108441 2110644 2110819) (-1193 "ULSCCAT.spad" 2106152 2106174 2108377 2108382) (-1192 "ULSCAT.spad" 2104368 2104384 2105998 2106147) (-1191 "ULS2.spad" 2103880 2103933 2104358 2104363) (-1190 "UFD.spad" 2102945 2102954 2103806 2103875) (-1189 "UFD.spad" 2102072 2102083 2102935 2102940) (-1188 "UDVO.spad" 2100919 2100928 2102062 2102067) (-1187 "UDPO.spad" 2098346 2098357 2100875 2100880) (-1186 "TYPE.spad" 2098268 2098277 2098326 2098341) (-1185 "TYPEAST.spad" 2098187 2098196 2098258 2098263) (-1184 "TWOFACT.spad" 2096837 2096852 2098177 2098182) (-1183 "TUPLE.spad" 2096223 2096234 2096736 2096741) (-1182 "TUBETOOL.spad" 2093060 2093069 2096213 2096218) (-1181 "TUBE.spad" 2091701 2091718 2093050 2093055) (-1180 "TS.spad" 2090290 2090306 2091266 2091363) (-1179 "TSETCAT.spad" 2077405 2077422 2090246 2090285) (-1178 "TSETCAT.spad" 2064518 2064537 2077361 2077366) (-1177 "TRMANIP.spad" 2058884 2058901 2064224 2064229) (-1176 "TRIMAT.spad" 2057843 2057868 2058874 2058879) (-1175 "TRIGMNIP.spad" 2056360 2056377 2057833 2057838) (-1174 "TRIGCAT.spad" 2055872 2055881 2056350 2056355) (-1173 "TRIGCAT.spad" 2055382 2055393 2055862 2055867) (-1172 "TREE.spad" 2053953 2053964 2054989 2055016) (-1171 "TRANFUN.spad" 2053784 2053793 2053943 2053948) (-1170 "TRANFUN.spad" 2053613 2053624 2053774 2053779) (-1169 "TOPSP.spad" 2053287 2053296 2053603 2053608) (-1168 "TOOLSIGN.spad" 2052950 2052961 2053277 2053282) (-1167 "TEXTFILE.spad" 2051507 2051516 2052940 2052945) (-1166 "TEX.spad" 2048524 2048533 2051497 2051502) (-1165 "TEX1.spad" 2048080 2048091 2048514 2048519) (-1164 "TEMUTL.spad" 2047635 2047644 2048070 2048075) (-1163 "TBCMPPK.spad" 2045728 2045751 2047625 2047630) (-1162 "TBAGG.spad" 2044752 2044775 2045696 2045723) (-1161 "TBAGG.spad" 2043796 2043821 2044742 2044747) (-1160 "TANEXP.spad" 2043172 2043183 2043786 2043791) (-1159 "TABLE.spad" 2041583 2041606 2041853 2041880) (-1158 "TABLEAU.spad" 2041064 2041075 2041573 2041578) (-1157 "TABLBUMP.spad" 2037847 2037858 2041054 2041059) (-1156 "SYSTEM.spad" 2037121 2037130 2037837 2037842) (-1155 "SYSSOLP.spad" 2034594 2034605 2037111 2037116) (-1154 "SYNTAX.spad" 2030786 2030795 2034584 2034589) (-1153 "SYMTAB.spad" 2028842 2028851 2030776 2030781) (-1152 "SYMS.spad" 2024827 2024836 2028832 2028837) (-1151 "SYMPOLY.spad" 2023834 2023845 2023916 2024043) (-1150 "SYMFUNC.spad" 2023309 2023320 2023824 2023829) (-1149 "SYMBOL.spad" 2020645 2020654 2023299 2023304) (-1148 "SWITCH.spad" 2017402 2017411 2020635 2020640) (-1147 "SUTS.spad" 2014301 2014329 2015869 2015966) (-1146 "SUPXS.spad" 2011315 2011343 2012433 2012582) (-1145 "SUP.spad" 2008084 2008095 2008865 2009018) (-1144 "SUPFRACF.spad" 2007189 2007207 2008074 2008079) (-1143 "SUP2.spad" 2006579 2006592 2007179 2007184) (-1142 "SUMRF.spad" 2005545 2005556 2006569 2006574) (-1141 "SUMFS.spad" 2005178 2005195 2005535 2005540) (-1140 "SULS.spad" 1995719 1995747 1996825 1997254) (-1139 "SUCHTAST.spad" 1995488 1995497 1995709 1995714) (-1138 "SUCH.spad" 1995168 1995183 1995478 1995483) (-1137 "SUBSPACE.spad" 1987175 1987190 1995158 1995163) (-1136 "SUBRESP.spad" 1986335 1986349 1987131 1987136) (-1135 "STTF.spad" 1982434 1982450 1986325 1986330) (-1134 "STTFNC.spad" 1978902 1978918 1982424 1982429) (-1133 "STTAYLOR.spad" 1971300 1971311 1978783 1978788) (-1132 "STRTBL.spad" 1969805 1969822 1969954 1969981) (-1131 "STRING.spad" 1969214 1969223 1969228 1969255) (-1130 "STRICAT.spad" 1968990 1968999 1969170 1969209) (-1129 "STREAM.spad" 1965758 1965769 1968515 1968530) (-1128 "STREAM3.spad" 1965303 1965318 1965748 1965753) (-1127 "STREAM2.spad" 1964371 1964384 1965293 1965298) (-1126 "STREAM1.spad" 1964075 1964086 1964361 1964366) (-1125 "STINPROD.spad" 1962981 1962997 1964065 1964070) (-1124 "STEP.spad" 1962182 1962191 1962971 1962976) (-1123 "STBL.spad" 1960708 1960736 1960875 1960890) (-1122 "STAGG.spad" 1959773 1959784 1960688 1960703) (-1121 "STAGG.spad" 1958846 1958859 1959763 1959768) (-1120 "STACK.spad" 1958197 1958208 1958453 1958480) (-1119 "SREGSET.spad" 1955901 1955918 1957843 1957870) (-1118 "SRDCMPK.spad" 1954446 1954466 1955891 1955896) (-1117 "SRAGG.spad" 1949531 1949540 1954402 1954441) (-1116 "SRAGG.spad" 1944648 1944659 1949521 1949526) (-1115 "SQMATRIX.spad" 1942264 1942282 1943180 1943267) (-1114 "SPLTREE.spad" 1936816 1936829 1941700 1941727) (-1113 "SPLNODE.spad" 1933404 1933417 1936806 1936811) (-1112 "SPFCAT.spad" 1932181 1932190 1933394 1933399) (-1111 "SPECOUT.spad" 1930731 1930740 1932171 1932176) (-1110 "SPADXPT.spad" 1922860 1922869 1930711 1930726) (-1109 "spad-parser.spad" 1922325 1922334 1922850 1922855) (-1108 "SPADAST.spad" 1922026 1922035 1922315 1922320) (-1107 "SPACEC.spad" 1906039 1906050 1922016 1922021) (-1106 "SPACE3.spad" 1905815 1905826 1906029 1906034) (-1105 "SORTPAK.spad" 1905360 1905373 1905771 1905776) (-1104 "SOLVETRA.spad" 1903117 1903128 1905350 1905355) (-1103 "SOLVESER.spad" 1901637 1901648 1903107 1903112) (-1102 "SOLVERAD.spad" 1897647 1897658 1901627 1901632) (-1101 "SOLVEFOR.spad" 1896067 1896085 1897637 1897642) (-1100 "SNTSCAT.spad" 1895655 1895672 1896023 1896062) (-1099 "SMTS.spad" 1893915 1893941 1895220 1895317) (-1098 "SMP.spad" 1891354 1891374 1891744 1891871) (-1097 "SMITH.spad" 1890197 1890222 1891344 1891349) (-1096 "SMATCAT.spad" 1888295 1888325 1890129 1890192) (-1095 "SMATCAT.spad" 1886337 1886369 1888173 1888178) (-1094 "SKAGG.spad" 1885286 1885297 1886293 1886332) (-1093 "SINT.spad" 1883594 1883603 1885152 1885281) (-1092 "SIMPAN.spad" 1883322 1883331 1883584 1883589) (-1091 "SIG.spad" 1882650 1882659 1883312 1883317) (-1090 "SIGNRF.spad" 1881758 1881769 1882640 1882645) (-1089 "SIGNEF.spad" 1881027 1881044 1881748 1881753) (-1088 "SIGAST.spad" 1880408 1880417 1881017 1881022) (-1087 "SHP.spad" 1878326 1878341 1880364 1880369) (-1086 "SHDP.spad" 1869311 1869338 1869820 1869951) (-1085 "SGROUP.spad" 1868919 1868928 1869301 1869306) (-1084 "SGROUP.spad" 1868525 1868536 1868909 1868914) (-1083 "SGCF.spad" 1861406 1861415 1868515 1868520) (-1082 "SFRTCAT.spad" 1860322 1860339 1861362 1861401) (-1081 "SFRGCD.spad" 1859385 1859405 1860312 1860317) (-1080 "SFQCMPK.spad" 1854022 1854042 1859375 1859380) (-1079 "SFORT.spad" 1853457 1853471 1854012 1854017) (-1078 "SEXOF.spad" 1853300 1853340 1853447 1853452) (-1077 "SEX.spad" 1853192 1853201 1853290 1853295) (-1076 "SEXCAT.spad" 1850296 1850336 1853182 1853187) (-1075 "SET.spad" 1848596 1848607 1849717 1849756) (-1074 "SETMN.spad" 1847030 1847047 1848586 1848591) (-1073 "SETCAT.spad" 1846515 1846524 1847020 1847025) (-1072 "SETCAT.spad" 1845998 1846009 1846505 1846510) (-1071 "SETAGG.spad" 1842507 1842518 1845966 1845993) (-1070 "SETAGG.spad" 1839036 1839049 1842497 1842502) (-1069 "SEQAST.spad" 1838739 1838748 1839026 1839031) (-1068 "SEGXCAT.spad" 1837851 1837864 1838719 1838734) (-1067 "SEG.spad" 1837664 1837675 1837770 1837775) (-1066 "SEGCAT.spad" 1836483 1836494 1837644 1837659) (-1065 "SEGBIND.spad" 1835555 1835566 1836438 1836443) (-1064 "SEGBIND2.spad" 1835251 1835264 1835545 1835550) (-1063 "SEGAST.spad" 1834965 1834974 1835241 1835246) (-1062 "SEG2.spad" 1834390 1834403 1834921 1834926) (-1061 "SDVAR.spad" 1833666 1833677 1834380 1834385) (-1060 "SDPOL.spad" 1831056 1831067 1831347 1831474) (-1059 "SCPKG.spad" 1829135 1829146 1831046 1831051) (-1058 "SCOPE.spad" 1828280 1828289 1829125 1829130) (-1057 "SCACHE.spad" 1826962 1826973 1828270 1828275) (-1056 "SASTCAT.spad" 1826871 1826880 1826952 1826957) (-1055 "SAOS.spad" 1826743 1826752 1826861 1826866) (-1054 "SAERFFC.spad" 1826456 1826476 1826733 1826738) (-1053 "SAE.spad" 1824631 1824647 1825242 1825377) (-1052 "SAEFACT.spad" 1824332 1824352 1824621 1824626) (-1051 "RURPK.spad" 1821973 1821989 1824322 1824327) (-1050 "RULESET.spad" 1821414 1821438 1821963 1821968) (-1049 "RULE.spad" 1819618 1819642 1821404 1821409) (-1048 "RULECOLD.spad" 1819470 1819483 1819608 1819613) (-1047 "RSTRCAST.spad" 1819187 1819196 1819460 1819465) (-1046 "RSETGCD.spad" 1815565 1815585 1819177 1819182) (-1045 "RSETCAT.spad" 1805337 1805354 1815521 1815560) (-1044 "RSETCAT.spad" 1795141 1795160 1805327 1805332) (-1043 "RSDCMPK.spad" 1793593 1793613 1795131 1795136) (-1042 "RRCC.spad" 1791977 1792007 1793583 1793588) (-1041 "RRCC.spad" 1790359 1790391 1791967 1791972) (-1040 "RPTAST.spad" 1790061 1790070 1790349 1790354) (-1039 "RPOLCAT.spad" 1769421 1769436 1789929 1790056) (-1038 "RPOLCAT.spad" 1748495 1748512 1769005 1769010) (-1037 "ROUTINE.spad" 1744358 1744367 1747142 1747169) (-1036 "ROMAN.spad" 1743590 1743599 1744224 1744353) (-1035 "ROIRC.spad" 1742670 1742702 1743580 1743585) (-1034 "RNS.spad" 1741573 1741582 1742572 1742665) (-1033 "RNS.spad" 1740562 1740573 1741563 1741568) (-1032 "RNG.spad" 1740297 1740306 1740552 1740557) (-1031 "RMODULE.spad" 1739935 1739946 1740287 1740292) (-1030 "RMCAT2.spad" 1739343 1739400 1739925 1739930) (-1029 "RMATRIX.spad" 1738022 1738041 1738510 1738549) (-1028 "RMATCAT.spad" 1733543 1733574 1737966 1738017) (-1027 "RMATCAT.spad" 1728966 1728999 1733391 1733396) (-1026 "RINTERP.spad" 1728854 1728874 1728956 1728961) (-1025 "RING.spad" 1728211 1728220 1728834 1728849) (-1024 "RING.spad" 1727576 1727587 1728201 1728206) (-1023 "RIDIST.spad" 1726960 1726969 1727566 1727571) (-1022 "RGCHAIN.spad" 1725539 1725555 1726445 1726472) (-1021 "RGBCSPC.spad" 1725320 1725332 1725529 1725534) (-1020 "RGBCMDL.spad" 1724850 1724862 1725310 1725315) (-1019 "RF.spad" 1722464 1722475 1724840 1724845) (-1018 "RFFACTOR.spad" 1721926 1721937 1722454 1722459) (-1017 "RFFACT.spad" 1721661 1721673 1721916 1721921) (-1016 "RFDIST.spad" 1720649 1720658 1721651 1721656) (-1015 "RETSOL.spad" 1720066 1720079 1720639 1720644) (-1014 "RETRACT.spad" 1719415 1719426 1720056 1720061) (-1013 "RETRACT.spad" 1718762 1718775 1719405 1719410) (-1012 "RETAST.spad" 1718574 1718583 1718752 1718757) (-1011 "RESULT.spad" 1716634 1716643 1717221 1717248) (-1010 "RESRING.spad" 1715981 1716028 1716572 1716629) (-1009 "RESLATC.spad" 1715305 1715316 1715971 1715976) (-1008 "REPSQ.spad" 1715034 1715045 1715295 1715300) (-1007 "REP.spad" 1712586 1712595 1715024 1715029) (-1006 "REPDB.spad" 1712291 1712302 1712576 1712581) (-1005 "REP2.spad" 1701863 1701874 1712133 1712138) (-1004 "REP1.spad" 1695853 1695864 1701813 1701818) (-1003 "REGSET.spad" 1693650 1693667 1695499 1695526) (-1002 "REF.spad" 1692979 1692990 1693605 1693610) (-1001 "REDORDER.spad" 1692155 1692172 1692969 1692974) (-1000 "RECLOS.spad" 1690938 1690958 1691642 1691735) (-999 "REALSOLV.spad" 1690071 1690079 1690928 1690933) (-998 "REAL.spad" 1689944 1689952 1690061 1690066) (-997 "REAL0Q.spad" 1687227 1687241 1689934 1689939) (-996 "REAL0.spad" 1684056 1684070 1687217 1687222) (-995 "RDUCEAST.spad" 1683778 1683786 1684046 1684051) (-994 "RDIV.spad" 1683430 1683454 1683768 1683773) (-993 "RDIST.spad" 1682994 1683004 1683420 1683425) (-992 "RDETRS.spad" 1681791 1681808 1682984 1682989) (-991 "RDETR.spad" 1679899 1679916 1681781 1681786) (-990 "RDEEFS.spad" 1678973 1678989 1679889 1679894) (-989 "RDEEF.spad" 1677970 1677986 1678963 1678968) (-988 "RCFIELD.spad" 1675157 1675165 1677872 1677965) (-987 "RCFIELD.spad" 1672430 1672440 1675147 1675152) (-986 "RCAGG.spad" 1670333 1670343 1672410 1672425) (-985 "RCAGG.spad" 1668173 1668185 1670252 1670257) (-984 "RATRET.spad" 1667534 1667544 1668163 1668168) (-983 "RATFACT.spad" 1667227 1667238 1667524 1667529) (-982 "RANDSRC.spad" 1666547 1666555 1667217 1667222) (-981 "RADUTIL.spad" 1666302 1666310 1666537 1666542) (-980 "RADIX.spad" 1663093 1663106 1664770 1664863) (-979 "RADFF.spad" 1661507 1661543 1661625 1661781) (-978 "RADCAT.spad" 1661101 1661109 1661497 1661502) (-977 "RADCAT.spad" 1660693 1660703 1661091 1661096) (-976 "QUEUE.spad" 1660036 1660046 1660300 1660327) (-975 "QUAT.spad" 1658618 1658628 1658960 1659025) (-974 "QUATCT2.spad" 1658237 1658255 1658608 1658613) (-973 "QUATCAT.spad" 1656402 1656412 1658167 1658232) (-972 "QUATCAT.spad" 1654318 1654330 1656085 1656090) (-971 "QUAGG.spad" 1653132 1653142 1654274 1654313) (-970 "QQUTAST.spad" 1652901 1652909 1653122 1653127) (-969 "QFORM.spad" 1652364 1652378 1652891 1652896) (-968 "QFCAT.spad" 1651055 1651065 1652254 1652359) (-967 "QFCAT.spad" 1649350 1649362 1650551 1650556) (-966 "QFCAT2.spad" 1649041 1649057 1649340 1649345) (-965 "QEQUAT.spad" 1648598 1648606 1649031 1649036) (-964 "QCMPACK.spad" 1643345 1643364 1648588 1648593) (-963 "QALGSET.spad" 1639420 1639452 1643259 1643264) (-962 "QALGSET2.spad" 1637416 1637434 1639410 1639415) (-961 "PWFFINTB.spad" 1634726 1634747 1637406 1637411) (-960 "PUSHVAR.spad" 1634055 1634074 1634716 1634721) (-959 "PTRANFN.spad" 1630181 1630191 1634045 1634050) (-958 "PTPACK.spad" 1627269 1627279 1630171 1630176) (-957 "PTFUNC2.spad" 1627090 1627104 1627259 1627264) (-956 "PTCAT.spad" 1626172 1626182 1627046 1627085) (-955 "PSQFR.spad" 1625479 1625503 1626162 1626167) (-954 "PSEUDLIN.spad" 1624337 1624347 1625469 1625474) (-953 "PSETPK.spad" 1609770 1609786 1624215 1624220) (-952 "PSETCAT.spad" 1603678 1603701 1609738 1609765) (-951 "PSETCAT.spad" 1597572 1597597 1603634 1603639) (-950 "PSCURVE.spad" 1596555 1596563 1597562 1597567) (-949 "PSCAT.spad" 1595322 1595351 1596453 1596550) (-948 "PSCAT.spad" 1594179 1594210 1595312 1595317) (-947 "PRTITION.spad" 1593022 1593030 1594169 1594174) (-946 "PRTDAST.spad" 1592741 1592749 1593012 1593017) (-945 "PRS.spad" 1582303 1582320 1592697 1592702) (-944 "PRQAGG.spad" 1581722 1581732 1582259 1582298) (-943 "PROPLOG.spad" 1581125 1581133 1581712 1581717) (-942 "PROPFRML.spad" 1579043 1579054 1581115 1581120) (-941 "PROPERTY.spad" 1578537 1578545 1579033 1579038) (-940 "PRODUCT.spad" 1576217 1576229 1576503 1576558) (-939 "PR.spad" 1574603 1574615 1575308 1575435) (-938 "PRINT.spad" 1574355 1574363 1574593 1574598) (-937 "PRIMES.spad" 1572606 1572616 1574345 1574350) (-936 "PRIMELT.spad" 1570587 1570601 1572596 1572601) (-935 "PRIMCAT.spad" 1570210 1570218 1570577 1570582) (-934 "PRIMARR.spad" 1569215 1569225 1569393 1569420) (-933 "PRIMARR2.spad" 1567938 1567950 1569205 1569210) (-932 "PREASSOC.spad" 1567310 1567322 1567928 1567933) (-931 "PPCURVE.spad" 1566447 1566455 1567300 1567305) (-930 "PORTNUM.spad" 1566222 1566230 1566437 1566442) (-929 "POLYROOT.spad" 1564994 1565016 1566178 1566183) (-928 "POLY.spad" 1562291 1562301 1562808 1562935) (-927 "POLYLIFT.spad" 1561552 1561575 1562281 1562286) (-926 "POLYCATQ.spad" 1559654 1559676 1561542 1561547) (-925 "POLYCAT.spad" 1553060 1553081 1559522 1559649) (-924 "POLYCAT.spad" 1545768 1545791 1552232 1552237) (-923 "POLY2UP.spad" 1545216 1545230 1545758 1545763) (-922 "POLY2.spad" 1544811 1544823 1545206 1545211) (-921 "POLUTIL.spad" 1543752 1543781 1544767 1544772) (-920 "POLTOPOL.spad" 1542500 1542515 1543742 1543747) (-919 "POINT.spad" 1541339 1541349 1541426 1541453) (-918 "PNTHEORY.spad" 1538005 1538013 1541329 1541334) (-917 "PMTOOLS.spad" 1536762 1536776 1537995 1538000) (-916 "PMSYM.spad" 1536307 1536317 1536752 1536757) (-915 "PMQFCAT.spad" 1535894 1535908 1536297 1536302) (-914 "PMPRED.spad" 1535363 1535377 1535884 1535889) (-913 "PMPREDFS.spad" 1534807 1534829 1535353 1535358) (-912 "PMPLCAT.spad" 1533877 1533895 1534739 1534744) (-911 "PMLSAGG.spad" 1533458 1533472 1533867 1533872) (-910 "PMKERNEL.spad" 1533025 1533037 1533448 1533453) (-909 "PMINS.spad" 1532601 1532611 1533015 1533020) (-908 "PMFS.spad" 1532174 1532192 1532591 1532596) (-907 "PMDOWN.spad" 1531460 1531474 1532164 1532169) (-906 "PMASS.spad" 1530472 1530480 1531450 1531455) (-905 "PMASSFS.spad" 1529441 1529457 1530462 1530467) (-904 "PLOTTOOL.spad" 1529221 1529229 1529431 1529436) (-903 "PLOT.spad" 1524052 1524060 1529211 1529216) (-902 "PLOT3D.spad" 1520472 1520480 1524042 1524047) (-901 "PLOT1.spad" 1519613 1519623 1520462 1520467) (-900 "PLEQN.spad" 1506829 1506856 1519603 1519608) (-899 "PINTERP.spad" 1506445 1506464 1506819 1506824) (-898 "PINTERPA.spad" 1506227 1506243 1506435 1506440) (-897 "PI.spad" 1505834 1505842 1506201 1506222) (-896 "PID.spad" 1504790 1504798 1505760 1505829) (-895 "PICOERCE.spad" 1504447 1504457 1504780 1504785) (-894 "PGROEB.spad" 1503044 1503058 1504437 1504442) (-893 "PGE.spad" 1494297 1494305 1503034 1503039) (-892 "PGCD.spad" 1493179 1493196 1494287 1494292) (-891 "PFRPAC.spad" 1492322 1492332 1493169 1493174) (-890 "PFR.spad" 1488979 1488989 1492224 1492317) (-889 "PFOTOOLS.spad" 1488237 1488253 1488969 1488974) (-888 "PFOQ.spad" 1487607 1487625 1488227 1488232) (-887 "PFO.spad" 1487026 1487053 1487597 1487602) (-886 "PF.spad" 1486600 1486612 1486831 1486924) (-885 "PFECAT.spad" 1484266 1484274 1486526 1486595) (-884 "PFECAT.spad" 1481960 1481970 1484222 1484227) (-883 "PFBRU.spad" 1479830 1479842 1481950 1481955) (-882 "PFBR.spad" 1477368 1477391 1479820 1479825) (-881 "PERM.spad" 1473049 1473059 1477198 1477213) (-880 "PERMGRP.spad" 1467785 1467795 1473039 1473044) (-879 "PERMCAT.spad" 1466337 1466347 1467765 1467780) (-878 "PERMAN.spad" 1464869 1464883 1466327 1466332) (-877 "PENDTREE.spad" 1464142 1464152 1464498 1464503) (-876 "PDRING.spad" 1462633 1462643 1464122 1464137) (-875 "PDRING.spad" 1461132 1461144 1462623 1462628) (-874 "PDEPROB.spad" 1460089 1460097 1461122 1461127) (-873 "PDEPACK.spad" 1454091 1454099 1460079 1460084) (-872 "PDECOMP.spad" 1453553 1453570 1454081 1454086) (-871 "PDECAT.spad" 1451907 1451915 1453543 1453548) (-870 "PCOMP.spad" 1451758 1451771 1451897 1451902) (-869 "PBWLB.spad" 1450340 1450357 1451748 1451753) (-868 "PATTERN.spad" 1444771 1444781 1450330 1450335) (-867 "PATTERN2.spad" 1444507 1444519 1444761 1444766) (-866 "PATTERN1.spad" 1442809 1442825 1444497 1444502) (-865 "PATRES.spad" 1440356 1440368 1442799 1442804) (-864 "PATRES2.spad" 1440018 1440032 1440346 1440351) (-863 "PATMATCH.spad" 1438175 1438206 1439726 1439731) (-862 "PATMAB.spad" 1437600 1437610 1438165 1438170) (-861 "PATLRES.spad" 1436684 1436698 1437590 1437595) (-860 "PATAB.spad" 1436448 1436458 1436674 1436679) (-859 "PARTPERM.spad" 1433810 1433818 1436438 1436443) (-858 "PARSURF.spad" 1433238 1433266 1433800 1433805) (-857 "PARSU2.spad" 1433033 1433049 1433228 1433233) (-856 "script-parser.spad" 1432553 1432561 1433023 1433028) (-855 "PARSCURV.spad" 1431981 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(-548 "INTG0.spad" 898595 898613 905064 905069) (-547 "INTFTBL.spad" 892624 892632 898585 898590) (-546 "INTFACT.spad" 891683 891693 892614 892619) (-545 "INTEF.spad" 889998 890014 891673 891678) (-544 "INTDOM.spad" 888613 888621 889924 889993) (-543 "INTDOM.spad" 887290 887300 888603 888608) (-542 "INTCAT.spad" 885543 885553 887204 887285) (-541 "INTBIT.spad" 885046 885054 885533 885538) (-540 "INTALG.spad" 884228 884255 885036 885041) (-539 "INTAF.spad" 883720 883736 884218 884223) (-538 "INTABL.spad" 882238 882269 882401 882428) (-537 "INS.spad" 879705 879713 882140 882233) (-536 "INS.spad" 877258 877268 879695 879700) (-535 "INPSIGN.spad" 876692 876705 877248 877253) (-534 "INPRODPF.spad" 875758 875777 876682 876687) (-533 "INPRODFF.spad" 874816 874840 875748 875753) (-532 "INNMFACT.spad" 873787 873804 874806 874811) (-531 "INMODGCD.spad" 873271 873301 873777 873782) (-530 "INFSP.spad" 871556 871578 873261 873266) (-529 "INFPROD0.spad" 870606 870625 871546 871551) (-528 "INFORM.spad" 867767 867775 870596 870601) (-527 "INFORM1.spad" 867392 867402 867757 867762) (-526 "INFINITY.spad" 866944 866952 867382 867387) (-525 "INEP.spad" 865476 865498 866934 866939) (-524 "INDE.spad" 865205 865222 865466 865471) (-523 "INCRMAPS.spad" 864626 864636 865195 865200) (-522 "INBFILE.spad" 863955 863963 864616 864621) (-521 "INBFF.spad" 859725 859736 863945 863950) (-520 "INBCON.spad" 859025 859033 859715 859720) (-519 "INBCON.spad" 858323 858333 859015 859020) (-518 "INAST.spad" 857988 857996 858313 858318) (-517 "IMPTAST.spad" 857696 857704 857978 857983) (-516 "IMATRIX.spad" 856641 856667 857153 857180) (-515 "IMATQF.spad" 855735 855779 856597 856602) (-514 "IMATLIN.spad" 854340 854364 855691 855696) (-513 "ILIST.spad" 852996 853011 853523 853550) (-512 "IIARRAY2.spad" 852384 852422 852603 852630) (-511 "IFF.spad" 851794 851810 852065 852158) (-510 "IFAST.spad" 851408 851416 851784 851789) (-509 "IFARRAY.spad" 848895 848910 850591 850618) (-508 "IFAMON.spad" 848757 848774 848851 848856) (-507 "IEVALAB.spad" 848146 848158 848747 848752) (-506 "IEVALAB.spad" 847533 847547 848136 848141) (-505 "IDPO.spad" 847331 847343 847523 847528) (-504 "IDPOAMS.spad" 847087 847099 847321 847326) (-503 "IDPOAM.spad" 846807 846819 847077 847082) (-502 "IDPC.spad" 845741 845753 846797 846802) (-501 "IDPAM.spad" 845486 845498 845731 845736) (-500 "IDPAG.spad" 845233 845245 845476 845481) (-499 "IDENT.spad" 845150 845158 845223 845228) (-498 "IDECOMP.spad" 842387 842405 845140 845145) (-497 "IDEAL.spad" 837310 837349 842322 842327) (-496 "ICDEN.spad" 836461 836477 837300 837305) (-495 "ICARD.spad" 835650 835658 836451 836456) (-494 "IBPTOOLS.spad" 834243 834260 835640 835645) (-493 "IBITS.spad" 833442 833455 833879 833906) (-492 "IBATOOL.spad" 830317 830336 833432 833437) (-491 "IBACHIN.spad" 828804 828819 830307 830312) (-490 "IARRAY2.spad" 827792 827818 828411 828438) (-489 "IARRAY1.spad" 826837 826852 826975 827002) (-488 "IAN.spad" 825050 825058 826653 826746) (-487 "IALGFACT.spad" 824651 824684 825040 825045) (-486 "HYPCAT.spad" 824075 824083 824641 824646) (-485 "HYPCAT.spad" 823497 823507 824065 824070) (-484 "HOSTNAME.spad" 823305 823313 823487 823492) (-483 "HOAGG.spad" 820563 820573 823285 823300) (-482 "HOAGG.spad" 817606 817618 820330 820335) (-481 "HEXADEC.spad" 815476 815484 816074 816167) (-480 "HEUGCD.spad" 814491 814502 815466 815471) (-479 "HELLFDIV.spad" 814081 814105 814481 814486) (-478 "HEAP.spad" 813473 813483 813688 813715) (-477 "HEADAST.spad" 813004 813012 813463 813468) (-476 "HDP.spad" 804121 804137 804498 804629) (-475 "HDMP.spad" 801297 801312 801915 802042) (-474 "HB.spad" 799534 799542 801287 801292) (-473 "HASHTBL.spad" 798004 798035 798215 798242) (-472 "HASAST.spad" 797720 797728 797994 797999) (-471 "HACKPI.spad" 797203 797211 797622 797715) (-470 "GTSET.spad" 796142 796158 796849 796876) (-469 "GSTBL.spad" 794661 794696 794835 794850) (-468 "GSERIES.spad" 791828 791855 792793 792942) (-467 "GROUP.spad" 791097 791105 791808 791823) (-466 "GROUP.spad" 790374 790384 791087 791092) (-465 "GROEBSOL.spad" 788862 788883 790364 790369) (-464 "GRMOD.spad" 787433 787445 788852 788857) (-463 "GRMOD.spad" 786002 786016 787423 787428) (-462 "GRIMAGE.spad" 778607 778615 785992 785997) (-461 "GRDEF.spad" 776986 776994 778597 778602) (-460 "GRAY.spad" 775445 775453 776976 776981) (-459 "GRALG.spad" 774492 774504 775435 775440) (-458 "GRALG.spad" 773537 773551 774482 774487) (-457 "GPOLSET.spad" 772991 773014 773219 773246) (-456 "GOSPER.spad" 772256 772274 772981 772986) (-455 "GMODPOL.spad" 771394 771421 772224 772251) (-454 "GHENSEL.spad" 770463 770477 771384 771389) (-453 "GENUPS.spad" 766564 766577 770453 770458) (-452 "GENUFACT.spad" 766141 766151 766554 766559) (-451 "GENPGCD.spad" 765725 765742 766131 766136) (-450 "GENMFACT.spad" 765177 765196 765715 765720) (-449 "GENEEZ.spad" 763116 763129 765167 765172) (-448 "GDMP.spad" 760134 760151 760910 761037) (-447 "GCNAALG.spad" 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713672) (-426 "FSPECF.spad" 710611 710627 712524 712529) (-425 "FS.spad" 704661 704671 710374 710606) (-424 "FS.spad" 698501 698513 704216 704221) (-423 "FSINT.spad" 698159 698175 698491 698496) (-422 "FSERIES.spad" 697346 697358 697979 698078) (-421 "FSCINT.spad" 696659 696675 697336 697341) (-420 "FSAGG.spad" 695764 695774 696603 696654) (-419 "FSAGG.spad" 694843 694855 695684 695689) (-418 "FSAGG2.spad" 693542 693558 694833 694838) (-417 "FS2UPS.spad" 687931 687965 693532 693537) (-416 "FS2.spad" 687576 687592 687921 687926) (-415 "FS2EXPXP.spad" 686699 686722 687566 687571) (-414 "FRUTIL.spad" 685641 685651 686689 686694) (-413 "FR.spad" 679336 679346 684666 684735) (-412 "FRNAALG.spad" 674423 674433 679278 679331) (-411 "FRNAALG.spad" 669522 669534 674379 674384) (-410 "FRNAAF2.spad" 668976 668994 669512 669517) (-409 "FRMOD.spad" 668370 668400 668907 668912) (-408 "FRIDEAL.spad" 667565 667586 668350 668365) (-407 "FRIDEAL2.spad" 667167 667199 667555 667560) (-406 "FRETRCT.spad" 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(-385 "FNLA.spad" 638223 638245 638767 638794) (-384 "FNCAT.spad" 636551 636559 638213 638218) (-383 "FNAME.spad" 636443 636451 636541 636546) (-382 "FMTC.spad" 636241 636249 636369 636438) (-381 "FMONOID.spad" 633296 633306 636197 636202) (-380 "FM.spad" 632991 633003 633230 633257) (-379 "FMFUN.spad" 630011 630019 632971 632986) (-378 "FMC.spad" 629053 629061 629991 630006) (-377 "FMCAT.spad" 626707 626725 629021 629048) (-376 "FM1.spad" 626064 626076 626641 626668) (-375 "FLOATRP.spad" 623785 623799 626054 626059) (-374 "FLOAT.spad" 616949 616957 623651 623780) (-373 "FLOATCP.spad" 614366 614380 616939 616944) (-372 "FLINEXP.spad" 614078 614088 614346 614361) (-371 "FLINEXP.spad" 613744 613756 614014 614019) (-370 "FLASORT.spad" 613064 613076 613734 613739) (-369 "FLALG.spad" 610710 610729 612990 613059) (-368 "FLAGG.spad" 607716 607726 610678 610705) (-367 "FLAGG.spad" 604635 604647 607599 607604) (-366 "FLAGG2.spad" 603316 603332 604625 604630) (-365 "FINRALG.spad" 601345 601358 603272 603311) (-364 "FINRALG.spad" 599300 599315 601229 601234) (-363 "FINITE.spad" 598452 598460 599290 599295) (-362 "FINAALG.spad" 587433 587443 598394 598447) (-361 "FINAALG.spad" 576426 576438 587389 587394) (-360 "FILE.spad" 576009 576019 576416 576421) (-359 "FILECAT.spad" 574527 574544 575999 576004) (-358 "FIELD.spad" 573933 573941 574429 574522) (-357 "FIELD.spad" 573425 573435 573923 573928) (-356 "FGROUP.spad" 572034 572044 573405 573420) (-355 "FGLMICPK.spad" 570821 570836 572024 572029) (-354 "FFX.spad" 570196 570211 570537 570630) (-353 "FFSLPE.spad" 569685 569706 570186 570191) (-352 "FFPOLY.spad" 560937 560948 569675 569680) (-351 "FFPOLY2.spad" 559997 560014 560927 560932) (-350 "FFP.spad" 559394 559414 559713 559806) (-349 "FF.spad" 558842 558858 559075 559168) (-348 "FFNBX.spad" 557354 557374 558558 558651) (-347 "FFNBP.spad" 555867 555884 557070 557163) (-346 "FFNB.spad" 554332 554353 555548 555641) (-345 "FFINTBAS.spad" 551746 551765 554322 554327) (-344 "FFIELDC.spad" 549321 549329 551648 551741) (-343 "FFIELDC.spad" 546982 546992 549311 549316) (-342 "FFHOM.spad" 545730 545747 546972 546977) (-341 "FFF.spad" 543165 543176 545720 545725) (-340 "FFCGX.spad" 542012 542032 542881 542974) (-339 "FFCGP.spad" 540901 540921 541728 541821) (-338 "FFCG.spad" 539693 539714 540582 540675) (-337 "FFCAT.spad" 532720 532742 539532 539688) (-336 "FFCAT.spad" 525826 525850 532640 532645) (-335 "FFCAT2.spad" 525571 525611 525816 525821) (-334 "FEXPR.spad" 517280 517326 525327 525366) (-333 "FEVALAB.spad" 516986 516996 517270 517275) (-332 "FEVALAB.spad" 516477 516489 516763 516768) (-331 "FDIV.spad" 515919 515943 516467 516472) (-330 "FDIVCAT.spad" 513961 513985 515909 515914) (-329 "FDIVCAT.spad" 512001 512027 513951 513956) (-328 "FDIV2.spad" 511655 511695 511991 511996) (-327 "FCPAK1.spad" 510208 510216 511645 511650) (-326 "FCOMP.spad" 509587 509597 510198 510203) (-325 "FC.spad" 499412 499420 509577 509582) (-324 "FAXF.spad" 492347 492361 499314 499407) (-323 "FAXF.spad" 485334 485350 492303 492308) (-322 "FARRAY.spad" 483480 483490 484517 484544) (-321 "FAMR.spad" 481600 481612 483378 483475) (-320 "FAMR.spad" 479704 479718 481484 481489) (-319 "FAMONOID.spad" 479354 479364 479658 479663) (-318 "FAMONC.spad" 477576 477588 479344 479349) (-317 "FAGROUP.spad" 477182 477192 477472 477499) (-316 "FACUTIL.spad" 475378 475395 477172 477177) (-315 "FACTFUNC.spad" 474554 474564 475368 475373) (-314 "EXPUPXS.spad" 471387 471410 472686 472835) (-313 "EXPRTUBE.spad" 468615 468623 471377 471382) (-312 "EXPRODE.spad" 465487 465503 468605 468610) (-311 "EXPR.spad" 460762 460772 461476 461883) (-310 "EXPR2UPS.spad" 456854 456867 460752 460757) (-309 "EXPR2.spad" 456557 456569 456844 456849) (-308 "EXPEXPAN.spad" 453496 453521 454130 454223) (-307 "EXIT.spad" 453167 453175 453486 453491) (-306 "EXITAST.spad" 452903 452911 453157 453162) (-305 "EVALCYC.spad" 452361 452375 452893 452898) (-304 "EVALAB.spad" 451925 451935 452351 452356) (-303 "EVALAB.spad" 451487 451499 451915 451920) (-302 "EUCDOM.spad" 449029 449037 451413 451482) (-301 "EUCDOM.spad" 446633 446643 449019 449024) (-300 "ESTOOLS.spad" 438473 438481 446623 446628) (-299 "ESTOOLS2.spad" 438074 438088 438463 438468) (-298 "ESTOOLS1.spad" 437759 437770 438064 438069) (-297 "ES.spad" 430306 430314 437749 437754) (-296 "ES.spad" 422759 422769 430204 430209) (-295 "ESCONT.spad" 419532 419540 422749 422754) (-294 "ESCONT1.spad" 419281 419293 419522 419527) (-293 "ES2.spad" 418776 418792 419271 419276) (-292 "ES1.spad" 418342 418358 418766 418771) (-291 "ERROR.spad" 415663 415671 418332 418337) (-290 "EQTBL.spad" 414135 414157 414344 414371) (-289 "EQ.spad" 409009 409019 411808 411920) (-288 "EQ2.spad" 408725 408737 408999 409004) (-287 "EP.spad" 405039 405049 408715 408720) (-286 "ENV.spad" 403741 403749 405029 405034) (-285 "ENTIRER.spad" 403409 403417 403685 403736) (-284 "EMR.spad" 402610 402651 403335 403404) (-283 "ELTAGG.spad" 400850 400869 402600 402605) (-282 "ELTAGG.spad" 399054 399075 400806 400811) (-281 "ELTAB.spad" 398501 398519 399044 399049) (-280 "ELFUTS.spad" 397880 397899 398491 398496) (-279 "ELEMFUN.spad" 397569 397577 397870 397875) (-278 "ELEMFUN.spad" 397256 397266 397559 397564) (-277 "ELAGG.spad" 395187 395197 397224 397251) (-276 "ELAGG.spad" 393067 393079 395106 395111) (-275 "ELABEXPR.spad" 391998 392006 393057 393062) (-274 "EFUPXS.spad" 388774 388804 391954 391959) (-273 "EFULS.spad" 385610 385633 388730 388735) (-272 "EFSTRUC.spad" 383565 383581 385600 385605) (-271 "EF.spad" 378331 378347 383555 383560) (-270 "EAB.spad" 376607 376615 378321 378326) (-269 "E04UCFA.spad" 376143 376151 376597 376602) (-268 "E04NAFA.spad" 375720 375728 376133 376138) (-267 "E04MBFA.spad" 375300 375308 375710 375715) (-266 "E04JAFA.spad" 374836 374844 375290 375295) (-265 "E04GCFA.spad" 374372 374380 374826 374831) (-264 "E04FDFA.spad" 373908 373916 374362 374367) (-263 "E04DGFA.spad" 373444 373452 373898 373903) (-262 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-23) T) ((-1196 . -1074) T) ((-1196 . -597) 134037) ((-1196 . -101) T) ((-1196 . -25) T) ((-1196 . -130) T) ((-1196 . -143) 133962) ((-1196 . -145) 133887) ((-1196 . -598) 133560) ((-1196 . -227) 133530) ((-1196 . -876) 133381) ((-1196 . -229) 133286) ((-1196 . -358) 133265) ((-1196 . -1190) 133244) ((-1196 . -897) 133223) ((-1196 . -545) 133174) ((-1196 . -170) 133105) ((-1196 . -446) 133084) ((-1196 . -302) 133063) ((-1196 . -285) 133014) ((-1196 . -239) 132993) ((-1196 . -333) 132963) ((-1196 . -507) 132823) ((-1196 . -304) 132762) ((-1196 . -372) 132732) ((-1196 . -621) 132640) ((-1196 . -395) 132610) ((-1196 . -1185) 132589) ((-1196 . -862) 132462) ((-1196 . -800) 132415) ((-1196 . -771) 132368) ((-1196 . -772) 132321) ((-1196 . -827) 132220) ((-1196 . -774) 132173) ((-1196 . -777) 132126) ((-1196 . -825) 132079) ((-1196 . -860) 132049) ((-1196 . -886) 132002) ((-1196 . -996) 131955) ((-1196 . -1014) 131741) ((-1196 . -1124) 131693) ((-1196 . -967) 131663) ((-1191 . -1195) 131624) ((-1191 . -978) 131590) ((-1191 . -1171) 131556) ((-1191 . -1174) 131522) ((-1191 . -486) 131488) ((-1191 . -279) 131454) ((-1191 . -94) 131420) ((-1191 . -35) 131386) ((-1191 . -1210) 131363) ((-1191 . -47) 131340) ((-1191 . -698) 131136) ((-1191 . -628) 130988) ((-1191 . -1031) 130778) ((-1191 . -111) 130547) ((-1191 . -38) 130343) ((-1191 . -949) 130312) ((-1191 . -281) 130160) ((-1191 . -1193) 130144) ((-1191 . -707) T) ((-1191 . -1085) T) ((-1191 . -1032) T) ((-1191 . -1025) T) ((-1191 . -21) T) ((-1191 . -23) T) ((-1191 . -1074) T) ((-1191 . -597) 130126) ((-1191 . -101) T) ((-1191 . -25) T) ((-1191 . -130) T) ((-1191 . -143) 130033) ((-1191 . -145) 129940) ((-1191 . -598) NIL) ((-1191 . -227) 129892) ((-1191 . -876) 129725) ((-1191 . -229) 129612) ((-1191 . -358) 129591) ((-1191 . -1190) 129570) ((-1191 . -897) 129549) ((-1191 . -545) 129500) ((-1191 . -170) 129431) ((-1191 . -446) 129410) ((-1191 . -302) 129389) ((-1191 . -285) 129340) ((-1191 . -239) 129319) ((-1191 . -333) 129271) ((-1191 . -507) 129040) ((-1191 . -304) 128925) ((-1191 . -372) 128877) ((-1191 . -621) 128829) ((-1191 . -395) 128781) ((-1191 . -1185) 128760) ((-1191 . -862) NIL) ((-1191 . -800) NIL) ((-1191 . -771) NIL) ((-1191 . -772) NIL) ((-1191 . -827) NIL) ((-1191 . -774) NIL) ((-1191 . -777) NIL) ((-1191 . -825) NIL) ((-1191 . -860) 128712) ((-1191 . -886) NIL) ((-1191 . -996) NIL) ((-1191 . -1014) 128678) ((-1191 . -1124) NIL) ((-1191 . -967) 128630) ((-1186 . -1056) T) ((-1186 . -597) 128596) ((-1186 . -1074) T) ((-1186 . -101) T) ((-1186 . -92) T) ((-1183 . -597) 128508) ((-1183 . -1074) 128486) ((-1183 . -101) 128464) ((-1178 . -721) 128440) ((-1178 . -35) 128406) ((-1178 . -94) 128372) ((-1178 . -279) 128338) ((-1178 . -486) 128304) ((-1178 . -1174) 128270) ((-1178 . -1171) 128236) ((-1178 . -978) 128202) ((-1178 . -47) 128171) ((-1178 . -38) 128068) ((-1178 . -698) 127965) ((-1178 . -285) 127944) ((-1178 . -545) 127923) ((-1178 . -111) 127792) ((-1178 . -1031) 127675) ((-1178 . -170) 127626) ((-1178 . -145) 127605) ((-1178 . -143) 127584) ((-1178 . -628) 127509) ((-1178 . -949) 127471) ((-1178 . -1025) T) ((-1178 . -1032) T) ((-1178 . -1085) T) ((-1178 . -707) T) ((-1178 . -21) T) ((-1178 . -23) T) ((-1178 . -1074) T) ((-1178 . -597) 127453) ((-1178 . -101) T) ((-1178 . -25) T) ((-1178 . -130) T) ((-1178 . -876) 127434) ((-1178 . -507) 127401) ((-1178 . -304) 127388) ((-1172 . -986) 127372) ((-1172 . -34) T) ((-1172 . -1185) T) ((-1172 . -597) 127304) ((-1172 . -304) 127242) ((-1172 . -507) 127175) ((-1172 . -1074) 127153) ((-1172 . -101) 127131) ((-1172 . -483) 127115) ((-1167 . -360) 127089) ((-1167 . -101) T) ((-1167 . -597) 127071) ((-1167 . -1074) T) ((-1165 . -1074) T) ((-1165 . -597) 127053) ((-1165 . -101) T) ((-1158 . -1162) 127032) ((-1158 . -225) 126982) ((-1158 . -106) 126932) ((-1158 . -304) 126736) ((-1158 . -507) 126528) ((-1158 . -483) 126465) ((-1158 . -149) 126415) ((-1158 . -598) NIL) ((-1158 . -231) 126365) ((-1158 . -594) 126344) ((-1158 . -283) 126323) ((-1158 . -281) 126302) ((-1158 . -101) T) ((-1158 . -1074) T) ((-1158 . -597) 126284) ((-1158 . -1185) T) ((-1158 . -34) T) ((-1158 . -588) 126263) ((-1154 . -1227) T) ((-1154 . -1074) T) ((-1154 . -597) 126245) ((-1154 . -101) T) ((-1153 . -597) 126227) ((-1152 . -597) 126209) ((-1151 . -321) 126186) ((-1151 . -1014) 126082) ((-1151 . -407) 126066) ((-1151 . -38) 125963) ((-1151 . -628) 125888) ((-1151 . -707) T) ((-1151 . -1085) T) ((-1151 . -1032) T) ((-1151 . -1025) T) ((-1151 . -111) 125757) ((-1151 . -1031) 125640) ((-1151 . -21) T) ((-1151 . -23) T) ((-1151 . -1074) T) ((-1151 . -597) 125622) ((-1151 . -101) T) ((-1151 . -25) T) ((-1151 . -130) T) ((-1151 . -698) 125519) ((-1151 . -143) 125498) ((-1151 . -145) 125477) ((-1151 . -170) 125428) ((-1151 . -545) 125407) ((-1151 . -285) 125386) ((-1151 . -47) 125363) ((-1149 . -827) T) ((-1149 . -101) T) ((-1149 . -597) 125345) ((-1149 . -1074) T) ((-1149 . -598) 125267) ((-1149 . -801) T) ((-1149 . -862) 125234) ((-1148 . -597) 125216) ((-1147 . -1224) 125200) ((-1147 . -229) 125159) ((-1147 . -628) 125084) ((-1147 . -130) T) ((-1147 . -25) T) ((-1147 . -101) T) ((-1147 . -597) 125066) ((-1147 . -1074) T) ((-1147 . -23) T) ((-1147 . -21) T) ((-1147 . -707) T) ((-1147 . -1085) T) ((-1147 . -1032) T) ((-1147 . -1025) T) ((-1147 . -281) 125051) ((-1147 . -876) 124964) ((-1147 . -949) 124933) ((-1147 . -38) 124830) ((-1147 . -111) 124699) ((-1147 . -1031) 124582) ((-1147 . -698) 124479) ((-1147 . -143) 124458) ((-1147 . -145) 124437) ((-1147 . -170) 124388) ((-1147 . -545) 124367) ((-1147 . -285) 124346) ((-1147 . -47) 124323) ((-1147 . -1210) 124300) ((-1147 . -35) 124266) ((-1147 . -94) 124232) ((-1147 . -279) 124198) ((-1147 . -486) 124164) ((-1147 . -1174) 124130) ((-1147 . -1171) 124096) ((-1147 . -978) 124062) ((-1146 . -1216) 124023) ((-1146 . -358) 124002) ((-1146 . -1190) 123981) ((-1146 . -897) 123960) ((-1146 . -545) 123911) ((-1146 . -170) 123842) ((-1146 . -698) 123683) ((-1146 . -38) 123524) ((-1146 . -446) 123503) ((-1146 . -302) 123482) ((-1146 . -628) 123379) ((-1146 . -707) T) ((-1146 . -1085) T) ((-1146 . -1032) T) ((-1146 . -1025) T) ((-1146 . -111) 123200) ((-1146 . -1031) 123035) ((-1146 . -21) T) ((-1146 . -23) T) ((-1146 . -1074) T) ((-1146 . -597) 123017) ((-1146 . -101) T) ((-1146 . -25) T) ((-1146 . -130) T) ((-1146 . -285) 122968) ((-1146 . -239) 122947) ((-1146 . -978) 122913) ((-1146 . -1171) 122879) ((-1146 . -1174) 122845) ((-1146 . -486) 122811) ((-1146 . -279) 122777) ((-1146 . -94) 122743) ((-1146 . -35) 122709) ((-1146 . -1210) 122679) ((-1146 . -47) 122649) ((-1146 . -145) 122628) ((-1146 . -143) 122607) ((-1146 . -949) 122569) ((-1146 . -876) 122475) ((-1146 . -281) 122460) ((-1146 . -229) 122412) ((-1146 . -1214) 122396) ((-1146 . -1014) 122331) ((-1143 . -1207) 122315) ((-1143 . -1124) 122293) ((-1143 . -598) NIL) ((-1143 . -304) 122280) ((-1143 . -507) 122227) ((-1143 . -321) 122204) ((-1143 . -1014) 122084) ((-1143 . -407) 122068) ((-1143 . -38) 121897) ((-1143 . -111) 121706) ((-1143 . -1031) 121529) ((-1143 . -628) 121454) ((-1143 . -698) 121283) ((-1143 . -143) 121262) ((-1143 . -145) 121241) ((-1143 . -47) 121218) ((-1143 . -372) 121202) ((-1143 . -621) 121150) ((-1143 . -827) 121129) ((-1143 . -876) 121072) ((-1143 . -862) NIL) ((-1143 . -886) 121051) ((-1143 . -1190) 121030) ((-1143 . -926) 120999) ((-1143 . -897) 120978) ((-1143 . -545) 120889) ((-1143 . -285) 120800) ((-1143 . -170) 120691) ((-1143 . -446) 120622) ((-1143 . -302) 120601) ((-1143 . -281) 120528) ((-1143 . -229) T) ((-1143 . -130) T) ((-1143 . -25) T) ((-1143 . -101) T) ((-1143 . -597) 120510) ((-1143 . -1074) T) ((-1143 . -23) T) ((-1143 . -21) T) ((-1143 . -707) T) ((-1143 . -1085) T) ((-1143 . -1032) T) ((-1143 . -1025) T) ((-1143 . -227) 120494) ((-1140 . -1195) 120455) ((-1140 . -978) 120421) ((-1140 . -1171) 120387) ((-1140 . -1174) 120353) ((-1140 . -486) 120319) ((-1140 . -279) 120285) ((-1140 . -94) 120251) ((-1140 . -35) 120217) ((-1140 . -1210) 120194) ((-1140 . -47) 120171) ((-1140 . -698) 119967) ((-1140 . -628) 119819) ((-1140 . -1031) 119609) ((-1140 . -111) 119378) ((-1140 . -38) 119174) ((-1140 . -949) 119143) ((-1140 . -281) 118991) ((-1140 . -1193) 118975) ((-1140 . -707) T) ((-1140 . -1085) T) ((-1140 . -1032) T) ((-1140 . -1025) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1074) T) ((-1140 . -597) 118957) ((-1140 . -101) T) ((-1140 . -25) T) ((-1140 . -130) T) ((-1140 . -143) 118864) ((-1140 . -145) 118771) ((-1140 . -598) NIL) ((-1140 . -227) 118723) ((-1140 . -876) 118556) ((-1140 . -229) 118443) ((-1140 . -358) 118422) ((-1140 . -1190) 118401) ((-1140 . -897) 118380) ((-1140 . -545) 118331) ((-1140 . -170) 118262) ((-1140 . -446) 118241) ((-1140 . -302) 118220) ((-1140 . -285) 118171) ((-1140 . -239) 118150) ((-1140 . -333) 118102) ((-1140 . -507) 117871) ((-1140 . -304) 117756) ((-1140 . -372) 117708) ((-1140 . -621) 117660) ((-1140 . -395) 117612) ((-1140 . -1185) 117591) ((-1140 . -862) NIL) ((-1140 . -800) NIL) ((-1140 . -771) NIL) ((-1140 . -772) NIL) ((-1140 . -827) NIL) ((-1140 . -774) NIL) ((-1140 . -777) NIL) ((-1140 . -825) NIL) ((-1140 . -860) 117543) ((-1140 . -886) NIL) ((-1140 . -996) NIL) ((-1140 . -1014) 117509) ((-1140 . -1124) NIL) ((-1140 . -967) 117461) ((-1139 . -1056) T) ((-1139 . -597) 117427) ((-1139 . -1074) T) ((-1139 . -101) T) ((-1139 . -92) T) ((-1138 . -1074) T) ((-1138 . -597) 117409) ((-1138 . -101) T) ((-1137 . -1074) T) ((-1137 . -597) 117391) ((-1137 . -101) T) ((-1132 . -1162) 117367) ((-1132 . -225) 117314) ((-1132 . -106) 117261) ((-1132 . -304) 117056) ((-1132 . -507) 116839) ((-1132 . -483) 116773) ((-1132 . -149) 116720) ((-1132 . -598) NIL) ((-1132 . -231) 116667) ((-1132 . -594) 116643) ((-1132 . -283) 116619) ((-1132 . -281) 116595) ((-1132 . -101) T) ((-1132 . -1074) T) ((-1132 . -597) 116577) ((-1132 . -1185) T) ((-1132 . -34) T) ((-1132 . -588) 116553) ((-1131 . -1130) T) ((-1131 . -19) 116535) ((-1131 . -631) 116517) ((-1131 . -283) 116492) ((-1131 . -281) 116467) ((-1131 . -588) 116442) ((-1131 . -598) NIL) ((-1131 . -483) 116424) ((-1131 . -507) NIL) ((-1131 . -304) NIL) ((-1131 . -1185) T) ((-1131 . -34) T) ((-1131 . -149) 116406) ((-1131 . -827) T) ((-1131 . -367) 116388) ((-1131 . -1117) T) ((-1131 . -101) T) ((-1131 . -597) 116370) ((-1131 . -1074) T) ((-1131 . -801) T) ((-1126 . -654) 116354) ((-1126 . -631) 116338) ((-1126 . -283) 116315) ((-1126 . -281) 116292) ((-1126 . -588) 116269) ((-1126 . -598) 116230) ((-1126 . -483) 116214) ((-1126 . -101) 116192) ((-1126 . -1074) 116170) ((-1126 . -507) 116103) ((-1126 . -304) 116041) ((-1126 . -597) 115973) ((-1126 . -1185) T) ((-1126 . -34) T) ((-1126 . -149) 115957) ((-1126 . -1220) 115941) ((-1126 . -986) 115925) ((-1126 . -1122) 115909) ((-1123 . -1162) 115888) ((-1123 . -225) 115838) ((-1123 . -106) 115788) ((-1123 . -304) 115592) ((-1123 . -507) 115384) ((-1123 . -483) 115321) ((-1123 . -149) 115271) ((-1123 . -598) NIL) ((-1123 . -231) 115221) ((-1123 . -594) 115200) ((-1123 . -283) 115179) ((-1123 . -281) 115158) ((-1123 . -101) T) ((-1123 . -1074) T) ((-1123 . -597) 115140) ((-1123 . -1185) T) ((-1123 . -34) T) ((-1123 . -588) 115119) ((-1120 . -1094) 115103) ((-1120 . -483) 115087) ((-1120 . -101) 115065) ((-1120 . -1074) 115043) ((-1120 . -507) 114976) ((-1120 . -304) 114914) ((-1120 . -597) 114846) ((-1120 . -1185) T) ((-1120 . -34) T) ((-1120 . -106) 114830) ((-1119 . -1082) 114799) ((-1119 . -1180) 114768) ((-1119 . -597) 114730) ((-1119 . -149) 114714) ((-1119 . -34) T) ((-1119 . -1185) T) ((-1119 . -304) 114652) ((-1119 . -507) 114585) ((-1119 . -1074) T) ((-1119 . -101) T) ((-1119 . -483) 114569) ((-1119 . -598) 114530) ((-1119 . -952) 114499) ((-1119 . -1045) 114468) ((-1115 . -1096) 114413) ((-1115 . -483) 114397) ((-1115 . -507) 114330) ((-1115 . -304) 114268) ((-1115 . -1185) T) ((-1115 . -34) T) ((-1115 . -1028) 114208) ((-1115 . -1014) 114104) ((-1115 . -407) 114088) ((-1115 . -621) 114036) ((-1115 . -372) 114020) ((-1115 . -229) 113999) ((-1115 . -876) 113958) ((-1115 . -227) 113942) ((-1115 . -698) 113874) ((-1115 . -628) 113848) ((-1115 . -130) T) ((-1115 . -25) T) ((-1115 . -101) T) ((-1115 . -597) 113810) ((-1115 . -1074) T) ((-1115 . -23) T) ((-1115 . -21) T) ((-1115 . -1031) 113794) ((-1115 . -111) 113773) ((-1115 . -1025) T) ((-1115 . -1032) T) ((-1115 . -1085) T) ((-1115 . -707) T) ((-1115 . -38) 113733) ((-1115 . -598) 113694) ((-1114 . -986) 113665) ((-1114 . -34) T) ((-1114 . -1185) T) ((-1114 . -597) 113647) ((-1114 . -304) 113573) ((-1114 . -507) 113492) ((-1114 . -1074) T) ((-1114 . -101) T) ((-1114 . -483) 113463) ((-1113 . -1074) T) ((-1113 . -597) 113445) ((-1113 . -101) T) ((-1108 . -1110) T) ((-1108 . -1227) T) ((-1108 . -92) T) ((-1108 . -101) T) ((-1108 . -597) 113411) ((-1108 . -1074) T) ((-1108 . -1056) T) ((-1106 . -1107) 113395) ((-1106 . -101) T) ((-1106 . -597) 113377) ((-1106 . -1074) T) ((-1099 . -721) 113356) ((-1099 . -35) 113322) ((-1099 . -94) 113288) ((-1099 . -279) 113254) ((-1099 . -486) 113220) ((-1099 . -1174) 113186) ((-1099 . -1171) 113152) ((-1099 . -978) 113118) ((-1099 . -47) 113090) ((-1099 . -38) 112987) ((-1099 . -698) 112884) ((-1099 . -285) 112863) ((-1099 . -545) 112842) ((-1099 . -111) 112711) ((-1099 . -1031) 112594) ((-1099 . -170) 112545) ((-1099 . -145) 112524) ((-1099 . -143) 112503) ((-1099 . -628) 112428) ((-1099 . -949) 112395) ((-1099 . -1025) T) ((-1099 . -1032) T) ((-1099 . -1085) T) ((-1099 . -707) T) ((-1099 . -21) T) ((-1099 . -23) T) ((-1099 . -1074) T) ((-1099 . -597) 112377) ((-1099 . -101) T) ((-1099 . -25) T) ((-1099 . -130) T) ((-1099 . -876) 112361) ((-1099 . -507) 112331) ((-1099 . -304) 112318) ((-1098 . -926) 112285) ((-1098 . -1014) 112168) ((-1098 . -1190) 112147) ((-1098 . -886) 112126) ((-1098 . -862) 111985) ((-1098 . -876) 111969) ((-1098 . -827) 111948) ((-1098 . -507) 111900) ((-1098 . -446) 111851) ((-1098 . -621) 111799) ((-1098 . -372) 111783) ((-1098 . -47) 111755) ((-1098 . -38) 111604) ((-1098 . -698) 111453) ((-1098 . -285) 111384) ((-1098 . -545) 111315) ((-1098 . -111) 111144) ((-1098 . -1031) 110987) ((-1098 . -170) 110898) ((-1098 . -145) 110877) ((-1098 . -143) 110856) ((-1098 . -628) 110781) ((-1098 . -130) T) ((-1098 . -25) T) ((-1098 . -101) T) ((-1098 . -597) 110763) ((-1098 . -1074) T) ((-1098 . -23) T) ((-1098 . -21) T) ((-1098 . -1025) T) ((-1098 . -1032) T) ((-1098 . -1085) T) ((-1098 . -707) T) ((-1098 . -407) 110747) ((-1098 . -321) 110719) ((-1098 . -304) 110706) ((-1098 . -598) 110454) ((-1093 . -537) T) ((-1093 . -1190) T) ((-1093 . -1124) T) ((-1093 . -1014) 110436) ((-1093 . -598) 110351) ((-1093 . -996) T) ((-1093 . -862) 110333) ((-1093 . -825) T) ((-1093 . -777) T) ((-1093 . -774) T) ((-1093 . -827) T) ((-1093 . -772) T) ((-1093 . -771) T) ((-1093 . -800) T) ((-1093 . -621) 110315) ((-1093 . -897) T) ((-1093 . -545) T) ((-1093 . -285) T) ((-1093 . -170) T) ((-1093 . -698) 110302) ((-1093 . -1031) 110289) ((-1093 . -111) 110274) ((-1093 . -38) 110261) ((-1093 . -446) T) ((-1093 . -302) T) ((-1093 . -229) T) ((-1093 . -141) T) ((-1093 . -1025) T) ((-1093 . -1032) T) ((-1093 . -1085) T) ((-1093 . -707) T) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1074) T) ((-1093 . -597) 110243) ((-1093 . -101) T) ((-1093 . -25) T) ((-1093 . -130) T) ((-1093 . -628) 110230) ((-1093 . -145) T) ((-1093 . -642) T) ((-1093 . -801) T) ((-1089 . -1056) T) ((-1089 . -597) 110196) ((-1089 . -1074) T) ((-1089 . -101) T) ((-1089 . -92) T) ((-1088 . -1074) T) ((-1088 . -597) 110178) ((-1088 . -101) T) ((-1086 . -234) 110157) ((-1086 . -1239) 110127) ((-1086 . -771) 110106) ((-1086 . -825) 110085) ((-1086 . -777) 110036) ((-1086 . -774) 109987) ((-1086 . -827) 109938) ((-1086 . -772) 109889) ((-1086 . -773) 109868) ((-1086 . -283) 109845) ((-1086 . -281) 109822) ((-1086 . -483) 109806) ((-1086 . -507) 109739) ((-1086 . -304) 109677) ((-1086 . -1185) T) ((-1086 . -34) T) ((-1086 . -588) 109654) ((-1086 . -1014) 109481) ((-1086 . -407) 109450) ((-1086 . -621) 109356) ((-1086 . -372) 109325) ((-1086 . -363) 109304) ((-1086 . -229) 109256) ((-1086 . -876) 109188) ((-1086 . -227) 109157) ((-1086 . -111) 109047) ((-1086 . -1031) 108944) ((-1086 . -170) 108923) ((-1086 . -597) 108654) ((-1086 . -698) 108596) ((-1086 . -628) 108444) ((-1086 . -130) 108314) ((-1086 . -23) 108184) ((-1086 . -21) 108094) ((-1086 . -1025) 108024) ((-1086 . -1032) 107954) ((-1086 . -1085) 107864) ((-1086 . -707) 107774) ((-1086 . -38) 107744) ((-1086 . -1074) 107534) ((-1086 . -101) 107324) ((-1086 . -25) 107175) ((-1079 . -391) T) ((-1079 . -1185) T) ((-1079 . -597) 107157) ((-1078 . -1077) 107121) ((-1078 . -101) T) ((-1078 . -597) 107103) ((-1078 . -1074) T) ((-1076 . -1077) 107055) ((-1076 . -101) T) ((-1076 . -597) 107037) ((-1076 . -1074) T) ((-1075 . -363) T) ((-1075 . -101) T) ((-1075 . -597) 107019) ((-1075 . -1074) T) ((-1070 . -421) 107003) ((-1070 . -1072) 106987) ((-1070 . -363) 106966) ((-1070 . -231) 106950) ((-1070 . -598) 106911) ((-1070 . -149) 106895) ((-1070 . -483) 106879) ((-1070 . -101) T) ((-1070 . -1074) T) ((-1070 . -507) 106812) ((-1070 . -304) 106750) ((-1070 . -597) 106732) ((-1070 . -1185) T) ((-1070 . -34) T) ((-1070 . -106) 106716) ((-1070 . -225) 106700) ((-1069 . -1056) T) ((-1069 . -597) 106666) ((-1069 . -1074) T) ((-1069 . -101) T) ((-1069 . -92) T) ((-1065 . -1185) T) ((-1065 . -1074) 106644) ((-1065 . -597) 106611) ((-1065 . -101) 106589) ((-1064 . -1056) T) ((-1064 . -597) 106555) ((-1064 . -1074) T) ((-1064 . -101) T) ((-1064 . -92) T) ((-1062 . -1067) 106539) ((-1062 . -1185) T) ((-1062 . -1074) 106517) ((-1062 . -597) 106484) ((-1062 . -101) 106462) ((-1062 . -1068) 106420) ((-1061 . -261) 106404) ((-1061 . -1014) 106388) ((-1061 . -1074) T) ((-1061 . -597) 106370) ((-1061 . -101) T) ((-1061 . -827) T) ((-1060 . -248) 106307) ((-1060 . -1014) 106134) ((-1060 . -598) NIL) ((-1060 . -321) 106095) ((-1060 . -407) 106079) ((-1060 . -38) 105928) ((-1060 . -111) 105757) ((-1060 . -1031) 105600) ((-1060 . -628) 105525) ((-1060 . -698) 105374) ((-1060 . -143) 105353) ((-1060 . -145) 105332) ((-1060 . -170) 105243) ((-1060 . -545) 105174) ((-1060 . -285) 105105) ((-1060 . -47) 105066) ((-1060 . -372) 105050) ((-1060 . -621) 104998) ((-1060 . -446) 104949) ((-1060 . -507) 104816) ((-1060 . -827) 104795) ((-1060 . -876) 104730) ((-1060 . -862) NIL) ((-1060 . -886) 104709) ((-1060 . -1190) 104688) ((-1060 . -926) 104633) ((-1060 . -304) 104620) ((-1060 . -229) 104599) ((-1060 . -130) T) ((-1060 . -25) T) ((-1060 . -101) T) ((-1060 . -597) 104581) ((-1060 . -1074) T) ((-1060 . -23) T) ((-1060 . -21) T) ((-1060 . -707) T) ((-1060 . -1085) T) ((-1060 . -1032) T) ((-1060 . -1025) T) ((-1060 . -227) 104565) ((-1058 . -597) 104547) ((-1055 . -827) T) ((-1055 . -101) T) ((-1055 . -597) 104529) ((-1055 . -1074) T) ((-1052 . -705) 104508) ((-1052 . -1014) 104404) ((-1052 . -407) 104388) ((-1052 . -621) 104336) ((-1052 . -372) 104320) ((-1052 . -365) 104299) ((-1052 . -145) 104278) ((-1052 . -698) 104146) ((-1052 . -628) 104056) ((-1052 . -1031) 103966) ((-1052 . -111) 103862) ((-1052 . -38) 103730) ((-1052 . -405) 103709) ((-1052 . -397) 103688) ((-1052 . -143) 103639) ((-1052 . -1124) 103618) ((-1052 . -345) 103597) ((-1052 . -363) 103548) ((-1052 . -239) 103499) ((-1052 . -285) 103450) ((-1052 . -302) 103401) ((-1052 . -446) 103352) ((-1052 . -545) 103303) ((-1052 . -897) 103254) ((-1052 . -1190) 103205) ((-1052 . -358) 103156) ((-1052 . -229) 103081) ((-1052 . -876) 103014) ((-1052 . -227) 102984) ((-1052 . -598) 102968) ((-1052 . -21) T) ((-1052 . -23) T) ((-1052 . -1074) T) ((-1052 . -597) 102950) ((-1052 . -101) T) ((-1052 . -25) T) ((-1052 . -130) T) ((-1052 . -1025) T) ((-1052 . -1032) T) ((-1052 . -1085) T) ((-1052 . -707) T) ((-1052 . -170) T) ((-1050 . -1074) T) ((-1050 . -597) 102932) ((-1050 . -101) T) ((-1050 . -281) 102911) ((-1049 . -1074) T) ((-1049 . -597) 102893) ((-1049 . -101) T) ((-1048 . -1074) T) ((-1048 . -597) 102875) ((-1048 . -101) T) ((-1048 . -281) 102854) ((-1048 . -1014) 102831) ((-1047 . -1056) T) ((-1047 . -597) 102797) ((-1047 . -1074) T) ((-1047 . -101) T) ((-1047 . -92) T) ((-1040 . -1056) T) ((-1040 . -597) 102763) ((-1040 . -1074) T) ((-1040 . -101) T) ((-1040 . -92) T) ((-1037 . -1162) 102738) ((-1037 . -225) 102684) ((-1037 . -106) 102630) ((-1037 . -304) 102481) ((-1037 . -507) 102325) ((-1037 . -483) 102256) ((-1037 . -149) 102202) ((-1037 . -598) NIL) ((-1037 . -231) 102148) ((-1037 . -594) 102123) ((-1037 . -283) 102098) ((-1037 . -281) 102073) ((-1037 . -101) T) ((-1037 . -1074) T) ((-1037 . -597) 102055) ((-1037 . -1185) T) ((-1037 . -34) T) ((-1037 . -588) 102030) ((-1036 . -537) T) ((-1036 . -1190) T) ((-1036 . -1124) T) ((-1036 . -1014) 102012) ((-1036 . -598) 101927) ((-1036 . -996) T) ((-1036 . -862) 101909) ((-1036 . -825) T) ((-1036 . -777) T) ((-1036 . -774) T) ((-1036 . -827) T) ((-1036 . -772) T) ((-1036 . -771) T) ((-1036 . -800) T) ((-1036 . -621) 101891) ((-1036 . -897) T) ((-1036 . -545) T) ((-1036 . -285) T) ((-1036 . -170) T) ((-1036 . -698) 101878) ((-1036 . -1031) 101865) ((-1036 . -111) 101850) ((-1036 . -38) 101837) ((-1036 . -446) T) ((-1036 . -302) T) ((-1036 . -229) T) ((-1036 . -141) T) ((-1036 . -1025) T) ((-1036 . -1032) T) ((-1036 . -1085) T) ((-1036 . -707) T) ((-1036 . -21) T) ((-1036 . -23) T) ((-1036 . -1074) T) ((-1036 . -597) 101819) ((-1036 . -101) T) ((-1036 . -25) T) ((-1036 . -130) T) ((-1036 . -628) 101806) ((-1036 . -145) T) ((-1035 . -1042) 101785) ((-1035 . -101) T) ((-1035 . -597) 101767) ((-1035 . -1074) T) ((-1029 . -1028) 101707) ((-1029 . -698) 101649) ((-1029 . -34) T) ((-1029 . -1185) T) ((-1029 . -304) 101587) ((-1029 . -507) 101520) ((-1029 . -483) 101504) ((-1029 . -628) 101488) ((-1029 . -130) T) ((-1029 . -25) T) ((-1029 . -101) T) ((-1029 . -597) 101450) ((-1029 . -1074) T) ((-1029 . -23) T) ((-1029 . -21) T) ((-1029 . -1031) 101434) ((-1029 . -111) 101413) ((-1029 . -1239) 101383) ((-1029 . -598) 101344) ((-1022 . -1045) 101273) ((-1022 . -952) 101202) ((-1022 . -598) 101144) ((-1022 . -483) 101109) ((-1022 . -101) T) ((-1022 . -1074) T) ((-1022 . -507) 101010) ((-1022 . -304) 100918) ((-1022 . -597) 100861) ((-1022 . -1185) T) ((-1022 . -34) T) ((-1022 . -149) 100826) ((-1022 . -1180) 100755) ((-1012 . -1056) T) ((-1012 . -597) 100721) ((-1012 . -1074) T) ((-1012 . -101) T) ((-1012 . -92) T) ((-1011 . -1162) 100696) ((-1011 . -225) 100642) ((-1011 . -106) 100588) ((-1011 . -304) 100439) ((-1011 . -507) 100283) ((-1011 . -483) 100214) ((-1011 . -149) 100160) ((-1011 . -598) NIL) ((-1011 . -231) 100106) ((-1011 . -594) 100081) ((-1011 . -283) 100056) ((-1011 . -281) 100031) ((-1011 . -101) T) ((-1011 . -1074) T) ((-1011 . -597) 100013) ((-1011 . -1185) T) ((-1011 . -34) T) ((-1011 . -588) 99988) ((-1010 . -170) T) ((-1010 . -707) T) ((-1010 . -1085) T) ((-1010 . -1032) T) ((-1010 . -1025) T) ((-1010 . -628) 99962) ((-1010 . -130) T) ((-1010 . -25) T) ((-1010 . -101) T) ((-1010 . -597) 99944) ((-1010 . -1074) T) ((-1010 . -23) T) ((-1010 . -21) T) ((-1010 . -1031) 99918) ((-1010 . -111) 99885) ((-1010 . -38) 99869) ((-1010 . -698) 99853) ((-1003 . -1045) 99822) ((-1003 . -952) 99791) ((-1003 . -598) 99752) ((-1003 . -483) 99736) ((-1003 . -101) T) ((-1003 . -1074) T) ((-1003 . -507) 99669) ((-1003 . -304) 99607) ((-1003 . -597) 99569) ((-1003 . -1185) T) ((-1003 . -34) T) ((-1003 . -149) 99553) ((-1003 . -1180) 99522) ((-1002 . -1185) T) ((-1002 . -1074) 99500) ((-1002 . -597) 99467) ((-1002 . -101) 99445) ((-1000 . -988) T) ((-1000 . -978) T) ((-1000 . -771) T) ((-1000 . -772) T) ((-1000 . -827) T) ((-1000 . -774) T) ((-1000 . -777) T) ((-1000 . -825) T) ((-1000 . -1014) 99325) ((-1000 . -407) 99287) ((-1000 . -239) T) ((-1000 . -285) T) ((-1000 . -302) T) ((-1000 . -446) T) ((-1000 . -38) 99224) ((-1000 . -698) 99161) ((-1000 . -545) T) ((-1000 . -897) T) ((-1000 . -1190) T) ((-1000 . -358) T) ((-1000 . -111) 99077) ((-1000 . -1031) 99014) ((-1000 . -170) T) ((-1000 . -145) T) ((-1000 . -628) 98951) ((-1000 . -130) T) ((-1000 . -25) T) ((-1000 . -101) T) ((-1000 . -597) 98933) ((-1000 . -1074) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -1025) T) ((-1000 . -1032) T) ((-1000 . -1085) T) ((-1000 . -707) T) ((-995 . -1056) T) ((-995 . -597) 98899) ((-995 . -1074) T) ((-995 . -101) T) ((-995 . -92) T) ((-980 . -967) 98881) ((-980 . -1124) T) ((-980 . -1014) 98841) ((-980 . -598) 98771) ((-980 . -996) T) ((-980 . -886) NIL) ((-980 . -860) 98753) ((-980 . -825) T) ((-980 . -777) T) ((-980 . -774) T) ((-980 . -827) T) ((-980 . -772) T) ((-980 . -771) T) ((-980 . -800) T) ((-980 . -862) 98735) ((-980 . -1185) T) ((-980 . -395) 98717) ((-980 . -621) 98699) ((-980 . -372) 98681) ((-980 . -281) NIL) ((-980 . -304) NIL) ((-980 . -507) NIL) ((-980 . -333) 98663) ((-980 . -239) T) ((-980 . -111) 98597) ((-980 . -1031) 98547) ((-980 . -285) T) ((-980 . -698) 98497) ((-980 . -628) 98447) ((-980 . -38) 98397) ((-980 . -302) T) ((-980 . -446) T) ((-980 . -170) T) ((-980 . -545) T) ((-980 . -897) T) ((-980 . -1190) T) ((-980 . -358) T) ((-980 . -229) T) ((-980 . -876) NIL) ((-980 . -227) 98379) ((-980 . -145) T) ((-980 . -143) NIL) ((-980 . -130) T) ((-980 . -25) T) ((-980 . -101) T) ((-980 . -597) 98361) ((-980 . -1074) T) ((-980 . -23) T) ((-980 . -21) T) ((-980 . -1025) T) ((-980 . -1032) T) ((-980 . -1085) T) ((-980 . -707) T) ((-979 . -337) 98335) ((-979 . -170) T) ((-979 . -707) T) ((-979 . -1085) T) ((-979 . -1032) T) ((-979 . -1025) T) ((-979 . -628) 98280) ((-979 . -130) T) ((-979 . -25) T) ((-979 . -101) T) ((-979 . -597) 98262) ((-979 . -1074) T) ((-979 . -23) T) ((-979 . -21) T) ((-979 . -1031) 98207) ((-979 . -111) 98136) ((-979 . -598) 98120) ((-979 . -227) 98097) ((-979 . -876) 98049) ((-979 . -229) 98021) ((-979 . -358) T) ((-979 . -1190) T) ((-979 . -897) T) ((-979 . -545) T) ((-979 . -698) 97966) ((-979 . -38) 97911) ((-979 . -446) T) ((-979 . -302) T) ((-979 . -285) T) ((-979 . -239) T) ((-979 . -363) NIL) ((-979 . -345) NIL) ((-979 . -1124) NIL) ((-979 . -143) 97883) ((-979 . -397) NIL) ((-979 . -405) 97855) ((-979 . -145) 97827) ((-979 . -365) 97799) ((-979 . -372) 97776) ((-979 . -621) 97715) ((-979 . -407) 97692) ((-979 . -1014) 97580) ((-979 . -705) 97552) ((-976 . -971) 97536) ((-976 . -483) 97520) ((-976 . -101) 97498) ((-976 . -1074) 97476) ((-976 . -507) 97409) ((-976 . -304) 97347) ((-976 . -597) 97279) ((-976 . -1185) T) ((-976 . -34) T) ((-976 . -106) 97263) ((-972 . -974) 97247) ((-972 . -827) 97226) ((-972 . -1014) 97122) ((-972 . -407) 97106) ((-972 . -621) 97054) ((-972 . -372) 97038) ((-972 . -281) 96996) ((-972 . -304) 96961) ((-972 . -507) 96873) ((-972 . -333) 96857) ((-972 . -38) 96805) ((-972 . -111) 96687) ((-972 . -1031) 96583) ((-972 . -628) 96521) ((-972 . -698) 96469) ((-972 . -285) 96420) ((-972 . -239) 96399) ((-972 . -229) 96378) ((-972 . -876) 96337) ((-972 . -227) 96321) ((-972 . -598) 96282) ((-972 . -145) 96261) ((-972 . -143) 96240) ((-972 . -130) T) ((-972 . -25) T) ((-972 . -101) T) ((-972 . -597) 96222) ((-972 . -1074) T) ((-972 . -23) T) ((-972 . -21) T) ((-972 . -1025) T) ((-972 . -1032) T) ((-972 . -1085) T) ((-972 . -707) T) ((-970 . -1056) T) ((-970 . -597) 96188) ((-970 . -1074) T) ((-970 . -101) T) ((-970 . -92) T) ((-969 . -21) T) ((-969 . -23) T) ((-969 . -1074) T) ((-969 . -597) 96170) ((-969 . -101) T) ((-969 . -25) T) ((-969 . -130) T) ((-965 . -597) 96152) ((-962 . -1074) T) ((-962 . -597) 96134) ((-962 . -101) T) ((-947 . -777) T) ((-947 . -774) T) ((-947 . -827) T) ((-947 . -772) T) ((-947 . -23) T) ((-947 . -1074) T) ((-947 . -597) 96116) ((-947 . -101) T) ((-947 . -25) T) ((-947 . -130) T) ((-947 . -598) 96091) ((-946 . -1056) T) ((-946 . -597) 96057) ((-946 . -1074) T) ((-946 . -101) T) ((-946 . -92) T) ((-942 . -943) T) ((-942 . -101) T) ((-942 . -597) 96039) ((-942 . -1074) T) ((-941 . -597) 96021) ((-940 . -1074) T) ((-940 . -597) 96003) ((-940 . -101) T) ((-940 . -363) 95956) ((-940 . -707) 95855) ((-940 . -1085) 95754) ((-940 . -23) 95565) ((-940 . -25) 95376) ((-940 . -130) 95231) ((-940 . -467) 95184) ((-940 . -21) 95139) ((-940 . -773) 95092) ((-940 . -772) 95045) ((-940 . -827) 94944) ((-940 . -774) 94897) ((-940 . -777) 94850) ((-934 . -19) 94834) ((-934 . -631) 94818) ((-934 . -283) 94795) ((-934 . -281) 94772) ((-934 . -588) 94749) ((-934 . -598) 94710) ((-934 . -483) 94694) ((-934 . -101) 94644) ((-934 . -1074) 94594) ((-934 . -507) 94527) ((-934 . -304) 94465) ((-934 . -597) 94377) ((-934 . -1185) T) ((-934 . -34) T) ((-934 . -149) 94361) ((-934 . -827) 94340) ((-934 . -367) 94324) ((-932 . -321) 94303) ((-932 . -1014) 94199) ((-932 . -407) 94183) ((-932 . -38) 94080) ((-932 . -628) 94005) ((-932 . -707) T) ((-932 . -1085) T) ((-932 . -1032) T) ((-932 . -1025) T) ((-932 . -111) 93874) ((-932 . -1031) 93757) ((-932 . -21) T) ((-932 . -23) T) ((-932 . -1074) T) ((-932 . -597) 93739) ((-932 . -101) T) ((-932 . -25) T) ((-932 . -130) T) ((-932 . -698) 93636) ((-932 . -143) 93615) ((-932 . -145) 93594) ((-932 . -170) 93545) ((-932 . -545) 93524) ((-932 . -285) 93503) ((-932 . -47) 93482) ((-930 . -1074) T) ((-930 . -597) 93448) ((-930 . -101) T) ((-922 . -926) 93409) ((-922 . -1014) 93289) ((-922 . -1190) 93268) ((-922 . -886) 93247) ((-922 . -862) 93172) ((-922 . -876) 93153) ((-922 . -827) 93132) ((-922 . -507) 93079) ((-922 . -446) 93030) ((-922 . -621) 92978) ((-922 . -372) 92962) ((-922 . -47) 92931) ((-922 . -38) 92780) ((-922 . -698) 92629) ((-922 . -285) 92560) ((-922 . -545) 92491) ((-922 . -111) 92320) ((-922 . -1031) 92163) ((-922 . -170) 92074) ((-922 . -145) 92053) ((-922 . -143) 92032) ((-922 . -628) 91957) ((-922 . -130) T) ((-922 . -25) T) ((-922 . -101) T) ((-922 . -597) 91939) ((-922 . -1074) T) ((-922 . -23) T) ((-922 . -21) T) ((-922 . -1025) T) ((-922 . -1032) T) ((-922 . -1085) T) ((-922 . -707) T) ((-922 . -407) 91923) ((-922 . -321) 91892) ((-922 . -304) 91879) ((-922 . -598) 91740) ((-919 . -956) 91724) ((-919 . -19) 91708) ((-919 . -631) 91692) ((-919 . -283) 91669) ((-919 . -281) 91646) ((-919 . -588) 91623) ((-919 . -598) 91584) ((-919 . -483) 91568) ((-919 . -101) 91518) ((-919 . -1074) 91468) ((-919 . -507) 91401) ((-919 . -304) 91339) ((-919 . -597) 91251) ((-919 . -1185) T) ((-919 . -34) T) ((-919 . -149) 91235) ((-919 . -827) 91214) ((-919 . -367) 91198) ((-919 . -1230) 91182) ((-903 . -950) T) ((-903 . -597) 91164) ((-901 . -931) T) ((-901 . -597) 91146) ((-895 . -774) T) ((-895 . -827) T) ((-895 . -1074) T) ((-895 . -597) 91128) ((-895 . -101) T) ((-895 . -25) T) ((-895 . -707) T) ((-895 . -1085) T) ((-890 . -358) T) ((-890 . -1190) T) ((-890 . -897) T) ((-890 . -545) T) ((-890 . -170) T) ((-890 . -698) 91080) ((-890 . -38) 91032) ((-890 . -446) T) ((-890 . -302) T) ((-890 . -628) 90984) ((-890 . -707) T) ((-890 . -1085) T) ((-890 . -1032) T) ((-890 . -1025) T) ((-890 . -111) 90922) ((-890 . -1031) 90874) ((-890 . -21) T) ((-890 . -23) T) ((-890 . -1074) T) ((-890 . -597) 90856) ((-890 . -101) T) ((-890 . -25) T) ((-890 . -130) T) ((-890 . -285) T) ((-890 . -239) T) ((-882 . -345) T) ((-882 . -1124) T) ((-882 . -363) T) ((-882 . -143) T) ((-882 . -358) T) ((-882 . -1190) T) ((-882 . -897) T) ((-882 . -545) T) ((-882 . -170) T) ((-882 . -698) 90821) ((-882 . -38) 90786) ((-882 . -446) T) ((-882 . -302) T) ((-882 . -111) 90742) ((-882 . -1031) 90707) ((-882 . -628) 90672) ((-882 . -285) T) ((-882 . -239) T) ((-882 . -397) T) ((-882 . -1025) T) ((-882 . -1032) T) ((-882 . -1085) T) ((-882 . -707) T) ((-882 . -21) T) ((-882 . -23) T) ((-882 . -1074) T) ((-882 . -597) 90654) ((-882 . -101) T) ((-882 . -25) T) ((-882 . -130) T) ((-882 . -229) T) ((-882 . -324) 90641) ((-882 . -145) 90623) ((-882 . -1014) 90610) ((-882 . -1239) 90597) ((-882 . -1250) 90584) ((-882 . -598) 90566) ((-881 . -1074) T) ((-881 . -597) 90548) ((-881 . -101) T) ((-878 . -880) 90532) ((-878 . -827) 90483) ((-878 . -707) T) ((-878 . -1074) T) ((-878 . -597) 90465) ((-878 . -101) T) ((-878 . -1085) T) ((-878 . -467) T) ((-877 . -119) 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NIL) ((-847 . -827) NIL) ((-847 . -772) NIL) ((-847 . -771) NIL) ((-847 . -800) NIL) ((-847 . -862) NIL) ((-847 . -1185) T) ((-847 . -395) 88366) ((-847 . -621) 88343) ((-847 . -372) 88320) ((-847 . -281) 88271) ((-847 . -304) 88228) ((-847 . -507) 88136) ((-847 . -333) 88113) ((-847 . -239) T) ((-847 . -111) 88042) ((-847 . -1031) 87987) ((-847 . -285) T) ((-847 . -698) 87932) ((-847 . -628) 87877) ((-847 . -38) 87822) ((-847 . -302) T) ((-847 . -446) T) ((-847 . -170) T) ((-847 . -545) T) ((-847 . -897) T) ((-847 . -1190) T) ((-847 . -358) T) ((-847 . -229) NIL) ((-847 . -876) NIL) ((-847 . -227) 87799) ((-847 . -145) T) ((-847 . -143) NIL) ((-847 . -130) T) ((-847 . -25) T) ((-847 . -101) T) ((-847 . -597) 87781) ((-847 . -1074) T) ((-847 . -23) T) ((-847 . -21) T) ((-847 . -1025) T) ((-847 . -1032) T) ((-847 . -1085) T) ((-847 . -707) T) ((-845 . -846) 87765) ((-845 . -897) T) ((-845 . -545) T) ((-845 . -285) T) ((-845 . -170) T) ((-845 . -698) 87752) ((-845 . -1031) 87739) ((-845 . -111) 87724) ((-845 . -38) 87711) ((-845 . -446) T) ((-845 . -302) T) ((-845 . -1025) T) ((-845 . -1032) T) ((-845 . -1085) T) ((-845 . -707) T) ((-845 . -21) T) ((-845 . -23) T) ((-845 . -1074) T) ((-845 . -597) 87693) ((-845 . -101) T) ((-845 . -25) T) ((-845 . -130) T) ((-845 . -628) 87680) ((-845 . -145) T) ((-842 . -1025) T) ((-842 . -1032) T) ((-842 . -1085) T) ((-842 . -707) T) ((-842 . -21) T) ((-842 . -23) T) ((-842 . -1074) T) ((-842 . -597) 87662) ((-842 . -101) T) ((-842 . -25) T) ((-842 . -130) T) ((-842 . -628) 87622) ((-842 . -38) 87592) ((-842 . -111) 87557) ((-842 . -1031) 87527) ((-842 . -698) 87497) ((-841 . -821) T) ((-841 . -827) T) ((-841 . -1074) T) ((-841 . -597) 87479) ((-841 . -101) T) ((-841 . -363) T) ((-841 . -598) 87401) ((-840 . -1074) T) ((-840 . -597) 87383) ((-840 . -101) T) ((-839 . -838) T) ((-839 . -171) T) ((-839 . -597) 87365) ((-835 . -827) T) ((-835 . -101) T) ((-835 . -597) 87347) ((-835 . -1074) T) ((-832 . -829) 87331) ((-832 . -1014) 87227) ((-832 . -407) 87211) ((-832 . -698) 87181) ((-832 . -628) 87155) ((-832 . -130) T) ((-832 . -25) T) ((-832 . -101) T) ((-832 . -597) 87137) ((-832 . -1074) T) ((-832 . -23) T) ((-832 . -21) T) ((-832 . -1031) 87121) ((-832 . -111) 87100) ((-832 . -1025) T) ((-832 . -1032) T) ((-832 . -1085) T) ((-832 . -707) T) ((-832 . -38) 87070) ((-831 . -829) 87054) ((-831 . -1014) 86950) ((-831 . -407) 86934) ((-831 . -698) 86904) ((-831 . -628) 86878) ((-831 . -130) T) ((-831 . -25) T) ((-831 . -101) T) ((-831 . -597) 86860) ((-831 . -1074) T) ((-831 . -23) T) ((-831 . -21) T) ((-831 . -1031) 86844) ((-831 . -111) 86823) ((-831 . -1025) T) ((-831 . -1032) T) ((-831 . -1085) T) ((-831 . -707) T) ((-831 . -38) 86793) ((-819 . -1074) T) ((-819 . -597) 86775) ((-819 . -101) T) ((-819 . -407) 86759) ((-819 . -1014) 86655) ((-819 . -21) 86607) ((-819 . -23) 86559) ((-819 . -25) 86511) ((-819 . -130) 86463) ((-819 . -825) 86442) ((-819 . -628) 86415) ((-819 . -1032) 86394) ((-819 . -1025) 86373) 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85406) ((-812 . -1085) 85385) ((-812 . -707) 85364) ((-808 . -689) 85348) ((-808 . -698) 85318) ((-808 . -628) 85292) ((-808 . -130) T) ((-808 . -25) T) ((-808 . -101) T) ((-808 . -597) 85274) ((-808 . -1074) T) ((-808 . -23) T) ((-808 . -21) T) ((-808 . -1031) 85258) ((-808 . -111) 85237) ((-808 . -1025) T) ((-808 . -1032) T) ((-808 . -1085) T) ((-808 . -707) T) ((-808 . -38) 85207) ((-808 . -229) 85186) ((-806 . -1074) T) ((-806 . -597) 85168) ((-806 . -101) T) ((-805 . -1074) T) ((-805 . -597) 85150) ((-805 . -101) T) ((-804 . -1074) T) ((-804 . -597) 85132) ((-804 . -101) T) ((-799 . -823) T) ((-799 . -827) T) ((-799 . -834) T) ((-799 . -1085) T) ((-799 . -101) T) ((-799 . -597) 85114) ((-799 . -1074) T) ((-799 . -707) T) ((-799 . -1014) 85098) ((-798 . -261) 85082) ((-798 . -1014) 85066) ((-798 . -1074) T) ((-798 . -597) 85048) ((-798 . -101) T) ((-798 . -827) T) ((-797 . -111) 84990) ((-797 . -1031) 84941) ((-797 . -21) T) ((-797 . -23) T) ((-797 . -1074) T) ((-797 . -597) 84923) 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74925) ((-717 . -483) 74909) ((-717 . -101) T) ((-717 . -1074) T) ((-717 . -507) 74842) ((-717 . -304) 74780) ((-717 . -597) 74762) ((-717 . -1185) T) ((-717 . -34) T) ((-717 . -106) 74746) ((-717 . -675) 74730) ((-716 . -1025) T) ((-716 . -1032) T) ((-716 . -1085) T) ((-716 . -707) T) ((-716 . -21) T) ((-716 . -23) T) ((-716 . -1074) T) ((-716 . -597) 74712) ((-716 . -101) T) ((-716 . -25) T) ((-716 . -130) T) ((-716 . -628) 74672) ((-716 . -1014) 74643) ((-716 . -145) 74622) ((-716 . -143) 74601) ((-716 . -38) 74571) ((-716 . -111) 74536) ((-716 . -1031) 74506) ((-716 . -698) 74476) ((-716 . -363) 74429) ((-712 . -926) 74382) ((-712 . -1014) 74258) ((-712 . -1190) 74237) ((-712 . -886) 74216) ((-712 . -862) NIL) ((-712 . -876) 74193) ((-712 . -827) 74172) ((-712 . -507) 74115) ((-712 . -446) 74066) ((-712 . -621) 74014) ((-712 . -372) 73998) ((-712 . -47) 73963) ((-712 . -38) 73812) ((-712 . -698) 73661) ((-712 . -285) 73592) ((-712 . -545) 73523) ((-712 . -111) 73352) ((-712 . 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. -1032) T) ((-166 . -1085) T) ((-166 . -707) T) ((-166 . -21) T) ((-166 . -23) T) ((-166 . -1074) T) ((-166 . -597) 8583) ((-166 . -101) T) ((-166 . -25) T) ((-166 . -130) T) ((-166 . -143) 8534) ((-166 . -801) 8513) ((-160 . -1056) T) ((-160 . -597) 8479) ((-160 . -1074) T) ((-160 . -101) T) ((-160 . -92) T) ((-159 . -1074) T) ((-159 . -597) 8461) ((-159 . -101) T) ((-155 . -25) T) ((-155 . -101) T) ((-155 . -597) 8443) ((-155 . -1074) T) ((-154 . -1056) T) ((-154 . -597) 8409) ((-154 . -1074) T) ((-154 . -101) T) ((-154 . -92) T) ((-152 . -1056) T) ((-152 . -597) 8375) ((-152 . -1074) T) ((-152 . -101) T) ((-152 . -92) T) ((-150 . -1025) T) ((-150 . -1032) T) ((-150 . -1085) T) ((-150 . -707) T) ((-150 . -21) T) ((-150 . -23) T) ((-150 . -1074) T) ((-150 . -597) 8357) ((-150 . -101) T) ((-150 . -25) T) ((-150 . -130) T) ((-150 . -628) 8331) ((-150 . -38) 8315) ((-150 . -111) 8294) ((-150 . -1031) 8278) ((-150 . -698) 8262) ((-150 . -1239) 8246) ((-142 . -821) T) ((-142 . -827) T) 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122960) ((-814 . -628) 122920) ((-807 . -628) 122894) ((-314 . -25) T) ((-314 . -21) T) ((-638 . -281) 122873) ((-566 . -1073) T) ((-552 . -1073) T) ((-488 . -1073) T) ((-241 . -283) 122850) ((-308 . -227) 122811) ((-1145 . -862) NIL) ((-1098 . -862) 122670) ((-129 . -827) T) ((-1145 . -1014) 122550) ((-1098 . -1014) 122433) ((-181 . -597) 122415) ((-831 . -1014) 122311) ((-762 . -281) 122238) ((-797 . -1085) T) ((-1010 . -707) T) ((-586 . -631) 122222) ((-1022 . -952) 122151) ((-975 . -101) T) ((-797 . -23) T) ((-693 . -1124) 122129) ((-674 . -1032) T) ((-586 . -368) 122113) ((-346 . -446) T) ((-338 . -285) T) ((-1233 . -1073) T) ((-244 . -1073) T) ((-394 . -101) T) ((-284 . -21) T) ((-284 . -25) T) ((-356 . -707) T) ((-691 . -1073) T) ((-679 . -1073) T) ((-356 . -467) T) ((-1180 . -597) 122095) ((-1145 . -372) 122079) ((-1098 . -372) 122063) ((-1000 . -406) 122025) ((-139 . -225) 122007) ((-374 . -774) T) ((-374 . -771) T) ((-846 . -170) T) ((-374 . -707) T) ((-692 . -597) 121989) 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T) ((-213 . -1190) T) ((-975 . -304) 121007) ((-221 . -1014) 120967) ((-40 . -285) T) ((-1053 . -21) T) ((-1053 . -25) T) ((-1093 . -808) T) ((-481 . -544) T) ((-354 . -25) T) ((-213 . -544) T) ((-354 . -21) T) ((-348 . -25) T) ((-348 . -21) T) ((-695 . -628) 120927) ((-340 . -25) T) ((-340 . -21) T) ((-107 . -25) T) ((-107 . -21) T) ((-48 . -1032) T) ((-566 . -170) T) ((-552 . -170) T) ((-488 . -170) T) ((-638 . -597) 120909) ((-718 . -717) 120893) ((-331 . -597) 120875) ((-67 . -378) T) ((-67 . -390) T) ((-1075 . -106) 120859) ((-1036 . -862) 120841) ((-928 . -862) 120766) ((-633 . -1085) T) ((-605 . -698) 120753) ((-475 . -862) NIL) ((-1119 . -101) T) ((-1036 . -1014) 120735) ((-96 . -597) 120717) ((-471 . -145) T) ((-928 . -1014) 120597) ((-117 . -698) 120542) ((-633 . -23) T) ((-475 . -1014) 120418) ((-1060 . -598) NIL) ((-1060 . -597) 120400) ((-762 . -598) NIL) ((-762 . -597) 120361) ((-760 . -598) 119995) ((-760 . -597) 119909) ((-1086 . -621) 119815) ((-455 . -597) 119797) 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T) ((-1232 . -507) 117725) ((-1216 . -628) 117622) ((-1195 . -628) 117492) ((-848 . -774) 117471) ((-848 . -771) 117450) ((-848 . -707) T) ((-481 . -23) T) ((-219 . -597) 117432) ((-172 . -446) T) ((-218 . -304) 117370) ((-85 . -435) T) ((-85 . -390) T) ((-213 . -23) T) ((-1256 . -1249) 117349) ((-566 . -285) T) ((-552 . -285) T) ((-657 . -1014) 117333) ((-488 . -285) T) ((-135 . -464) 117288) ((-48 . -1073) T) ((-693 . -227) 117272) ((-847 . -876) NIL) ((-1205 . -862) NIL) ((-865 . -101) T) ((-861 . -101) T) ((-383 . -1073) T) ((-167 . -372) 117256) ((-167 . -333) 117240) ((-1205 . -1014) 117120) ((-832 . -1014) 117016) ((-1115 . -101) T) ((-633 . -130) T) ((-117 . -507) 116924) ((-642 . -772) 116903) ((-642 . -775) 116882) ((-559 . -1014) 116864) ((-289 . -1239) 116834) ((-842 . -101) T) ((-939 . -544) 116813) ((-1180 . -1031) 116696) ((-476 . -621) 116602) ((-880 . -1073) T) ((-1000 . -698) 116539) ((-692 . -1031) 116504) ((-600 . -101) T) ((-586 . -34) T) ((-1120 . -1186) T) 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T) ((-1067 . -1186) T) ((-246 . -1085) 99721) ((-245 . -1085) 99631) ((-1000 . -1025) T) ((-979 . -1032) T) ((-338 . -628) 99576) ((-603 . -38) 99560) ((-1245 . -597) 99522) ((-1245 . -598) 99483) ((-1050 . -597) 99465) ((-1000 . -239) T) ((-349 . -1025) T) ((-795 . -1239) 99435) ((-246 . -23) T) ((-245 . -23) T) ((-963 . -597) 99417) ((-718 . -598) 99378) ((-718 . -597) 99360) ((-779 . -827) 99339) ((-975 . -507) 99251) ((-349 . -229) T) ((-349 . -239) T) ((-1132 . -149) 99198) ((-980 . -25) T) ((-139 . -598) 99157) ((-139 . -597) 99139) ((-886 . -302) T) ((-980 . -21) T) ((-947 . -25) T) ((-890 . -21) T) ((-890 . -25) T) ((-422 . -21) T) ((-422 . -25) T) ((-820 . -406) 99123) ((-48 . -1025) T) ((-1254 . -1246) 99107) ((-1252 . -1246) 99091) ((-1011 . -588) 99066) ((-311 . -598) 98927) ((-311 . -597) 98909) ((-308 . -598) NIL) ((-308 . -597) 98891) ((-48 . -239) T) ((-48 . -229) T) ((-634 . -281) 98852) ((-538 . -231) 98802) ((-135 . -597) 98784) ((-114 . -597) 98766) ((-471 . -38) 98731) ((-1256 . -1253) 98710) ((-1247 . -130) T) ((-1255 . -1032) T) ((-1055 . -101) T) ((-87 . -1186) T) ((-493 . -304) NIL) ((-976 . -106) 98694) ((-865 . -1073) T) ((-861 . -1073) T) ((-1232 . -631) 98678) ((-1232 . -368) 98662) ((-322 . -1186) T) ((-578 . -827) T) ((-1115 . -1073) T) ((-1115 . -1028) 98602) ((-102 . -507) 98535) ((-903 . -597) 98517) ((-338 . -707) T) ((-30 . -597) 98499) ((-842 . -1073) T) ((-820 . -1032) 98478) ((-40 . -628) 98423) ((-221 . -1190) T) ((-402 . -1032) T) ((-1131 . -149) 98405) ((-975 . -285) 98356) ((-600 . -1073) T) ((-221 . -544) T) ((-314 . -1213) 98340) ((-314 . -1210) 98310) ((-1159 . -1162) 98289) ((-1048 . -597) 98271) ((-627 . -149) 98255) ((-614 . -149) 98201) ((-1159 . -106) 98151) ((-473 . -1162) 98130) ((-481 . -145) T) ((-481 . -143) NIL) ((-1093 . -598) 98045) ((-433 . -597) 98027) ((-213 . -145) T) ((-213 . -143) NIL) ((-1093 . -597) 98009) ((-129 . -101) T) ((-52 . -101) T) ((-1196 . -621) 97961) ((-473 . -106) 97911) ((-969 . -23) T) ((-1256 . -38) 97881) ((-1145 . -1085) T) ((-1098 . -1085) T) ((-1036 . -1190) T) ((-306 . -101) T) ((-831 . -1085) T) ((-928 . -1190) 97860) ((-475 . -1190) 97839) ((-712 . -827) 97818) ((-1036 . -544) T) ((-928 . -544) 97749) ((-1145 . -23) T) ((-1098 . -23) T) ((-831 . -23) T) ((-475 . -544) 97680) ((-1115 . -698) 97612) ((-1119 . -507) 97545) ((-1011 . -598) NIL) ((-1011 . -597) 97527) ((-95 . -1056) T) ((-842 . -698) 97497) ((-1180 . -47) 97466) ((-246 . -130) T) ((-245 . -130) T) ((-1077 . -1073) T) ((-979 . -1073) T) ((-61 . -597) 97448) ((-1140 . -827) NIL) ((-1000 . -772) T) ((-1000 . -775) T) ((-1260 . -1031) 97435) ((-1260 . -111) 97420) ((-846 . -628) 97407) ((-1224 . -25) T) ((-1224 . -21) T) ((-1217 . -21) T) ((-1217 . -25) T) ((-1196 . -21) T) ((-1196 . -25) T) ((-1003 . -149) 97391) ((-848 . -800) 97370) ((-848 . -896) T) ((-693 . -281) 97297) ((-581 . -21) T) ((-581 . -25) T) ((-580 . -21) T) ((-40 . -707) T) ((-218 . -507) 97230) ((-580 . -25) T) ((-470 . -149) 97214) ((-457 . -149) 97198) ((-897 . -774) T) ((-897 . -707) T) ((-751 . -773) T) ((-751 . -774) T) ((-499 . -1073) T) ((-495 . -1073) T) ((-751 . -707) T) ((-221 . -358) T) ((-1129 . -1073) 97176) ((-847 . -1190) T) ((-634 . -597) 97158) ((-847 . -544) T) ((-674 . -363) NIL) ((-354 . -1239) 97142) ((-650 . -101) T) ((-348 . -1239) 97126) ((-340 . -1239) 97110) ((-1255 . -1073) T) ((-513 . -827) 97089) ((-797 . -446) 97068) ((-1022 . -1073) T) ((-1022 . -1045) 96997) ((-1003 . -952) 96966) ((-799 . -1085) T) ((-979 . -698) 96911) ((-381 . -1085) T) ((-470 . -952) 96880) ((-457 . -952) 96849) ((-110 . -149) 96831) ((-72 . -597) 96813) ((-869 . -597) 96795) ((-1053 . -705) 96774) ((-1260 . -1025) T) ((-796 . -621) 96722) ((-289 . -1032) 96664) ((-167 . -1190) 96569) ((-221 . -1085) T) ((-319 . -23) T) ((-1140 . -968) 96521) ((-820 . -1073) T) ((-1099 . -721) 96500) ((-1218 . -1031) 96405) ((-1216 . -896) 96384) ((-846 . -707) T) ((-167 . -544) 96295) ((-1195 . -896) 96274) ((-566 . -628) 96261) ((-402 . -1073) T) ((-552 . -628) 96248) ((-258 . -1073) T) ((-488 . -628) 96213) ((-221 . -23) T) ((-1195 . -800) 96166) ((-1254 . -101) T) ((-349 . -1251) 96143) ((-1252 . -101) T) ((-1218 . -111) 96035) ((-142 . -597) 96017) ((-969 . -130) T) ((-44 . -101) T) ((-236 . -827) 95968) ((-1205 . -1190) 95947) ((-102 . -483) 95931) ((-1255 . -698) 95901) ((-1060 . -47) 95862) ((-1036 . -1085) T) ((-928 . -1085) T) ((-127 . -34) T) ((-121 . -34) T) ((-762 . -47) 95839) ((-760 . -47) 95811) ((-1205 . -544) 95722) ((-349 . -363) T) ((-475 . -1085) T) ((-1145 . -130) T) ((-1098 . -130) T) ((-448 . -47) 95701) ((-847 . -358) T) ((-831 . -130) T) ((-150 . -101) T) ((-1036 . -23) T) ((-928 . -23) T) ((-559 . -544) T) ((-796 . -25) T) ((-796 . -21) T) ((-1115 . -507) 95634) ((-577 . -1056) T) ((-571 . -1014) 95618) ((-475 . -23) T) ((-346 . -1032) T) ((-1180 . -876) 95599) ((-650 . -304) 95537) ((-1086 . -1239) 95507) ((-679 . -628) 95472) ((-979 . -170) T) ((-939 . -143) 95451) 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. -1014) 93747) ((-117 . -628) 93692) ((-448 . -1014) 93568) ((-629 . -1014) 93552) ((-609 . -101) T) ((-218 . -483) 93536) ((-1232 . -34) T) ((-617 . -698) 93520) ((-591 . -698) 93504) ((-650 . -38) 93464) ((-314 . -101) T) ((-84 . -597) 93446) ((-50 . -1014) 93430) ((-1093 . -1031) 93417) ((-1060 . -372) 93401) ((-762 . -372) 93385) ((-59 . -56) 93347) ((-679 . -774) T) ((-679 . -771) T) ((-567 . -1014) 93334) ((-511 . -1014) 93311) ((-679 . -707) T) ((-319 . -130) T) ((-311 . -1025) 93201) ((-308 . -1025) T) ((-167 . -1085) T) ((-760 . -372) 93185) ((-45 . -149) 93135) ((-980 . -968) 93117) ((-448 . -372) 93101) ((-402 . -170) T) ((-311 . -239) 93080) ((-308 . -239) T) ((-308 . -229) NIL) ((-289 . -1073) 92862) ((-221 . -130) T) ((-1093 . -111) 92847) ((-167 . -23) T) ((-779 . -145) 92826) ((-779 . -143) 92805) ((-246 . -621) 92711) ((-245 . -621) 92617) ((-314 . -279) 92583) ((-1129 . -507) 92516) ((-1106 . -1073) T) ((-221 . -1034) T) ((-795 . -304) 92454) ((-1060 . -876) 92389) 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-598) 91718) ((-975 . -597) 91700) ((-965 . -597) 91682) ((-116 . -1032) T) ((-634 . -1031) 91666) ((-221 . -486) T) ((-394 . -597) 91648) ((-394 . -598) 91625) ((-1029 . -1239) 91595) ((-634 . -111) 91574) ((-1115 . -483) 91558) ((-795 . -38) 91528) ((-62 . -435) T) ((-62 . -390) T) ((-1132 . -101) T) ((-847 . -130) T) ((-478 . -101) 91506) ((-1260 . -363) T) ((-1053 . -101) T) ((-1035 . -101) T) ((-346 . -698) 91451) ((-712 . -145) 91430) ((-712 . -143) 91409) ((-1000 . -628) 91346) ((-516 . -1073) 91324) ((-354 . -101) T) ((-348 . -101) T) ((-340 . -101) T) ((-107 . -101) T) ((-497 . -1073) T) ((-349 . -628) 91269) ((-1145 . -621) 91217) ((-1098 . -621) 91165) ((-380 . -502) 91144) ((-813 . -825) 91123) ((-374 . -1190) T) ((-674 . -707) T) ((-334 . -1032) T) ((-1196 . -968) 91075) ((-172 . -1032) T) ((-102 . -597) 91007) ((-1147 . -143) 90986) ((-1147 . -145) 90965) ((-374 . -544) T) ((-1146 . -145) 90944) ((-1146 . -143) 90923) ((-1140 . -143) 90830) ((-402 . -285) T) ((-1140 . -145) 90737) ((-1099 . -145) 90716) ((-1099 . -143) 90695) ((-314 . -38) 90536) ((-167 . -130) T) ((-308 . -775) NIL) ((-308 . -772) NIL) ((-634 . -1025) T) ((-48 . -628) 90501) ((-1139 . -101) T) ((-970 . -101) T) ((-969 . -21) T) ((-127 . -986) 90485) ((-121 . -986) 90469) ((-969 . -25) T) ((-877 . -119) 90453) ((-1131 . -101) T) ((-796 . -827) 90432) ((-1205 . -130) T) ((-1145 . -25) T) ((-1145 . -21) T) ((-832 . -130) T) ((-1098 . -25) T) ((-1098 . -21) T) ((-831 . -25) T) ((-831 . -21) T) ((-762 . -302) 90411) ((-627 . -101) 90389) ((-614 . -101) T) ((-1132 . -304) 90184) ((-559 . -130) T) ((-603 . -825) 90163) ((-1129 . -483) 90147) ((-1123 . -149) 90097) ((-1119 . -597) 90059) ((-1119 . -598) 90020) ((-1000 . -771) T) ((-1000 . -774) T) ((-1000 . -707) T) ((-478 . -304) 89958) ((-447 . -412) 89928) ((-346 . -170) T) ((-284 . -38) 89915) ((-269 . -101) T) ((-268 . -101) T) ((-267 . -101) T) ((-266 . -101) T) ((-265 . -101) T) ((-264 . -101) T) ((-263 . -101) T) ((-338 . -1014) 89892) ((-208 . -101) T) ((-207 . -101) T) ((-205 . -101) T) ((-204 . -101) T) ((-203 . -101) T) ((-202 . -101) T) ((-199 . -101) T) ((-198 . -101) T) ((-693 . -1031) 89715) ((-197 . -101) T) ((-196 . -101) T) ((-195 . -101) T) ((-194 . -101) T) ((-193 . -101) T) ((-192 . -101) T) ((-191 . -101) T) ((-190 . -101) T) ((-189 . -101) T) ((-349 . -707) T) ((-693 . -111) 89524) ((-650 . -227) 89508) ((-567 . -302) T) ((-511 . -302) T) ((-289 . -507) 89457) ((-107 . -304) NIL) ((-71 . -390) T) ((-1086 . -101) 89247) ((-813 . -406) 89231) ((-1093 . -775) T) ((-1093 . -772) T) ((-681 . -1073) T) ((-565 . -597) 89213) ((-374 . -358) T) ((-167 . -486) 89191) ((-209 . -1073) T) ((-218 . -597) 89123) ((-133 . -1073) T) ((-116 . -1073) T) ((-48 . -707) T) ((-1022 . -483) 89088) ((-499 . -92) T) ((-139 . -420) 89070) ((-139 . -363) T) ((-1003 . -101) T) ((-505 . -502) 89049) ((-470 . -101) T) ((-457 . -101) T) ((-1010 . -1085) T) ((-1147 . -35) 89015) ((-1147 . -94) 88981) ((-1147 . -1174) 88947) 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-38) 87681) ((-348 . -38) 87646) ((-340 . -38) 87611) ((-79 . -435) T) ((-79 . -390) T) ((-221 . -25) T) ((-221 . -21) T) ((-814 . -1085) T) ((-107 . -38) 87561) ((-807 . -1085) T) ((-754 . -1073) T) ((-116 . -698) 87548) ((-652 . -1014) 87532) ((-596 . -101) T) ((-814 . -23) T) ((-807 . -23) T) ((-1129 . -281) 87509) ((-1086 . -304) 87447) ((-1075 . -231) 87431) ((-63 . -391) T) ((-63 . -390) T) ((-110 . -101) T) ((-40 . -372) 87408) ((-95 . -101) T) ((-633 . -829) 87392) ((-1108 . -1056) T) ((-1036 . -21) T) ((-1036 . -25) T) ((-795 . -227) 87361) ((-928 . -25) T) ((-928 . -21) T) ((-603 . -1032) T) ((-475 . -25) T) ((-475 . -21) T) ((-1003 . -304) 87299) ((-865 . -597) 87281) ((-861 . -597) 87263) ((-246 . -827) 87214) ((-245 . -827) 87165) ((-516 . -507) 87098) ((-847 . -621) 87075) ((-470 . -304) 87013) ((-457 . -304) 86951) ((-346 . -285) T) ((-1129 . -1220) 86935) ((-1115 . -597) 86897) ((-1115 . -598) 86858) ((-1113 . -101) T) ((-975 . -1031) 86754) ((-40 . -876) 86706) ((-1129 . -588) 86683) ((-1260 . -628) 86670) ((-1037 . -149) 86616) ((-848 . -1190) T) ((-975 . -111) 86498) ((-334 . -698) 86482) ((-842 . -597) 86464) ((-172 . -698) 86396) ((-402 . -281) 86354) ((-848 . -544) T) ((-107 . -395) 86336) ((-83 . -379) T) ((-83 . -390) T) ((-681 . -170) T) ((-600 . -597) 86318) ((-98 . -707) T) ((-476 . -101) 86108) ((-98 . -467) T) ((-116 . -170) T) ((-1086 . -38) 86078) ((-167 . -621) 86026) ((-1029 . -101) T) ((-847 . -25) T) ((-795 . -234) 86005) ((-847 . -21) T) ((-798 . -101) T) ((-409 . -101) T) ((-380 . -101) T) ((-110 . -304) NIL) ((-223 . -101) 85983) ((-127 . -1186) T) ((-121 . -1186) T) ((-1010 . -130) T) ((-650 . -362) 85967) ((-975 . -1025) T) ((-1205 . -621) 85915) ((-1077 . -597) 85897) ((-979 . -597) 85879) ((-508 . -23) T) ((-503 . -23) T) ((-338 . -302) T) ((-501 . -23) T) ((-317 . -130) T) ((-3 . -1073) T) ((-979 . -598) 85863) ((-975 . -239) 85842) ((-975 . -229) 85821) ((-1260 . -707) T) ((-1224 . -143) 85800) ((-813 . -1073) T) ((-1224 . -145) 85779) ((-1217 . -145) 85758) ((-1217 . -143) 85737) ((-1216 . -1190) 85716) ((-1196 . -143) 85623) ((-1196 . -145) 85530) ((-1195 . -1190) 85509) ((-374 . -130) T) ((-552 . -862) 85491) ((0 . -1073) T) ((-172 . -170) T) ((-167 . -21) T) ((-167 . -25) T) ((-49 . -1073) T) ((-1218 . -628) 85396) ((-1216 . -544) 85347) ((-695 . -1085) T) ((-1195 . -544) 85298) ((-552 . -1014) 85280) ((-580 . -145) 85259) ((-580 . -143) 85238) ((-488 . -1014) 85181) ((-1108 . -1110) T) ((-86 . -379) T) ((-86 . -390) T) ((-848 . -358) T) ((-814 . -130) T) ((-807 . -130) T) ((-695 . -23) T) ((-499 . -597) 85131) ((-495 . -597) 85113) ((-1256 . -1032) T) ((-374 . -1034) T) ((-1002 . -1073) 85091) ((-877 . -34) T) ((-476 . -304) 85029) ((-577 . -101) T) ((-1129 . -598) 84990) ((-1129 . -597) 84922) ((-1145 . -827) 84901) ((-45 . -101) T) ((-1098 . -827) 84880) ((-797 . -101) T) ((-1205 . -25) T) ((-1205 . -21) T) ((-832 . -25) T) ((-44 . -362) 84864) ((-832 . -21) T) ((-712 . -446) 84815) ((-1255 . -597) 84797) ((-1029 . -304) 84735) ((-651 . -1056) T) ((-590 . -1056) T) ((-385 . -1073) T) ((-559 . -25) T) ((-559 . -21) T) ((-178 . -1056) T) ((-159 . -1056) T) ((-154 . -1056) T) ((-152 . -1056) T) ((-603 . -1073) T) ((-679 . -862) 84717) ((-1232 . -1186) T) ((-223 . -304) 84655) ((-142 . -363) T) ((-1022 . -598) 84597) ((-1022 . -597) 84540) ((-308 . -885) NIL) ((-679 . -1014) 84485) ((-692 . -896) T) ((-468 . -1190) 84464) ((-1146 . -446) 84443) ((-1140 . -446) 84422) ((-325 . -101) T) ((-848 . -1085) T) ((-311 . -628) 84243) ((-308 . -628) 84172) ((-468 . -544) 84123) ((-334 . -507) 84089) ((-538 . -149) 84039) ((-40 . -302) T) ((-820 . -597) 84021) ((-681 . -285) T) ((-848 . -23) T) ((-374 . -486) T) ((-1053 . -227) 83991) ((-505 . -101) T) ((-402 . -598) 83799) ((-402 . -597) 83781) ((-258 . -597) 83763) ((-116 . -285) T) ((-1218 . -707) T) ((-1216 . -358) 83742) ((-1195 . -358) 83721) ((-1245 . -34) T) ((-117 . -1186) T) ((-107 . -227) 83703) ((-1151 . -101) T) ((-471 . -1073) T) ((-516 . -483) 83687) ((-718 . -34) T) ((-476 . -38) 83657) ((-139 . -34) T) ((-117 . -860) 83634) ((-117 . -862) NIL) ((-605 . -1014) 83517) ((-625 . -827) 83496) ((-1244 . -101) T) ((-290 . -101) T) ((-693 . -363) 83475) ((-117 . -1014) 83452) ((-385 . -698) 83436) ((-603 . -698) 83420) ((-45 . -304) 83224) ((-796 . -143) 83203) ((-796 . -145) 83182) ((-1255 . -377) 83161) ((-799 . -827) T) ((-1234 . -1073) T) ((-1132 . -225) 83108) ((-381 . -827) 83087) ((-1224 . -1174) 83053) ((-1224 . -1171) 83019) ((-1217 . -1171) 82985) ((-508 . -130) T) ((-1217 . -1174) 82951) ((-1196 . -1171) 82917) ((-1196 . -1174) 82883) ((-1224 . -35) 82849) ((-1224 . -94) 82815) ((-617 . -597) 82784) ((-591 . -597) 82753) ((-221 . -827) T) ((-1217 . -94) 82719) ((-1217 . -35) 82685) ((-1216 . -1085) T) ((-1093 . -628) 82672) ((-1196 . -94) 82638) ((-1195 . -1085) T) ((-578 . -149) 82620) ((-1053 . -344) 82599) ((-172 . -285) T) ((-117 . -372) 82576) ((-117 . -333) 82553) ((-1196 . -35) 82519) 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-25) T) ((-807 . -21) T) ((-1254 . -1032) T) ((-1252 . -1032) T) ((-634 . -707) T) ((-1255 . -1031) 79844) ((-1205 . -827) 79823) ((-795 . -406) 79792) ((-102 . -119) 79776) ((-129 . -1073) T) ((-52 . -1073) T) ((-902 . -597) 79758) ((-847 . -968) 79735) ((-803 . -101) T) ((-1255 . -111) 79714) ((-633 . -38) 79684) ((-559 . -827) T) ((-350 . -1085) T) ((-347 . -1085) T) ((-339 . -1085) T) ((-259 . -1085) T) ((-243 . -1085) T) ((-605 . -302) 79663) ((-1123 . -304) 79467) ((-517 . -1056) T) ((-306 . -1073) T) ((-644 . -23) T) ((-476 . -227) 79436) ((-150 . -1032) T) ((-350 . -23) T) ((-347 . -23) T) ((-339 . -23) T) ((-117 . -302) T) ((-259 . -23) T) ((-243 . -23) T) ((-979 . -1025) T) ((-693 . -885) 79415) ((-979 . -229) 79387) ((-979 . -239) T) ((-117 . -998) NIL) ((-886 . -1085) T) ((-1217 . -446) 79366) ((-1196 . -446) 79345) ((-516 . -597) 79277) ((-693 . -628) 79202) ((-402 . -1031) 79154) ((-497 . -597) 79136) ((-886 . -23) T) ((-481 . -304) NIL) ((-468 . -130) T) ((-213 . -304) NIL) ((-402 . -111) 79074) ((-795 . -1032) 79004) ((-718 . -1071) 78988) ((-1216 . -486) 78954) ((-1195 . -486) 78920) ((-471 . -285) T) ((-139 . -1071) 78902) ((-128 . -149) 78884) ((-1255 . -1025) T) ((-1037 . -101) T) ((-493 . -507) NIL) ((-683 . -101) T) ((-476 . -234) 78863) ((-1145 . -143) 78842) ((-1145 . -145) 78821) ((-1098 . -145) 78800) ((-1098 . -143) 78779) ((-617 . -1031) 78763) ((-591 . -1031) 78747) ((-650 . -1073) T) ((-650 . -1028) 78687) ((-1147 . -1223) 78671) ((-1147 . -1210) 78648) ((-481 . -1124) T) ((-1146 . -1215) 78609) ((-1146 . -1210) 78579) ((-1146 . -1213) 78563) ((-213 . -1124) T) ((-338 . -896) T) ((-798 . -261) 78547) ((-617 . -111) 78526) ((-591 . -111) 78505) ((-1140 . -1194) 78466) ((-820 . -1025) 78445) ((-1140 . -1210) 78422) ((-508 . -25) T) ((-488 . -297) T) ((-504 . -23) T) ((-503 . -25) T) ((-501 . -25) T) ((-500 . -23) T) ((-1140 . -1192) 78406) ((-402 . -1025) T) ((-314 . -1032) T) ((-674 . -302) T) ((-107 . -825) T) ((-402 . -239) T) ((-402 . -229) 78385) ((-693 . -707) T) ((-481 . -38) 78335) ((-213 . -38) 78285) ((-468 . -486) 78251) ((-1131 . -1117) T) ((-1074 . -101) T) ((-681 . -597) 78233) ((-681 . -598) 78148) ((-695 . -21) T) ((-695 . -25) T) ((-1108 . -101) T) ((-209 . -597) 78130) ((-133 . -597) 78112) ((-116 . -597) 78094) ((-155 . -25) T) ((-1254 . -1073) T) ((-848 . -621) 78042) ((-1252 . -1073) T) ((-939 . -101) T) ((-716 . -101) T) ((-696 . -101) T) ((-447 . -101) T) ((-796 . -446) 77993) ((-44 . -1073) T) ((-1061 . -827) T) ((-644 . -130) T) ((-1037 . -304) 77844) ((-650 . -698) 77828) ((-284 . -1032) T) ((-350 . -130) T) ((-347 . -130) T) ((-339 . -130) T) ((-259 . -130) T) ((-243 . -130) T) ((-413 . -101) T) ((-150 . -1073) T) ((-45 . -225) 77778) ((-934 . -827) 77757) ((-975 . -628) 77695) ((-236 . -1239) 77665) ((-1000 . -302) T) ((-289 . -1031) 77586) ((-886 . -130) T) ((-40 . -896) T) ((-481 . -395) 77568) ((-349 . -302) T) ((-213 . -395) 77550) ((-1053 . -406) 77534) ((-289 . -111) 77450) ((-848 . -25) T) ((-848 . -21) T) ((-334 . -597) 77432) ((-1218 . -47) 77376) ((-221 . -145) T) ((-172 . -597) 77358) ((-1086 . -825) 77337) ((-754 . -597) 77319) ((-592 . -231) 77266) ((-469 . -231) 77216) ((-1254 . -698) 77186) ((-48 . -302) T) ((-1252 . -698) 77156) ((-940 . -1073) T) ((-795 . -1073) 76946) ((-307 . -101) T) ((-877 . -1186) T) ((-48 . -998) T) ((-1195 . -621) 76854) ((-669 . -101) 76832) ((-44 . -698) 76816) ((-538 . -101) T) ((-66 . -378) T) ((-66 . -390) T) ((-642 . -23) T) ((-650 . -742) T) ((-1183 . -1073) 76794) ((-346 . -1031) 76739) ((-655 . -1073) 76717) ((-1036 . -145) T) ((-928 . -145) 76696) ((-928 . -143) 76675) ((-779 . -101) T) ((-150 . -698) 76659) ((-475 . -145) 76638) ((-475 . -143) 76617) ((-346 . -111) 76546) ((-1053 . -1032) T) ((-317 . -827) 76525) ((-1224 . -949) 76494) ((-609 . -1073) T) ((-1217 . -949) 76456) ((-504 . -130) T) ((-500 . -130) T) ((-290 . -225) 76406) ((-354 . -1032) T) ((-348 . -1032) T) ((-340 . -1032) T) ((-289 . -1025) 76348) 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((-346 . -229) T) ((-346 . -239) T) ((-308 . -1186) T) ((-284 . -1073) T) ((-1153 . -597) 75508) ((-692 . -1190) T) ((-1129 . -631) 75492) ((-1180 . -544) 75471) ((-692 . -544) T) ((-311 . -860) 75455) ((-311 . -862) 75380) ((-308 . -860) 75341) ((-308 . -862) NIL) ((-779 . -304) 75306) ((-314 . -698) 75147) ((-319 . -318) 75124) ((-479 . -101) T) ((-468 . -25) T) ((-468 . -21) T) ((-413 . -38) 75098) ((-311 . -1014) 74761) ((-221 . -1171) T) ((-221 . -1174) T) ((-3 . -597) 74743) ((-308 . -1014) 74673) ((-2 . -1073) T) ((-2 . |RecordCategory|) T) ((-813 . -597) 74655) ((-1086 . -1032) 74585) ((-566 . -896) T) ((-552 . -800) T) ((-552 . -896) T) ((-488 . -896) T) ((-135 . -1014) 74569) ((-221 . -94) T) ((-74 . -435) T) ((-74 . -390) T) ((0 . -597) 74551) ((-167 . -145) 74530) ((-167 . -143) 74481) ((-221 . -35) T) ((-49 . -597) 74463) ((-471 . -1032) T) ((-481 . -227) 74445) ((-478 . -944) 74429) ((-476 . -825) 74408) ((-213 . -227) 74390) ((-80 . -435) T) ((-80 . -390) T) ((-1119 . -34) T) ((-795 . -170) 74369) ((-712 . -101) T) ((-1002 . -597) 74336) ((-493 . -281) 74311) ((-311 . -372) 74280) ((-308 . -372) 74241) ((-308 . -333) 74202) ((-1058 . -597) 74184) ((-796 . -925) 74131) ((-642 . -130) T) ((-1205 . -143) 74110) ((-1205 . -145) 74089) ((-1147 . -101) T) ((-1146 . -101) T) ((-1140 . -101) T) ((-1132 . -1073) T) ((-1099 . -101) T) ((-218 . -34) T) ((-284 . -698) 74076) ((-1132 . -594) 74052) ((-578 . -304) NIL) ((-478 . -1073) 74030) ((-385 . -597) 74012) ((-503 . -827) T) ((-1123 . -225) 73962) ((-1224 . -1223) 73946) ((-1224 . -1210) 73923) ((-1217 . -1215) 73884) ((-1217 . -1210) 73854) ((-1217 . -1213) 73838) ((-1196 . -1194) 73799) ((-1196 . -1210) 73776) ((-603 . -597) 73758) ((-1196 . -1192) 73742) ((-679 . -896) T) ((-1147 . -279) 73708) ((-1146 . -279) 73674) ((-1140 . -279) 73640) ((-1053 . -1073) T) ((-1035 . -1073) T) ((-48 . -297) T) ((-311 . -876) 73606) ((-308 . -876) NIL) ((-1035 . -1042) 73585) ((-1093 . -862) 73567) ((-779 . -38) 73551) 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72287) ((-712 . -304) 72274) ((-644 . -25) T) ((-644 . -21) T) ((-448 . -544) 72205) ((-117 . -896) T) ((-117 . -800) NIL) ((-350 . -25) T) ((-350 . -21) T) ((-347 . -25) T) ((-347 . -21) T) ((-339 . -25) T) ((-339 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-82 . -379) T) ((-82 . -390) T) ((-243 . -25) T) ((-243 . -21) T) ((-1234 . -597) 72187) ((-1180 . -1085) T) ((-1180 . -23) T) ((-1140 . -304) 72072) ((-1099 . -304) 72059) ((-1053 . -698) 71927) ((-842 . -628) 71887) ((-919 . -956) 71871) ((-886 . -21) T) ((-284 . -170) T) ((-886 . -25) T) ((-306 . -92) T) ((-848 . -827) 71822) ((-692 . -1085) T) ((-692 . -23) T) ((-627 . -1073) 71800) ((-614 . -594) 71775) ((-614 . -1073) T) ((-567 . -1190) T) ((-511 . -1190) T) ((-567 . -544) T) ((-511 . -544) T) ((-354 . -698) 71727) ((-348 . -698) 71679) ((-340 . -698) 71631) ((-334 . -1031) 71615) ((-172 . -111) 71526) ((-172 . -1031) 71458) ((-107 . -698) 71408) ((-334 . -111) 71387) ((-269 . -1073) T) ((-268 . -1073) T) ((-267 . -1073) T) 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. -1031) 22195) ((-1053 . -1014) 22091) ((-980 . -111) 22025) ((-718 . -675) 22009) ((-259 . -227) 21993) ((-422 . -1031) 21977) ((-374 . -1032) T) ((-979 . -23) T) ((-890 . -111) 21915) ((-674 . -1174) NIL) ((-481 . -628) 21865) ((-107 . -860) 21847) ((-107 . -862) 21829) ((-674 . -1171) NIL) ((-213 . -628) 21779) ((-354 . -1014) 21763) ((-348 . -1014) 21747) ((-322 . -304) 21685) ((-340 . -1014) 21669) ((-221 . -285) T) ((-422 . -111) 21648) ((-59 . -597) 21580) ((-167 . -170) T) ((-1093 . -827) T) ((-107 . -1014) 21540) ((-868 . -1073) T) ((-814 . -1032) T) ((-807 . -1032) T) ((-674 . -35) NIL) ((-674 . -94) NIL) ((-308 . -968) 21501) ((-181 . -101) T) ((-566 . -446) T) ((-552 . -446) T) ((-488 . -446) T) ((-402 . -358) T) ((-236 . -1025) 21431) ((-1123 . -34) T) ((-471 . -896) T) ((-975 . -621) 21379) ((-246 . -588) 21356) ((-245 . -588) 21333) ((-1053 . -372) 21317) ((-847 . -507) 21225) ((-236 . -229) 21177) ((-1131 . -1186) T) ((-804 . -597) 21159) ((-1255 . -1085) T) ((-1247 . 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|DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| + |DictionaryOperations| |DiophantineSolutionPackage| + |DirectProductCategory&| |DirectProductCategory| + |DirectProductFunctions2| |DirectProduct| |DisplayPackage| + |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList| + |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |Domain| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| - |DequeueAggregate| |TopLevelDrawFunctions| - |TopLevelDrawFunctionsForCompiledFunctions| - |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| - |TopLevelDrawFunctionsForPoints| |DrawOption| |DrawOptionFunctions0| - |DrawOptionFunctions1| |DifferentialSparseMultivariatePolynomial| + |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| + |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| + |DrawNumericHack| |TopLevelDrawFunctions| + |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| + |DrawOptionFunctions1| |DrawOption| + |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| - |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| + |ExtAlgBasis| |ElementaryFunction| + |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElaboratedExpression| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| - |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| - |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment| - |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions| - |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1| - |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage| - |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| - |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |EuclideanDomain&| - |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| - |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2| - |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver| - |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| - |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| - |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| - |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| - |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| - |FortranCodePackage1| |FiniteDivisor| |FiniteDivisorFunctions2| - |FiniteDivisorCategory&| |FiniteDivisorCategory| |FullyEvalableOver&| - |FullyEvalableOver| |FortranExpression| |FiniteField| |FunctionFieldCategory&| - |FunctionFieldCategory| |FunctionFieldCategoryFunctions2| - |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| + |EllipticFunctionsUnivariateTaylorSeries| |Eltable| + |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| + |EntireRing| |Environment| |EigenPackage| |EquationFunctions2| + |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| + |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| + |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| + |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| + |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| + |Evalable&| |Evalable| |EvaluateCycleIndicators| |ExitAst| |Exit| + |ExponentialExpansion| |ExpressionFunctions2| + |ExpressionToUnivariatePowerSeries| |Expression| + |ExpressionSpaceODESolver| |ExpressionTubePlot| + |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| + |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| + |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| + |FiniteAbelianMonoidRing| |FlexibleArray| + |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| + |FortranCode| |FourierComponent| |FortranCodePackage1| + |FiniteDivisorFunctions2| |FiniteDivisorCategory&| + |FiniteDivisorCategory| |FiniteDivisor| |FullyEvalableOver&| + |FullyEvalableOver| |FortranExpression| + |FunctionFieldCategoryFunctions2| |FunctionFieldCategory&| + |FunctionFieldCategory| |FiniteFieldCyclicGroup| + |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| - |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| - |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| - |FiniteFieldNormalBasisExtensionByPolynomial| - |FiniteFieldNormalBasisExtension| |FiniteFieldExtensionByPolynomial| - |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| + |FiniteFieldHomomorphisms| |FiniteFieldCategory&| + |FiniteFieldCategory| |FunctionFieldIntegralBasis| + |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| + |FiniteFieldNormalBasisExtension| |FiniteField| + |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| + |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| - |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory| - |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| - |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&| - |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| - |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| - |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage| - |FloatingRealPackage| |FreeModule| |FreeModule1| |FortranMatrixCategory| - |FreeModuleCat| |FortranMatrixFunctionCategory| |FreeMonoid| - |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| - |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat| - |ScriptFormulaFormat1| |FortranPackage| |FortranProgramCategory| - |FortranFunctionCategory| |FortranProgram| |FullPartialFractionExpansion| - |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| - |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| - |Factored| |FactoredFunctions2| |Fraction| |FractionFunctions2| - |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| - |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| + |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| + |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| + |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| + |FiniteLinearAggregateFunctions2| |FiniteLinearAggregate&| + |FiniteLinearAggregate| |FreeLieAlgebra| |FiniteLinearAggregateSort| + |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| + |FloatingComplexPackage| |Float| |FloatingRealPackage| |FreeModule1| + |FreeModuleCat| |FortranMatrixCategory| + |FortranMatrixFunctionCategory| |FreeModule| |FreeMonoid| + |FortranMachineTypeCategory| |FileName| |FileNameCategory| + |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| + |ScriptFormulaFormat1| |ScriptFormulaFormat| |FortranProgramCategory| + |FortranFunctionCategory| |FortranPackage| |FortranProgram| + |FullPartialFractionExpansion| |FullyPatternMatchable| + |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| + |FloatingPointSystem&| |FloatingPointSystem| |FactoredFunctions2| + |FractionFunctions2| |Fraction| |FramedAlgebra&| |FramedAlgebra| + |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdealFunctions2| + |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| - |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&| - |FunctionSpace| |FunctionSpaceFunctions2| - |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| - |FiniteSetAggregate&| |FiniteSetAggregate| |FiniteSetAggregateFunctions2| - |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| + |FramedNonAssociativeAlgebra| |Factored| |FactoredFunctionUtilities| + |FunctionSpaceToExponentialExpansion| |FunctionSpaceFunctions2| + |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregateFunctions2| + |FiniteSetAggregate&| |FiniteSetAggregate| + |FunctionSpaceComplexIntegration| |FourierSeries| + |FunctionSpaceIntegration| |FunctionSpace&| |FunctionSpace| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| - |FunctionSpaceUnivariatePolynomialFactor| |FortranType| |FortranTemplate| - |FunctionCalled| |FortranVectorCategory| |FortranVectorFunctionCategory| - |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| - |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| - |GaussianFactorizationPackage| |GroebnerPackage| + |FunctionSpaceUnivariatePolynomialFactor| |FortranTemplate| + |FortranType| |FunctionCalled| |FortranVectorCategory| + |FortranVectorFunctionCategory| |GaloisGroupFactorizer| + |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| + |GaloisGroupUtilities| |GaussianFactorizationPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| - |GroebnerInternalPackage| |GcdDomain&| |GcdDomain| - |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| - |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| + |GroebnerInternalPackage| |GroebnerPackage| |GcdDomain&| |GcdDomain| + |GenericNonAssociativeAlgebra| + |GeneralDistributedMultivariatePolynomial| |GenExEuclid| + |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| - |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| - |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| - |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| - |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| - |Pi| |HasAst| |HashTable| |HallBasis| - |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| - |HeadAst| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| + |GeneralModulePolynomial| |GosperSummationMethod| + |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| + |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| + |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| + |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HasAst| |HashTable| + |HallBasis| |HomogeneousDistributedMultivariatePolynomial| + |HomogeneousDirectProduct| |HeadAst| |Heap| + |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousAggregate| |Hostname| - |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| - |InnerAlgebraicNumber| |IndexedOneDimensionalArray| + |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| + |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| - |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| - |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| - |Identifier| |IndexedDirectProductAbelianGroup| - |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| - |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| - |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable| - |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField| - |InnerIndexedTwoDimensionalArray| |IndexedList| - |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| - |IndexedMatrix| |ImportAst| |InAst| |InputByteConduit&| |InputByteConduit| + |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| + |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| + |IdealDecompositionPackage| |Identifier| + |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| + |IndexedDirectProductCategory| + |IndexedDirectProductOrderedAbelianMonoid| + |IndexedDirectProductOrderedAbelianMonoidSup| + |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| + |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| + |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| + |InnerMatrixLinearAlgebraFunctions| + |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| + |InAst| |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions| |InputBinaryFile| |IncrementingMaps| - |IndexedExponents| |InnerNumericEigenPackage| |Infinity| |InputForm| - |InputFormFunctions1| |InfiniteProductCharacteristicZero| + |IndexedExponents| |InnerNumericEigenPackage| |Infinity| + |InputFormFunctions1| |InputForm| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| - |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| - |IntegerNumberSystem&| |IntegerNumberSystem| |Integer| |InnerTable| - |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| - |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| - |IntegerFactorizationPackage| |IntegrationFunctionsTable| - |GenusZeroIntegration| |IntegerNumberTheoryFunctions| - |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| + |InfiniteProductFiniteField| |InfiniteProductPrimeField| + |InnerPolySign| |IntegerNumberSystem&| |IntegerNumberSystem| + |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| + |IntervalCategory| |IntegralDomain&| |IntegralDomain| + |ElementaryIntegration| |IntegerFactorizationPackage| + |IntegrationFunctionsTable| |GenusZeroIntegration| + |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| + |TranscendentalHermiteIntegration| |Integer| |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| - |TranscendentalIntegration| |InverseLaplaceTransform| |InputOutputByteConduit| - |IOMode| |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| - |IntegrationResult| |IntegrationResultFunctions2| - |IntegrationResultToFunction| |IntegerRoots| |IrredPolyOverFiniteField| - |IntegrationResultRFToFunction| |IrrRepSymNatPackage| - |InternalRationalUnivariateRepresentationPackage| |IsAst| |IndexedString| - |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| - |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| - |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| - |IndexedAggregate&| |IndexedAggregate| |JavaBytecode| |JoinAst| - |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| - |KeyedDictionary| |Kernel| |KernelFunctions2| |CoercibleTo| |ConvertibleTo| - |Kovacic| |KleeneTrivalentLogic| |LocalAlgebra| |LeftAlgebra&| |LeftAlgebra| - |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| - |LeadingCoefDetermination| |LetAst| |LieExponentials| |LexTriangularPackage| - |LiouvillianFunction| |LiouvillianFunctionCategory| |LinGroebnerPackage| - |Library| |AssociatedLieAlgebra| |LieAlgebra&| |LieAlgebra| - |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| - |LinearlyExplicitRingOver| |List| |ListFunctions2| |ListToMap| - |ListFunctions3| |Literal| |ListMultiDictionary| |LeftModule| |ListMonoidOps| - |LinearAggregate&| |LinearAggregate| |Localize| |ElementaryFunctionLODESolver| - |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| + |TranscendentalIntegration| |InverseLaplaceTransform| + |InputOutputByteConduit| |IOMode| |InnerPAdicInteger| + |InnerPrimeField| |InternalPrintPackage| |IntegrationResultToFunction| + |IntegrationResultFunctions2| |IntegrationResult| |IntegerRoots| + |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| + |IrrRepSymNatPackage| + |InternalRationalUnivariateRepresentationPackage| |IsAst| + |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| + |InnerTaylorSeries| |InfiniteTupleFunctions2| + |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| + |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| + |JavaBytecode| |JoinAst| |AssociatedJordanAlgebra| |KeyedAccessFile| + |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| + |CoercibleTo| |ConvertibleTo| |Kovacic| |KleeneTrivalentLogic| + |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| + |LaurentPolynomial| |LazardSetSolvingPackage| + |LeadingCoefDetermination| |LetAst| |LieExponentials| + |LexTriangularPackage| |LiouvillianFunctionCategory| + |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| + |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| + |RationalFunctionLimitPackage| |LinearDependence| + |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| + |ListFunctions3| |List| |Literal| |ListMultiDictionary| |LeftModule| + |ListMonoidOps| |LinearAggregate&| |LinearAggregate| + |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| - |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| + |LinearOrdinaryDifferentialOperator| + |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| - |ListAggregate| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| - |LinearSystemPolynomialPackage| |LieSquareMatrix| |ConstructAst| |LyndonWord| - |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| - |MacroAst| |Magma| |MappingPackageInternalHacks1| - |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingAst| - |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategory&| - |MatrixCategory| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| + |ListAggregate| |LinearSystemMatrixPackage1| + |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| + |LieSquareMatrix| |ConstructAst| |LyndonWord| |LazyStreamAggregate&| + |LazyStreamAggregate| |ThreeDimensionalMatrix| |MacroAst| |Magma| + |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| + |MappingPackageInternalHacks3| |MappingAst| |MappingPackage1| + |MappingPackage2| |MappingPackage3| |MatrixCategoryFunctions2| + |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |Maybe| - |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| - |MultiDictionary| |ModularDistinctDegreeFactorizer| - |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| - |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| - |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| - |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| - |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| - |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| - |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| - |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| - |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| - |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| - |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |Multiset| - |MultisetAggregate| |MoreSystemCommands| |MergeThing| - |MultivariateTaylorSeriesCategory| |MultivariateFactorize| - |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| + |MultiVariableCalculusFunctions| |MatrixCommonDenominator| + |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| + |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| + |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| + |MakeBinaryCompiledFunction| |MakeCachableSet| + |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| + |MakeUnaryCompiledFunction| |MultivariateLifting| + |MonogenicLinearOperator| |MultipleMap| |MathMLFormat| |ModularField| + |ModMonic| |ModuleMonomial| |ModuleOperator| |ModularRing| |Module&| + |Module| |MoebiusTransform| |Monad&| |Monad| |MonadWithUnit&| + |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| + |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| + |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| + |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| + |MonoidRingFunctions2| |MonoidRing| |MultisetAggregate| |Multiset| + |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| + |MultivariateFactorize| |MultivariateSquareFree| + |NonAssociativeAlgebra&| |NonAssociativeAlgebra| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| - |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| - |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| - |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| - |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| - |NumericComplexEigenPackage| |NumericContinuedFraction| - |NonCommutativeOperatorDivision| |NumberFieldIntegralBasis| - |NumericalIntegrationProblem| |NonLinearSolvePackage| |NonNegativeInteger| - |NonLinearFirstOrderODESolver| |None| |NoneFunctions1| - |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| - |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| - |NewSparseUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| - |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| - |Numeric| |NumberFormats| |NumericalIntegrationCategory| + |NagFittingPackage| |NagOptimisationPackage| + |NagMatrixOperationsPackage| |NagEigenPackage| + |NagLinearEquationSolvingPackage| |NagLapack| + |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| + |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| + |NonAssociativeRing| |NumericComplexEigenPackage| + |NumericContinuedFraction| |NonCommutativeOperatorDivision| + |NumberFieldIntegralBasis| |NumericalIntegrationProblem| + |NonLinearSolvePackage| |NonNegativeInteger| + |NonLinearFirstOrderODESolver| |NoneFunctions1| |None| + |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| + |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| + |NewSparseUnivariatePolynomialFunctions2| + |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| + |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| + |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| - |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OctonionCategory&| - |OctonionCategory| |OrderedCancellationAbelianMonoid| |Octonion| - |OctonionCategoryFunctions2| |OrdinaryDifferentialEquationsSolverCategory| - |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| - |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| - |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| - |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| - |OrderedDirectProduct| |OrderlyDifferentialPolynomial| - |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| - |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice| - |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| - |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| - |OpenMathServerPackage| |OnePointCompletion| |OnePointCompletionFunctions2| - |Operator| |OperationsQuery| |NumericalOptimizationCategory| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| + |OrderedCancellationAbelianMonoid| |OctonionCategory&| + |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| + |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| + |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| + |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| + |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| + |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| + |SystemODESolver| |ODETools| |OrderedDirectProduct| + |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| + |OrderlyDifferentialVariable| |OrderedFreeMonoid| + |OrderedIntegralDomain| |OpenMathConnection| |OpenMathDevice| + |OpenMathEncoding| |OpenMathErrorKind| |OpenMathError| + |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMath| + |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| + |OnePointCompletionFunctions2| |OnePointCompletion| |Operator| + |OperationsQuery| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| - |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| - |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| - |OrderedSet| |UnivariateSkewPolynomialCategory&| - |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| - |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| - |OrthogonalPolynomialFunctions| |OrderedSemiGroup| |OrdSetInts| - |OutputPackage| |OutputByteConduit&| |OutputByteConduit| |OutputBinaryFile| - |OutputForm| |OrderedVariableList| |OrdinaryWeightedPolynomials| - |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| - |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Pair| - |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| - |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| - |Parser| |ParametricSurfaceFunctions2| |ParametricSurface| - |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| - |PatternMatchable| |PatternMatch| |PatternMatchResult| - |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| - |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| + |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| + |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| + |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| + |UnivariateSkewPolynomialCategory| + |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| + |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| + |OrderedSemiGroup| |OrdSetInts| |OutputByteConduit&| + |OutputByteConduit| |OutputBinaryFile| |OutputForm| |OutputPackage| + |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| + |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| + |PAdicRational| |PAdicRationalConstructor| |Pair| |Palette| + |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| + |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| + |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| + |ParametricSurface| |PartitionsAndPermutations| |Patternable| + |PatternMatchListResult| |PatternMatchable| |PatternMatch| + |PatternMatchResultFunctions2| |PatternMatchResult| + |PatternFunctions1| |PatternFunctions2| |Pattern| + |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| - |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| - |PrimeField| |PolynomialFactorizationByRecursion| + |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| + |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| - |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| - |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| - |PermutationGroupExamples| |PolyGroebner| |PositiveInteger| |PiCoercions| - |PrincipalIdealDomain| |PolynomialInterpolation| - |PolynomialInterpolationAlgorithms| |ParametricLinearEquations| |Plot| - |PlotFunctions1| |Plot3D| |PlotTools| |PatternMatchAssertions| - |FunctionSpaceAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| + |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| + |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| + |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| + |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| + |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| + |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| + |PlotTools| |FunctionSpaceAssertions| |PatternMatchAssertions| + |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| - |AttachPredicates| |FunctionSpaceAttachPredicates| - |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| - |PolynomialNumberTheoryFunctions| |Point| |PolToPol| - |RealPolynomialUtilitiesPackage| |Polynomial| |PolynomialFunctions2| - |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| - |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| - |PolynomialRoots| |PortNumber| |PlottablePlaneCurveCategory| |PolynomialRing| - |PrecomputedAssociatedEquations| |PrimitiveArray| |PrimitiveArrayFunctions2| - |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| - |PrintPackage| |Product| |Property| |PropositionalFormula| - |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| - |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| - |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| - |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| - |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| - |PartialTranscendentalFunctions| |PushVariables| - |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| - |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategory&| - |QuotientFieldCategory| |QuotientFieldCategoryFunctions2| |QuadraticForm| - |QuasiquoteAst| |QueueAggregate| |Quaternion| |QuaternionCategory&| - |QuaternionCategory| |QuaternionCategoryFunctions2| |Queue| |RadicalCategory&| - |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| - |RandomNumberSource| |RationalFactorize| |RationalRetractions| - |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| - |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| - |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| - |ReducedDivisor| |ReduceAst| |RealConstant| |RealZeroPackage| - |RealZeroPackageQ| |RealSolvePackage| |RealClosure| |ReductionOfOrder| - |Reference| |RegularTriangularSet| |RadicalEigenPackage| - |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| + |FunctionSpaceAttachPredicates| |AttachPredicates| + |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| + |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| + |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| + |PolynomialToUnivariatePolynomial| |PolynomialCategory&| + |PolynomialCategory| |PolynomialCategoryQuotientFunctions| + |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| + |PortNumber| |PlottablePlaneCurveCategory| + |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| + |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| + |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| + |Property| |PropositionalFormula| |PropositionalLogic| + |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| + |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| + |PlottableSpaceCurveCategory| |PolynomialSetCategory&| + |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| + |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| + |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| + |PushVariables| |PAdicWildFunctionFieldIntegralBasis| + |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| + |QueryEquation| |QuotientFieldCategoryFunctions2| + |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| + |QuasiquoteAst| |QueueAggregate| |QuaternionCategory&| + |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| + |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| + |RadixExpansion| |RadixUtilities| |RandomNumberSource| + |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| + |RecursiveAggregate| |RealClosedField&| |RealClosedField| + |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| + |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| + |ReduceAst| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| + |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| + |RegularTriangularSet| |RepresentationPackage1| + |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |ReturnAst| |RetractableTo&| |RetractableTo| |RetractSolvePackage| - |RationalFunction| |RandomFloatDistributions| |RationalFunctionFactor| - |RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain| - |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| - |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| - |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| - |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| - |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| + |RandomFloatDistributions| |RationalFunctionFactor| + |RationalFunctionFactorizer| |RationalFunction| |RGBColorModel| + |RGBColorSpace| |RegularChain| |RandomIntegerDistributions| |Ring&| + |Ring| |RationalInterpolation| |RectangularMatrixCategory&| + |RectangularMatrixCategory| |RectangularMatrix| + |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| + |RealNumberSystem&| |RealNumberSystem| + |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| + |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| - |RegularTriangularSetGcdPackage| |RestrictAst| |RewriteRule| |RuleCalled| - |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtension| - |SimpleAlgebraicExtensionAlgFactor| |SAERationalFunctionAlgFactor| - |SingletonAsOrderedSet| |SpadSyntaxCategory| |SortedCache| |Scope| + |RegularTriangularSetGcdPackage| |RestrictAst| |RuleCalled| + |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| + |SimpleAlgebraicExtensionAlgFactor| |SimpleAlgebraicExtension| + |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| + |SpadSyntaxCategory| |SortedCache| |Scope| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| - |SequentialDifferentialVariable| |Segment| |SegmentFunctions2| |SegmentAst| - |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| - |SegmentExpansionCategory| |SequenceAst| |Set| |SetAggregate&| |SetAggregate| - |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |SExpression| - |SExpressionCategory| |SExpressionOf| |SimpleFortranProgram| - |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| - |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| - |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| - |Signature| |SignatureAst| |ElementaryFunctionSign| |RationalFunctionSign| - |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| - |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| - |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| - |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| - |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| - |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| + |SequentialDifferentialVariable| |SegmentFunctions2| |SegmentAst| + |SegmentBindingFunctions2| |SegmentBinding| |SegmentCategory| + |Segment| |SegmentExpansionCategory| |SequenceAst| |SetAggregate&| + |SetAggregate| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| + |Set| |SExpressionCategory| |SExpression| |SExpressionOf| + |SimpleFortranProgram| |SquareFreeQuasiComponentPackage| + |SquareFreeRegularTriangularSetGcdPackage| + |SquareFreeRegularTriangularSetCategory| + |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| + |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |SignatureAst| + |ElementaryFunctionSign| |RationalFunctionSign| |Signature| + |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| + |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| + |SmithNormalForm| |SparseMultivariatePolynomial| + |SparseMultivariateTaylorSeries| + |SquareFreeNormalizedTriangularSetCategory| + |PolynomialSolveByFormulas| |RadicalSolvePackage| + |TransSolvePackageService| |TransSolvePackage| |SortPackage| + |ThreeSpace| |ThreeSpaceCategory| |SpadAst| |SpadParser| |SpadAstExports| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| - |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| - |SparseTable| |StepThrough| |StreamInfiniteProduct| |Stream| - |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StringCategory| - |String| |StringTable| |StreamTaylorSeriesOperations| - |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| - |SubResultantPackage| |SubSpace| |SuchThat| |SuchThatAst| - |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| - |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| - |SupFractionFactorizer| |SparseUnivariatePuiseuxSeries| + |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| + |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| + |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |Stream| + |StringCategory| |String| |StringTable| |StreamTaylorSeriesOperations| + |StreamTranscendentalFunctionsNonCommutative| + |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| + |SuchThat| |SuchThatAst| |SparseUnivariateLaurentSeries| + |FunctionSpaceSum| |RationalFunctionSum| + |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| + |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| - |SystemSolvePackage| |System| |TableauxBumpers| |Table| |Tableau| + |SystemSolvePackage| |System| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| - |TabulatedComputationPackage| |TemplateUtilities| |TexFormat| |TexFormat1| - |TextFile| |ToolsForSign| |TopLevelThreeSpace| - |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| - |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| - |TrigonometricManipulations| |TriangularMatrixOperations| - |TranscendentalManipulations| |TaylorSeries| |TriangularSetCategory&| - |TriangularSetCategory| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| - |Type| |TypeAst| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| + |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| + |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| + |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| + |Tree| |TrigonometricFunctionCategory&| + |TrigonometricFunctionCategory| |TrigonometricManipulations| + |TriangularMatrixOperations| |TranscendentalManipulations| + |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| + |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |TypeAst| |Type| + |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| - |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| - |UnivariateLaurentSeriesCategory| + |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| - |UnivariateLaurentSeriesConstructor| |UnivariateFactorize| |UniversalSegment| - |UniversalSegmentFunctions2| |UnivariatePolynomial| - |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| + |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| + |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| + |UnivariatePolynomialFunctions2| + |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| - |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialCategory&| - |UnivariatePolynomialCategory| |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| + |UnivariatePolynomialCategoryFunctions2| + |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| - |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| - |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| + |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| + |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| - |UnivariatePuiseuxSeriesConstructor| - |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| - |UnaryRecursiveAggregate| |UnivariateTaylorSeries| + |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| + |UnivariatePuiseuxSeriesWithExponentialSingularity| + |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| - |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesODESolver| - |UTSodetools| |UnionType| |Variable| |VectorCategory&| |VectorCategory| - |Vector| |VectorFunctions2| |ViewportPackage| |TwoDimensionalViewport| - |ThreeDimensionalViewport| |ViewDefaultsPackage| |Void| |VectorSpace&| - |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| - |WhereAst| |WhileAst| |WeightedPolynomials| |WuWenTsunTriangularSet| - |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |ExtensionField&| - |ExtensionField| |XFreeAlgebra| |XPBWPolynomial| |XPolynomial| - |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| + |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| + |UnivariateTaylorSeriesODESolver| |UTSodetools| |UnionType| |Variable| + |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| + |TwoDimensionalViewport| |ThreeDimensionalViewport| + |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| + |VectorSpace| |WeierstrassPreparation| + |WildFunctionFieldIntegralBasis| |WhereAst| |WhileAst| + |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| + |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| + |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| + |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| - |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| - |Union| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot| |size?| - |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom| - |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank| - |rightRank| |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements| - |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus| - |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter| - |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid| - |radicalOfLeftTraceForm| |showTypeInOutput| |obj| |dom| |objectOf| |domainOf| - |any| |applyRules| |localUnquote| |setColumn!| |setRow!| |oneDimensionalArray| - |associatedSystem| |uncouplingMatrices| |associatedEquations| |arrayStack| - |setButtonValue| |setAttributeButtonStep| |resetAttributeButtons| - |getButtonValue| |decrease| |increase| |morphism| |balancedFactorisation| - |mapDown!| |mapUp!| |setleaves!| |balancedBinaryTree| |sylvesterMatrix| - |bezoutMatrix| |bezoutResultant| |bezoutDiscriminant| |bfEntry| |bfKeys| - |inspect| |extract!| |bag| |binding| |position!| |test| |setProperties| - |setProperty| |deleteProperty!| |has?| |comparison| |equality| |nary?| - |unary?| |nullary?| |properties| |derivative| |constantOperator| - |constantOpIfCan| |integerBound| |setright!| |setleft!| - |brillhartIrreducible?| |brillhartTrials| |noLinearFactor?| |insertRoot!| - |binarySearchTree| |nor| |nand| |node| |binaryTournament| |binaryTree| - |bitior| |bitand| |byte| |subtractIfCan| |setPosition| - |generalizedContinuumHypothesisAssumed| - |generalizedContinuumHypothesisAssumed?| |countable?| |Aleph| |unravel| - |ravel| |leviCivitaSymbol| |kroneckerDelta| |reindex| |alphanumeric| - |alphabetic| |hexDigit| |digit| |charClass| |alphanumeric?| |lowerCase?| - |upperCase?| |alphabetic?| |hexDigit?| |digit?| |escape| |char| |ord| - |mkIntegral| |radPoly| |rootPoly| |goodPoint| |chvar| |removeDuplicates| - |find| |e| |clipParametric| |clipWithRanges| |numberOfHues| |yellow| |iifact| - |iibinom| |iiperm| |iipow| |iidsum| |iidprod| |ipow| |factorial| |multinomial| - |permutation| |stirling1| |stirling2| |summation| |factorials| |mkcomm| - |polarCoordinates| |complex| |imaginary| |solid| |solid?| |denominators| - |numerators| |convergents| |approximants| |reducedForm| |partialQuotients| - |partialDenominators| |partialNumerators| |reducedContinuedFraction| |push| - |bindings| |cartesian| |polar| |cylindrical| |spherical| |parabolic| - |parabolicCylindrical| |paraboloidal| |ellipticCylindrical| - |prolateSpheroidal| |oblateSpheroidal| |bipolar| |bipolarCylindrical| - |toroidal| |conical| |modTree| |multiEuclideanTree| |complexZeros| - |divisorCascade| |graeffe| |pleskenSplit| |reciprocalPolynomial| |rootRadius| - |schwerpunkt| |setErrorBound| |startPolynomial| |cycleElt| - |computeCycleLength| |computeCycleEntry| |arity| |kind| |arguments| - |constructorName| |package| |domain| |category| |coerceP| |powerSum| - |elementary| |alternating| |cyclic| |dihedral| |cap| |cup| |wreath| - |SFunction| |skewSFunction| |cyclotomicDecomposition| - |cyclotomicFactorization| |rangeIsFinite| |functionIsContinuousAtEndPoints| - |functionIsOscillatory| |changeName| |exprHasWeightCosWXorSinWX| - |exprHasAlgebraicWeight| |exprHasLogarithmicWeights| - |combineFeatureCompatibility| |sparsityIF| |stiffnessAndStabilityFactor| - |stiffnessAndStabilityOfODEIF| |systemSizeIF| |expenseOfEvaluationIF| - |accuracyIF| |intermediateResultsIF| |subscriptedVariables| |central?| - |elliptic?| |doubleResultant| |distdfact| |separateDegrees| |trace2PowMod| - |tracePowMod| |irreducible?| |decimal| |innerint| |exteriorDifferential| - |totalDifferential| |homogeneous?| |leadingBasisTerm| |ignore?| |computeInt| - |checkForZero| |logGamma| |hypergeometric0F1| |rotatez| |rotatey| |rotatex| - |identity| |dictionary| |dioSolve| |directProduct| |newLine| |copies| |say| - |sayLength| |setnext!| |setprevious!| |next| |previous| |datalist| - |shanksDiscLogAlgorithm| |showSummary| |reflect| |reify| |separant| |initial| - |leader| |isobaric?| |weights| |differentialVariables| |extractBottom!| - |extractTop!| |insertBottom!| |insertTop!| |bottom!| |top!| |dequeue| - |makeObject| |recolor| |drawComplex| |drawComplexVectorField| |setRealSteps| - |setImagSteps| |setClipValue| |draw| |option?| |range| |colorFunction| - |curveColor| |pointColor| |clip| |clipBoolean| |style| |toScale| - |pointColorPalette| |curveColorPalette| |var1Steps| |var2Steps| |space| - |tubePoints| |tubeRadius| |option| |weight| |makeVariable| |finiteBound| - |sortConstraints| |sumOfSquares| |splitLinear| |simpleBounds?| |linearMatrix| - |linearPart| |nonLinearPart| |quadratic?| |changeNameToObjf| |optAttributes| - |Nul| |exponents| |iisqrt2| |iisqrt3| |iiexp| |iilog| |iisin| |iicos| |iitan| - |iicot| |iisec| |iicsc| |iiasin| |iiacos| |iiatan| |iiacot| |iiasec| |iiacsc| - |iisinh| |iicosh| |iitanh| |iicoth| |iisech| |iicsch| |iiasinh| |iiacosh| - |iiatanh| |iiacoth| |iiasech| |iiacsch| |specialTrigs| |localReal?| - |rischNormalize| |realElementary| |validExponential| |rootNormalize| |tanQ| - |callForm?| |getIdentifier| |getConstant| |type| |select!| |delete!| |sn| |cn| - |dn| |sncndn| |qsetelt!| |categoryFrame| |currentEnv| |setProperties!| - |getProperties| |setProperty!| |getProperty| |scopes| |eigenvalues| - |eigenvector| |generalizedEigenvector| |generalizedEigenvectors| - |eigenvectors| |factorAndSplit| |rightOne| |leftOne| |rightZero| |leftZero| - |swap| |error| |minPoly| |freeOf?| |operators| |tower| |kernels| |mainKernel| - |distribute| |subst| |functionIsFracPolynomial?| |problemPoints| |zerosOf| - |singularitiesOf| |polynomialZeros| |f2df| |ef2edf| |ocf2ocdf| |socf2socdf| - |df2fi| |edf2fi| |edf2df| |expenseOfEvaluation| |numberOfOperations| |edf2efi| - |dfRange| |dflist| |df2mf| |ldf2vmf| |edf2ef| |vedf2vef| |df2st| |f2st| - |ldf2lst| |sdf2lst| |getlo| |gethi| |outputMeasure| |measure2Result| - |att2Result| |iflist2Result| |pdf2ef| |pdf2df| |df2ef| |fi2df| |mat| |neglist| - |multiEuclidean| |extendedEuclidean| |euclideanSize| |sizeLess?| - |simplifyPower| |number?| |seriesSolve| |constantToUnaryFunction| |tubePlot| - |exponentialOrder| |completeEval| |lowerPolynomial| |raisePolynomial| - |normalDeriv| |ran| |highCommonTerms| |mapCoef| |nthCoef| |binomThmExpt| - |pomopo!| |mapExponents| |linearAssociatedLog| |linearAssociatedOrder| - |linearAssociatedExp| |createNormalElement| |setLabelValue| |getCode| - |printCode| |code| |operation| |common| |printStatement| |save| |stop| |block| - |cond| |returns| |call| |comment| |continue| |goto| |repeatUntilLoop| - |whileLoop| |forLoop| |sin?| |zeroVector| |zeroSquareMatrix| - |identitySquareMatrix| |lSpaceBasis| |finiteBasis| |principal?| |divisor| - |useNagFunctions| |rationalPoints| |nonSingularModel| |algSplitSimple| - |hyperelliptic| |elliptic| |integralDerivationMatrix| |integralRepresents| - |integralCoordinates| |yCoordinates| |inverseIntegralMatrixAtInfinity| - |integralMatrixAtInfinity| |inverseIntegralMatrix| |integralMatrix| - |reduceBasisAtInfinity| |normalizeAtInfinity| |complementaryBasis| |integral?| - |integralAtInfinity?| |integralBasisAtInfinity| |ramified?| - |ramifiedAtInfinity?| |singular?| |singularAtInfinity?| |branchPoint?| - |branchPointAtInfinity?| |rationalPoint?| |absolutelyIrreducible?| |genus| - |getZechTable| |createZechTable| |createMultiplicationTable| - |createMultiplicationMatrix| |createLowComplexityTable| - |createLowComplexityNormalBasis| |representationType| |createPrimitiveElement| - |tableForDiscreteLogarithm| |factorsOfCyclicGroupSize| |sizeMultiplication| - |getMultiplicationMatrix| |getMultiplicationTable| |primitive?| - |numberOfIrreduciblePoly| |numberOfPrimitivePoly| |numberOfNormalPoly| - |createIrreduciblePoly| |createPrimitivePoly| |createNormalPoly| - |createNormalPrimitivePoly| |createPrimitiveNormalPoly| |nextIrreduciblePoly| - |nextPrimitivePoly| |nextNormalPoly| |nextNormalPrimitivePoly| - |nextPrimitiveNormalPoly| |leastAffineMultiple| |reducedQPowers| - |rootOfIrreduciblePoly| |write!| |read!| |iomode| |close!| |reopen!| |open| - |rightUnit| |leftUnit| |rightMinimalPolynomial| |leftMinimalPolynomial| - |associatorDependence| |lieAlgebra?| |jordanAlgebra?| - |noncommutativeJordanAlgebra?| |jordanAdmissible?| |lieAdmissible?| - |jacobiIdentity?| |powerAssociative?| |alternative?| |flexible?| - |rightAlternative?| |leftAlternative?| |antiAssociative?| |associative?| - |antiCommutative?| |commutative?| |rightCharacteristicPolynomial| - |leftCharacteristicPolynomial| |rightNorm| |leftNorm| |rightTrace| |leftTrace| - |someBasis| |sort!| |copyInto!| |sorted?| |LiePoly| |quickSort| |heapSort| - |shellSort| |outputSpacing| |outputGeneral| |outputFixed| |outputFloating| - |exp1| |log10| |log2| |rationalApproximation| |relerror| |complexSolve| - |complexRoots| |realRoots| |leadingTerm| |writable?| |readable?| |exists?| - |extension| |directory| |filename| |shallowExpand| |deepExpand| - |clearFortranOutputStack| |showFortranOutputStack| |popFortranOutputStack| - |pushFortranOutputStack| |topFortranOutputStack| |setFormula!| |formula| - |linkToFortran| |setLegalFortranSourceExtensions| |fracPart| |polyPart| - |fullPartialFraction| |primeFrobenius| |discreteLog| |decreasePrecision| - |increasePrecision| |bits| |unitNormalize| |unit| |flagFactor| |sqfrFactor| - |primeFactor| |nthFlag| |nthExponent| |irreducibleFactor| |nilFactor| - |regularRepresentation| |traceMatrix| |randomLC| |minimize| |module| - |rightRegularRepresentation| |leftRegularRepresentation| |rightTraceMatrix| - |leftTraceMatrix| |rightDiscriminant| |leftDiscriminant| |represents| - |mergeFactors| |isMult| |applyQuote| |ground| |ground?| |exprToXXP| - |exprToUPS| |exprToGenUPS| |localAbs| |universe| |complement| |cardinality| - |internalIntegrate0| |makeCos| |makeSin| |iiGamma| |iiabs| |bringDown| - |newReduc| |logical?| |character?| |doubleComplex?| |complex?| |double?| - |ffactor| |qfactor| |UP2ifCan| |anfactor| |fortranCharacter| - |fortranDoubleComplex| |fortranComplex| |fortranLogical| |fortranInteger| - |fortranDouble| |fortranReal| |external?| |scalarTypeOf| - |fortranCarriageReturn| |fortranLiteral| |fortranLiteralLine| - |processTemplate| |makeFR| |musserTrials| |stopMusserTrials| |numberOfFactors| - |modularFactor| |useSingleFactorBound?| |useSingleFactorBound| - |useEisensteinCriterion?| |useEisensteinCriterion| |eisensteinIrreducible?| - |tryFunctionalDecomposition?| |tryFunctionalDecomposition| |btwFact| - |beauzamyBound| |bombieriNorm| |rootBound| |singleFactorBound| |quadraticNorm| - |infinityNorm| |scaleRoots| |shiftRoots| |degreePartition| |factorOfDegree| - |factorsOfDegree| |pascalTriangle| |rangePascalTriangle| |sizePascalTriangle| - |fillPascalTriangle| |safeCeiling| |safeFloor| |safetyMargin| |sumSquares| - |euclideanNormalForm| |euclideanGroebner| |factorGroebnerBasis| - |groebnerFactorize| |credPol| |redPol| |gbasis| |critT| |critM| |critB| - |critBonD| |critMTonD1| |critMonD1| |redPo| |hMonic| |updatF| |sPol| |updatD| - |minGbasis| |lepol| |prinshINFO| |prindINFO| |fprindINFO| |prinpolINFO| - |prinb| |critpOrder| |makeCrit| |virtualDegree| |lcm| - |conditionsForIdempotents| |genericRightDiscriminant| |genericRightTraceForm| - |genericLeftDiscriminant| |genericLeftTraceForm| |genericRightNorm| - |genericRightTrace| |genericRightMinimalPolynomial| |rightRankPolynomial| - |genericLeftNorm| |genericLeftTrace| |genericLeftMinimalPolynomial| - |leftRankPolynomial| |generic| |rightUnits| |leftUnits| |compBound| |tablePow| - |solveid| |testModulus| |HenselLift| |completeHensel| |multMonom| |build| - |leadingIndex| |leadingExponent| |GospersMethod| |nextSubsetGray| - |firstSubsetGray| |clipPointsDefault| |drawToScale| |adaptive| |figureUnits| - |putColorInfo| |appendPoint| |component| |ranges| |pointLists| - |makeGraphImage| |graphImage| |groebSolve| |testDim| |genericPosition| |lfunc| - |inHallBasis?| |reorder| |parameters| |headAst| |heap| |gcdprim| |gcdcofact| - |gcdcofactprim| |lintgcd| |hex| |parts| |count| |every?| |any?| |map!| |host| - |trueEqual| |factorList| |listConjugateBases| |matrixGcd| |divideIfCan!| - |leastPower| |idealiser| |idealiserMatrix| |moduleSum| |mapUnivariate| - |mapUnivariateIfCan| |mapMatrixIfCan| |mapBivariate| |fullDisplay| - |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal| - |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?| - |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp| - |contract| |leadingSupport| |shrinkable| |physicalLength!| |physicalLength| - |flexibleArray| |elseBranch| |thenBranch| |generalizedInverse| |imports| - |sequence| |iterationVar| |readBytes!| |readByteIfCan!| |setFieldInfo| |pol| - |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup| |normal?| |basis| - |normalElement| |minimalPolynomial| |eof?| |inputBinaryFile| |increment| - |incrementBy| |charpol| |solve1| |innerEigenvectors| |compile| |declare| - |parseString| |unparse| |flatten| |lambda| |binary| |packageCall| |interpret| - |innerSolve1| |innerSolve| |makeEq| |modularGcdPrimitive| |modularGcd| - |reduction| |signAround| |invmod| |powmod| |mulmod| |submod| |addmod| |mask| - |dec| |inc| |symmetricRemainder| |positiveRemainder| |bit?| |algint| - |algintegrate| |palgintegrate| |palginfieldint| |bitLength| |bitCoef| - |bitTruth| |contains?| |inf| |qinterval| |interval| |unit?| |associates?| - |unitCanonical| |unitNormal| |lfextendedint| |lflimitedint| |lfinfieldint| - |lfintegrate| |lfextlimint| |BasicMethod| |PollardSmallFactor| |showTheFTable| - |clearTheFTable| |fTable| |showAttributes| |entry| |palgint0| |palgextint0| - |palglimint0| |palgRDE0| |palgLODE0| |chineseRemainder| |divisors| |eulerPhi| - |fibonacci| |harmonic| |jacobi| |moebiusMu| |numberOfDivisors| |sumOfDivisors| - |sumOfKthPowerDivisors| |HermiteIntegrate| |palgint| |palgextint| |palglimint| - |palgRDE| |palgLODE| |splitConstant| |pmComplexintegrate| |pmintegrate| - |infieldint| |extendedint| |limitedint| |integerIfCan| |internalIntegrate| - |infieldIntegrate| |limitedIntegrate| |extendedIntegrate| |varselect| |kmax| - |ksec| |vark| |removeConstantTerm| |mkPrim| |intPatternMatch| |primintegrate| - |expintegrate| |tanintegrate| |primextendedint| |expextendedint| - |primlimitedint| |explimitedint| |primextintfrac| |primlimintfrac| - |primintfldpoly| |expintfldpoly| |monomialIntegrate| |monomialIntPoly| - |inverseLaplace| |bothWays| |input| |iprint| |elem?| |notelem| |logpart| - |ratpart| |mkAnswer| |perfectNthPower?| |perfectNthRoot| |approxNthRoot| - |perfectSquare?| |perfectSqrt| |approxSqrt| |generateIrredPoly| - |complexExpand| |complexIntegrate| |dimensionOfIrreducibleRepresentation| - |irreducibleRepresentation| |checkRur| |cAcsch| |cAsech| |cAcoth| |cAtanh| - |cAcosh| |cAsinh| |cCsch| |cSech| |cCoth| |cTanh| |cCosh| |cSinh| |cAcsc| - |cAsec| |cAcot| |cAtan| |cAcos| |cAsin| |cCsc| |cSec| |cCot| |cTan| |cCos| - |cSin| |cLog| |cExp| |cRationalPower| |cPower| |seriesToOutputForm| |iCompose| - |taylorQuoByVar| |iExquo| |getStream| |getRef| |makeSeries| GF2FG FG2F F2FG - |explogs2trigs| |trigs2explogs| |swap!| |fill!| |minIndex| |maxIndex| |entry?| - |indices| |index?| |entries| |categories| |search| |key?| |symbolIfCan| - |kernel| |argument| |constantKernel| |constantIfCan| |kovacic| |true| - |unknown| |false| |laplace| |trailingCoefficient| |normalizeIfCan| |polCase| - |distFact| |identification| |LyndonCoordinates| |LyndonBasis| - |zeroDimensional?| |fglmIfCan| |groebner| |lexTriangular| - |squareFreeLexTriangular| |belong?| |erf| |dilog| |li| |Ci| |Si| |Ei| - |linGenPos| |groebgen| |totolex| |minPol| |computeBasis| |coord| |anticoord| - |intcompBasis| |choosemon| |transform| |pack!| |library| |complexLimit| - |limit| |linearlyDependent?| |linearDependence| |solveLinear| |reducedSystem| - |setDifference| |setIntersection| |setUnion| |append| |null| |nil| - |substitute| |duplicates?| |mapGen| |mapExpon| |commutativeEquality| - |leftMult| |rightMult| |makeUnit| |reverse!| |reverse| |makeMulti| |makeTerm| - |listOfMonoms| |insert| |delete| |symmetricSquare| |factor1| - |symmetricProduct| |symmetricPower| |directSum| - |solveLinearPolynomialEquationByFractions| |hasSolution?| |linSolve| - |LyndonWordsList| |LyndonWordsList1| |lyndonIfCan| |lyndon| |lyndon?| - |numberOfComputedEntries| |rst| |frst| |lazyEvaluate| |lazy?| - |explicitlyEmpty?| |explicitEntries?| |matrixDimensions| |matrixConcat3D| - |setelt!| |plus| |identityMatrix| |zeroMatrix| |iter| |arg1| |arg2| |comp| - |mappingAst| |nullary| |fixedPoint| |id| |recur| |const| |curry| |diag| - |curryRight| |curryLeft| |constantRight| |constantLeft| |twist| - |setsubMatrix!| |subMatrix| |swapColumns!| |swapRows!| |vertConcat| - |horizConcat| |squareTop| |elRow1!| |elRow2!| |elColumn2!| - |fractionFreeGauss!| |invertIfCan| |copy!| |plus!| |minus!| |leftScalarTimes!| - |rightScalarTimes!| |times!| |power!| |nothing| |gradient| |divergence| - |laplacian| |hessian| |bandedHessian| |jacobian| |bandedJacobian| |duplicates| - |removeDuplicates!| |linears| |ddFact| |separateFactors| |exptMod| - |meshPar2Var| |meshFun2Var| |meshPar1Var| |ptFunc| |minimumExponent| - |maximumExponent| |precision| |mantissa| |rowEch| |rowEchLocal| - |rowEchelonLocal| |normalizedDivide| |maxint| |binaryFunction| - |makeFloatFunction| |function| |makeRecord| |unaryFunction| |compiledFunction| - |corrPoly| |lifting| |lifting1| |exprex| |coerceL| |coerceS| |frobenius| - |computePowers| |pow| |An| |UnVectorise| |Vectorise| |setPoly| |index| - |exponent| |exQuo| |moebius| |rightRecip| |leftRecip| |leftPower| |rightPower| - |derivationCoordinates| |generator| |one?| |splitSquarefree| |normalDenom| - |reshape| |totalfract| |pushdterm| |pushucoef| |pushuconst| - |numberOfMonomials| |members| |multiset| |systemCommand| |mergeDifference| - |squareFreePrim| |compdegd| |univcase| |consnewpol| |nsqfree| |intChoose| - |coefChoose| |myDegree| |normDeriv2| |plenaryPower| |c02aff| |c02agf| |c05adf| - |c05nbf| |c05pbf| |c06eaf| |c06ebf| |c06ecf| |c06ekf| |c06fpf| |c06fqf| - |c06frf| |c06fuf| |c06gbf| |c06gcf| |c06gqf| |c06gsf| |d01ajf| |d01akf| - |d01alf| |d01amf| |d01anf| |d01apf| |d01aqf| |d01asf| |d01bbf| |d01fcf| - |d01gaf| |d01gbf| |d02bbf| |d02bhf| |d02cjf| |d02ejf| |d02gaf| |d02gbf| - |d02kef| |d02raf| |d03edf| |d03eef| |d03faf| |e01baf| |e01bef| |e01bff| - |e01bgf| |e01bhf| |e01daf| |e01saf| |e01sbf| |e01sef| |e01sff| |e02adf| - |e02aef| |e02agf| |e02ahf| |e02ajf| |e02akf| |e02baf| |e02bbf| |e02bcf| - |e02bdf| |e02bef| |e02daf| |e02dcf| |e02ddf| |e02def| |e02dff| |e02gaf| - |e02zaf| |e04dgf| |e04fdf| |e04gcf| |e04jaf| |e04mbf| |e04naf| |e04ucf| - |e04ycf| |f01brf| |f01bsf| |f01maf| |f01mcf| |f01qcf| |f01qdf| |f01qef| - |f01rcf| |f01rdf| |f01ref| |f02aaf| |f02abf| |f02adf| |f02aef| |f02aff| - |f02agf| |f02ajf| |f02akf| |f02awf| |f02axf| |f02bbf| |f02bjf| |f02fjf| - |f02wef| |f02xef| |f04adf| |f04arf| |f04asf| |f04atf| |f04axf| |f04faf| - |f04jgf| |f04maf| |f04mbf| |f04mcf| |f04qaf| |f07adf| |f07aef| |f07fdf| - |f07fef| |s01eaf| |s13aaf| |s13acf| |s13adf| |s14aaf| |s14abf| |s14baf| - |s15adf| |s15aef| |s17acf| |s17adf| |s17aef| |s17aff| |s17agf| |s17ahf| - |s17ajf| |s17akf| |s17dcf| |s17def| |s17dgf| |s17dhf| |s17dlf| |s18acf| - |s18adf| |s18aef| |s18aff| |s18dcf| |s18def| |s19aaf| |s19abf| |s19acf| - |s19adf| |s20acf| |s20adf| |s21baf| |s21bbf| |s21bcf| |s21bdf| - |fortranCompilerName| |fortranLinkerArgs| |aspFilename| |dimensionsOf| - |checkPrecision| |restorePrecision| |antiCommutator| |commutator| |associator| - |complexEigenvalues| |complexEigenvectors| |shift| |normalizedAssociate| - |normalize| |outputArgs| |normInvertible?| |normFactors| |npcoef| |listexp| - |characteristicPolynomial| |realEigenvalues| |realEigenvectors| - |halfExtendedResultant2| |halfExtendedResultant1| |extendedResultant| - |subResultantsChain| |lazyPseudoQuotient| |lazyPseudoRemainder| |bernoulliB| - |eulerE| |numeric| |complexNumeric| |numericIfCan| |complexNumericIfCan| - |FormatArabic| |ScanArabic| |FormatRoman| |ScanRoman| |ScanFloatIgnoreSpaces| - |ScanFloatIgnoreSpacesIfCan| |numericalIntegration| |rk4| |rk4a| |rk4qc| - |rk4f| |aromberg| |asimpson| |atrapezoidal| |romberg| |simpson| |trapezoidal| - |rombergo| |simpsono| |trapezoidalo| |sup| |inv| |imagE| |imagk| |imagj| - |imagi| |octon| |ODESolve| |constDsolve| |showTheIFTable| |clearTheIFTable| - |keys| |iFTable| |showIntensityFunctions| |expint| |diff| |algDsolve| - |denomLODE| |indicialEquations| |indicialEquation| |denomRicDE| - |leadingCoefficientRicDE| |constantCoefficientRicDE| |changeVar| |ratDsolve| - |indicialEquationAtInfinity| |reduceLODE| |singRicDE| |polyRicDE| |ricDsolve| - |triangulate| |solveInField| |wronskianMatrix| |variationOfParameters| - |factors| |nthFactor| |nthExpon| |overlap| |hcrf| |hclf| |lexico| |OMmakeConn| - |OMcloseConn| |OMconnInDevice| |OMconnOutDevice| |OMconnectTCP| |OMbindTCP| - |OMopenFile| |OMopenString| |OMclose| |OMsetEncoding| |OMputApp| |OMputAtp| - |OMputAttr| |OMputBind| |OMputBVar| |OMputError| |OMputObject| |OMputEndApp| - |OMputEndAtp| |OMputEndAttr| |OMputEndBind| |OMputEndBVar| |OMputEndError| - |OMputEndObject| |OMputInteger| |OMputFloat| |OMputVariable| |OMputString| - |OMputSymbol| |OMgetApp| |OMgetAtp| |OMgetAttr| |OMgetBind| |OMgetBVar| - |OMgetError| |OMgetObject| |OMgetEndApp| |OMgetEndAtp| |OMgetEndAttr| - |OMgetEndBind| |OMgetEndBVar| |OMgetEndError| |OMgetEndObject| |OMgetInteger| - |OMgetFloat| |OMgetVariable| |OMgetString| |OMgetSymbol| |OMgetType| - |OMencodingBinary| |OMencodingSGML| |OMencodingXML| |OMencodingUnknown| - |omError| |errorInfo| |errorKind| |OMReadError?| |OMUnknownSymbol?| - |OMUnknownCD?| |OMParseError?| |OMwrite| |po| |op| |OMread| |OMreadFile| - |OMreadStr| |OMlistCDs| |OMlistSymbols| |OMsupportsCD?| |OMsupportsSymbol?| - |OMunhandledSymbol| |OMreceive| |OMsend| |OMserve| |infinity| |makeop| - |opeval| |evaluateInverse| |evaluate| |conjug| |adjoint| |getDatabase| - |numericalOptimization| |optimize| |goodnessOfFit| |whatInfinity| |infinite?| - |finite?| |minusInfinity| |plusInfinity| |pureLex| |totalLex| |reverseLex| - |leftLcm| |rightExtendedGcd| |rightGcd| |rightExactQuotient| |rightRemainder| - |rightQuotient| |rightLcm| |leftExtendedGcd| |leftGcd| |leftExactQuotient| - |leftRemainder| |leftQuotient| |times| |apply| |monicLeftDivide| - |monicRightDivide| |leftDivide| |rightDivide| |hermiteH| |laguerreL| - |legendreP| |outputList| |writeBytes!| |writeByteIfCan!| |isOpen?| - |outputBinaryFile| |quo| |rem| |div| >= > ~= |blankSeparate| - |semicolonSeparate| |commaSeparate| |pile| |paren| |bracket| |prod| - |overlabel| |overbar| |prime| |quote| |supersub| |presuper| |presub| |super| - |sub| |rarrow| |assign| |slash| |over| |zag| |box| |label| |infix?| |postfix| - |infix| |prefix| |vconcat| |hconcat| |rspace| |vspace| |hspace| |superHeight| - |subHeight| |height| |width| |doubleFloatFormat| |messagePrint| |message| - |padecf| |pade| |root| |quotientByP| |moduloP| |modulus| |digits| - |continuedFraction| |pair| |light| |pastel| |bright| |dim| |dark| - |getSyntaxFormsFromFile| |surface| |coordinate| |partitions| |conjugates| - |shuffle| |shufflein| |sequences| |permutations| |lists| |atoms| |makeResult| - |is?| |Is| |addMatchRestricted| |insertMatch| |addMatch| |getMatch| |failed| - |failed?| |optpair| |getBadValues| |resetBadValues| |hasTopPredicate?| - |topPredicate| |setTopPredicate| |patternVariable| |withPredicates| - |setPredicates| |predicates| |hasPredicate?| |optional?| |multiple?| - |generic?| |quoted?| |inR?| |isList| |isQuotient| |isOp| |Zero| |satisfy?| - |addBadValue| |badValues| |retractable?| |ListOfTerms| |One| |PDESolve| - |leftFactor| |rightFactorCandidate| |measure| D |ptree| |coerceImages| - |fixedPoints| |odd?| |even?| |numberOfCycles| |cyclePartition| - |coerceListOfPairs| |coercePreimagesImages| |listRepresentation| |permanent| - |cycles| |cycle| |initializeGroupForWordProblem| <= < |movedPoints| - |wordInGenerators| |wordInStrongGenerators| |orbits| |orbit| - |permutationGroup| |wordsForStrongGenerators| |strongGenerators| |base| - |generators| |bivariateSLPEBR| |solveLinearPolynomialEquationByRecursion| - |factorByRecursion| |factorSquareFreeByRecursion| |randomR| |factorSFBRlcUnit| - |charthRoot| |conditionP| |solveLinearPolynomialEquation| - |factorSquareFreePolynomial| |factorPolynomial| |squareFreePolynomial| - |gcdPolynomial| |torsion?| |torsionIfCan| |getGoodPrime| |badNum| |mix| - |doubleDisc| |polyred| |padicFraction| |padicallyExpand| - |numberOfFractionalTerms| |nthFractionalTerm| |firstNumer| |firstDenom| - |compactFraction| |partialFraction| |gcdPrimitive| |symmetricGroup| - |alternatingGroup| |abelianGroup| |cyclicGroup| |dihedralGroup| |mathieu11| - |mathieu12| |mathieu22| |mathieu23| |mathieu24| |janko2| |rubiksGroup| - |youngGroup| |lexGroebner| |totalGroebner| |expressIdealMember| - |principalIdeal| |LagrangeInterpolation| |psolve| |wrregime| |rdregime| - |bsolve| |dmp2rfi| |se2rfi| |pr2dmp| |hasoln| |ParCondList| |redpps| |B1solve| - |factorset| |maxrank| |minrank| |minset| |nextSublist| |overset?| |ParCond| - |redmat| |regime| |sqfree| |inconsistent?| |debug| |numFunEvals| |setAdaptive| - |adaptive?| |setScreenResolution| |screenResolution| |setMaxPoints| - |maxPoints| |setMinPoints| |minPoints| |parametric?| |plotPolar| |debug3D| - |numFunEvals3D| |setAdaptive3D| |adaptive3D?| |setScreenResolution3D| - |screenResolution3D| |setMaxPoints3D| |maxPoints3D| |setMinPoints3D| - |minPoints3D| |tValues| |tRange| |plot| |pointPlot| |calcRanges| |assert| - |optional| |multiple| |fixPredicate| |patternMatch| |patternMatchTimes| - |bernoulli| |chebyshevT| |chebyshevU| |cyclotomic| |euler| |fixedDivisor| - |laguerre| |legendre| |dmpToHdmp| |hdmpToDmp| |pToHdmp| |hdmpToP| |dmpToP| - |pToDmp| |sylvesterSequence| |sturmSequence| |boundOfCauchy| - |sturmVariationsOf| |lazyVariations| |content| |primitiveMonomials| - |totalDegree| |minimumDegree| |monomials| |isPlus| |isTimes| |isExpt| - |isPower| |rroot| |qroot| |froot| |nthr| |port| |firstUncouplingMatrix| - |integral| |primitiveElement| |nextPrime| |prevPrime| |primes| |print| - |selectsecond| |selectfirst| |makeprod| |property| |equivOperands| |equiv?| - |impliesOperands| |implies?| |orOperands| |or?| |andOperands| |and?| - |notOperand| |not?| |variable?| |term| |term?| |equiv| |implies| |or| |and| - |merge!| |resultantEuclidean| |semiResultantEuclidean2| - |semiResultantEuclidean1| |indiceSubResultant| |indiceSubResultantEuclidean| - |semiIndiceSubResultantEuclidean| |degreeSubResultant| - |degreeSubResultantEuclidean| |semiDegreeSubResultantEuclidean| - |lastSubResultantEuclidean| |semiLastSubResultantEuclidean| - |subResultantGcdEuclidean| |semiSubResultantGcdEuclidean2| - |semiSubResultantGcdEuclidean1| |discriminantEuclidean| - |semiDiscriminantEuclidean| |chainSubResultants| |schema| |resultantReduit| - |resultantReduitEuclidean| |semiResultantReduitEuclidean| |divide| |Lazard| - |Lazard2| |nextsousResultant2| |resultantnaif| |resultantEuclideannaif| - |semiResultantEuclideannaif| |pdct| |powers| |partition| |complete| |pole?| - |monomial| |leadingMonomial| |zRange| |yRange| |xRange| |listBranches| - |triangular?| |rewriteIdealWithRemainder| |rewriteIdealWithHeadRemainder| - |remainder| |headRemainder| |roughUnitIdeal?| |roughEqualIdeals?| - |roughSubIdeal?| |roughBase?| |trivialIdeal?| |sort| |collectUpper| |collect| - |collectUnder| |mainVariable?| |mainVariables| |removeSquaresIfCan| - |unprotectedRemoveRedundantFactors| |removeRedundantFactors| - |certainlySubVariety?| |possiblyNewVariety?| |probablyZeroDim?| - |selectPolynomials| |selectOrPolynomials| |selectAndPolynomials| - |quasiMonicPolynomials| |univariate?| |univariatePolynomials| |linear?| - |linearPolynomials| |bivariate?| |bivariatePolynomials| - |removeRoughlyRedundantFactorsInPols| |removeRoughlyRedundantFactorsInPol| - |interReduce| |roughBasicSet| |crushedSet| - |rewriteSetByReducingWithParticularGenerators| - |rewriteIdealWithQuasiMonicGenerators| |squareFreeFactors| - |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInContents| - |removeRedundantFactorsInContents| |removeRedundantFactorsInPols| - |irreducibleFactors| |lazyIrreducibleFactors| - |removeIrreducibleRedundantFactors| |normalForm| |changeBase| - |companionBlocks| |xCoord| |yCoord| |zCoord| |rCoord| |thetaCoord| |phiCoord| - |color| |hue| |shade| |nthRootIfCan| |expIfCan| |logIfCan| |sinIfCan| - |cosIfCan| |tanIfCan| |cotIfCan| |secIfCan| |cscIfCan| |asinIfCan| |acosIfCan| - |atanIfCan| |acotIfCan| |asecIfCan| |acscIfCan| |sinhIfCan| |coshIfCan| - |tanhIfCan| |cothIfCan| |sechIfCan| |cschIfCan| |asinhIfCan| |acoshIfCan| - |atanhIfCan| |acothIfCan| |asechIfCan| |acschIfCan| |pushdown| |pushup| - |reducedDiscriminant| |idealSimplify| |definingInequation| |definingEquations| - |setStatus| |quasiAlgebraicSet| |radicalSimplify| |random| |denominator| - |numerator| |denom| |numer| |quadraticForm| |back| |front| |rotate!| - |dequeue!| |enqueue!| |quatern| |imagK| |imagJ| |imagI| |conjugate| |queue| - |nthRoot| |fractRadix| |wholeRadix| |cycleRagits| |prefixRagits| |fractRagits| - |wholeRagits| |radix| |randnum| |reseed| |seed| |rational| |rational?| - |rationalIfCan| |setvalue!| |setchildren!| |node?| |child?| |distance| - |leaves| |nodes| |rename| |rename!| |mainValue| |mainDefiningPolynomial| - |mainForm| |sqrt| |rischDE| |rischDEsys| |monomRDE| |baseRDE| |polyRDE| - |monomRDEsys| |baseRDEsys| |weighted| |rdHack1| |operator| |midpoint| - |midpoints| |realZeros| |mainCharacterization| |algebraicOf| |ReduceOrder| = - |setref| |deref| |ref| |radicalEigenvectors| |radicalEigenvector| - |radicalEigenvalues| |eigenMatrix| |normalise| |gramschmidt| - |orthonormalBasis| |antisymmetricTensors| |createGenericMatrix| - |symmetricTensors| |tensorProduct| |permutationRepresentation| - |completeEchelonBasis| |createRandomElement| |cyclicSubmodule| - |standardBasisOfCyclicSubmodule| |areEquivalent?| |isAbsolutelyIrreducible?| - |meatAxe| |scanOneDimSubspaces| |double| |expt| |lift| |showArrayValues| - |showScalarValues| |solveRetract| |variables| |mainVariable| |univariate| - |multivariate| |uniform01| |normal01| |exponential1| |chiSquare1| |normal| - |exponential| |chiSquare| F |t| |factorFraction| |componentUpperBound| |blue| - |green| |red| |whitePoint| |uniform| |binomial| |poisson| |geometric| - |ridHack1| |interpolate| |nullSpace| |nullity| |rank| |rowEchelon| |column| - |row| |qelt| |ncols| |nrows| |maxColIndex| |minColIndex| |maxRowIndex| - |minRowIndex| |antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix| - |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart| - |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right| - |left| |roman| |recoverAfterFail| |showTheRoutinesTable| |deleteRoutine!| - |getExplanations| |getMeasure| |changeMeasure| |changeThreshhold| - |selectMultiDimensionalRoutines| |selectNonFiniteRoutines| - |selectSumOfSquaresRoutines| |selectFiniteRoutines| |selectODEIVPRoutines| - |selectPDERoutines| |selectOptimizationRoutines| |selectIntegrationRoutines| - |routines| |mainSquareFreePart| |mainPrimitivePart| |mainContent| - |primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient| - |subResultantChain| |halfExtendedSubResultantGcd2| - |halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!| - |exactQuotient| |primPartElseUnitCanonical!| |primPartElseUnitCanonical| - |retract| |retractIfCan| |lazyResidueClass| |monicModulo| |lazyPseudoDivide| - |lazyPremWithDefault| |lazyPquo| |lazyPrem| |pquo| |prem| |supRittWu?| - |RittWuCompare| |mainMonomials| |mainCoefficients| |leastMonomial| - |mainMonomial| |quasiMonic?| |monic?| |leadingCoefficient| |deepestInitial| - |iteratedInitials| |deepestTail| |head| |mdeg| |mvar| |iterators| - |relativeApprox| |rootOf| |allRootsOf| |definingPolynomial| |positive?| - |negative?| |zero?| |augment| |lastSubResultant| |lastSubResultantElseSplit| - |invertibleSet| |invertible?| |invertibleElseSplit?| - |purelyAlgebraicLeadingMonomial?| |algebraicCoefficients?| - |purelyTranscendental?| |purelyAlgebraic?| |prepareSubResAlgo| - |internalLastSubResultant| |integralLastSubResultant| |toseLastSubResultant| - |toseInvertible?| |toseInvertibleSet| |toseSquareFreePart| |expression| - |quotedOperators| |pattern| |suchThat| |rule| |rules| |ruleset| |rur| |create| - |clearCache| |cache| |enterInCache| |currentCategoryFrame| |currentScope| - |pushNewContour| |findBinding| |contours| |structuralConstants| |coordinates| - |bounds| |equation| |incr| |high| |low| |hi| |lo| BY |body| |union| |subset?| - |symmetricDifference| |difference| |intersect| |set| |brace| |part?| |latex| - |hash| |delta| |member?| |enumerate| |setOfMinN| |elements| - |replaceKthElement| |incrementKthElement| |cdr| |car| |expr| |float| |integer| - |symbol| |destruct| |float?| |integer?| |symbol?| |string?| |list?| |pair?| - |atom?| |null?| |eq| |fortran| |startTable!| |stopTable!| |supDimElseRittWu?| - |algebraicSort| |moreAlgebraic?| |subTriSet?| |subPolSet?| - |internalSubPolSet?| |internalInfRittWu?| |internalSubQuasiComponent?| - |subQuasiComponent?| |removeSuperfluousQuasiComponents| |subCase?| - |removeSuperfluousCases| |prepareDecompose| |branchIfCan| |startTableGcd!| - |stopTableGcd!| |startTableInvSet!| |stopTableInvSet!| - |stosePrepareSubResAlgo| |stoseInternalLastSubResultant| - |stoseIntegralLastSubResultant| |stoseLastSubResultant| - |stoseInvertible?sqfreg| |stoseInvertibleSetsqfreg| |stoseInvertible?reg| - |stoseInvertibleSetreg| |stoseInvertible?| |stoseInvertibleSet| - |stoseSquareFreePart| |coleman| |inverseColeman| |listYoungTableaus| - |makeYoungTableau| |nextColeman| |nextLatticePermutation| |nextPartition| - |numberOfImproperPartitions| |subSet| |unrankImproperPartitions0| - |unrankImproperPartitions1| |subresultantSequence| |SturmHabichtSequence| - |SturmHabichtCoefficients| |SturmHabicht| |countRealRoots| - |SturmHabichtMultiple| |countRealRootsMultiple| |source| |target| |signature| - |signatureAst| |Or| |And| |Not| |xor| |not| |min| |max| ~ |/\\| |\\/| |depth| - |top| |pop!| |push!| |minordet| |determinant| |diagonalProduct| |trace| - |diagonal| |diagonalMatrix| |scalarMatrix| |hermite| |completeHermite| |smith| - |completeSmith| |diophantineSystem| |csubst| |particularSolution| |mapSolve| - |linear| |quadratic| |cubic| |quartic| |aLinear| |aQuadratic| |aCubic| - |aQuartic| |radicalSolve| |radicalRoots| |contractSolve| |decomposeFunc| - |unvectorise| |bubbleSort!| |insertionSort!| |check| |objects| |lprop| - |llprop| |lllp| |lllip| |lp| |mesh?| |mesh| |polygon?| |polygon| - |closedCurve?| |closedCurve| |curve?| |curve| |point?| |enterPointData| - |composites| |components| |numberOfComposites| |numberOfComponents| - |create3Space| |parse| |outputAsFortran| |outputAsScript| |outputAsTex| |abs| - |Beta| |digamma| |polygamma| |Gamma| |besselJ| |besselY| |besselI| |besselK| - |airyAi| |airyBi| |subNode?| |infLex?| |setEmpty!| |setStatus!| - |setCondition!| |setValue!| |copy| |status| |value| |empty?| |splitNodeOf!| - |remove!| |remove| |subNodeOf?| |nodeOf?| |result| |conditions| - |updateStatus!| |extractSplittingLeaf| |squareMatrix| |transpose| |rightTrim| - |leftTrim| |trim| |split| |position| |replace| |match?| |match| |substring?| - |suffix?| |prefix?| |upperCase!| |upperCase| |lowerCase!| |lowerCase| - |KrullNumber| |numberOfVariables| |algebraicDecompose| - |transcendentalDecompose| |internalDecompose| |decompose| |upDateBranches| - |printInfo| |preprocess| |internalZeroSetSplit| |internalAugment| |stack| - |possiblyInfinite?| |explicitlyFinite?| |nextItem| |init| |infiniteProduct| - |evenInfiniteProduct| |oddInfiniteProduct| |generalInfiniteProduct| - |filterUntil| |filterWhile| |generate| |showAll?| |showAllElements| |output| - |cons| |delay| |findCycle| |repeating?| |repeating| |exquo| |recip| |integers| - |oddintegers| |int| |mapmult| |deriv| |gderiv| |compose| |addiag| - |lazyIntegrate| |nlde| |powern| |mapdiv| |lazyGintegrate| |power| |sincos| - |sinhcosh| |asin| |acos| |atan| |acot| |asec| |acsc| |sinh| |cosh| |tanh| - |coth| |sech| |csch| |asinh| |acosh| |atanh| |acoth| |asech| |acsch| - |subresultantVector| |primitivePart| |pointData| |parent| |level| - |extractProperty| |extractClosed| |extractIndex| |extractPoint| |traverse| - |defineProperty| |closeComponent| |modifyPoint| |addPointLast| |addPoint2| - |addPoint| |merge| |deepCopy| |shallowCopy| |numberOfChildren| |children| - |child| |birth| |internal?| |root?| |leaf?| |rhs| |lhs| |construct| - |predicate| |sum| |outputForm| NOT AND EQ OR GE LE GT LT |sample| |list| - |string| |argscript| |superscript| |subscript| |script| |scripts| |scripted?| - |name| |resetNew| |symFunc| |symbolTableOf| |argumentListOf| |returnTypeOf| - |printHeader| |returnType!| |argumentList!| |endSubProgram| - |currentSubProgram| |newSubProgram| |clearTheSymbolTable| |showTheSymbolTable| - |symbolTable| |printTypes| |newTypeLists| |typeLists| |externalList| - |typeList| |parametersOf| |fortranTypeOf| |declare!| |empty| |case| - |compound?| |getOperands| |getOperator| |nil?| |buildSyntax| |autoCoerce| - 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|segment| SEGMENT |fmecg| |commonDenominator| |clearDenominator| - |splitDenominator| |monicRightFactorIfCan| |rightFactorIfCan| - |leftFactorIfCan| |monicDecomposeIfCan| |monicCompleteDecompose| |divideIfCan| - |noKaratsuba| |karatsubaOnce| |karatsuba| |separate| |pseudoDivide| - |pseudoQuotient| |composite| |subResultantGcd| |resultant| |discriminant| - |pseudoRemainder| |shiftLeft| |shiftRight| |karatsubaDivide| |monicDivide| - |divideExponents| |unmakeSUP| |makeSUP| |vectorise| |eval| |extend| - |approximate| |truncate| |order| |center| |terms| |squareFreePart| - |BumInSepFFE| |multiplyExponents| |laurentIfCan| |laurent| |laurentRep| - |rationalPower| |puiseux| |dominantTerm| |limitPlus| |split!| |setlast!| - |setrest!| |setelt| |setfirst!| |cycleSplit!| |concat!| |cycleTail| - |cycleLength| |cycleEntry| |third| |second| |tail| |last| |rest| |elt| |first| - |concat| |invmultisect| |multisect| |revert| |generalLambert| |evenlambert| - |oddlambert| |lambert| |lagrange| |differentiate| |univariatePolynomial| - |integrate| ** |polynomial| |multiplyCoefficients| |quoByVar| |coefficients| - |series| |stFunc1| |stFunc2| |stFuncN| |fixedPointExquo| |ode1| |ode2| |ode| - |mpsode| UP2UTS UTS2UP LODO2FUN RF2UTS |variable| |magnitude| |length| |cross| - |outerProduct| |dot| - |zero| + |vector| |scan| |reduce| |graphCurves| - |drawCurves| |update| |show| |scale| |connect| |region| |points| |units| - |getGraph| |putGraph| |graphs| |graphStates| |graphState| |makeViewport2D| - |viewport2D| |getPickedPoints| |key| |close| |write| |colorDef| |reset| - |intensity| |lighting| |clipSurface| |showClipRegion| |showRegion| - |hitherPlane| |eyeDistance| |perspective| |translate| |zoom| |rotate| - |drawStyle| |outlineRender| |diagonals| |axes| |controlPanel| |viewpoint| - |dimensions| |title| |resize| |move| |options| |modifyPointData| |subspace| - |makeViewport3D| |viewport3D| |viewDeltaYDefault| |viewDeltaXDefault| - |viewZoomDefault| |viewPhiDefault| |viewThetaDefault| |pointColorDefault| - |lineColorDefault| |axesColorDefault| |unitsColorDefault| |pointSizeDefault| - |viewPosDefault| |viewSizeDefault| |viewDefaults| |viewWriteDefault| - |viewWriteAvailable| |var1StepsDefault| |var2StepsDefault| |tubePointsDefault| - |tubeRadiusDefault| |void| |dimension| |crest| |cfirst| |sts2stst| |clikeUniv| - |weierstrass| |qqq| |integralBasis| |localIntegralBasis| |qualifier| - |mainExpression| |condition| |changeWeightLevel| |characteristicSerie| - |characteristicSet| |medialSet| |Hausdorff| |Frobenius| |transcendenceDegree| - |extensionDegree| |inGroundField?| |transcendent?| |algebraic?| |varList| |sh| - |mirror| |monomial?| |monom| |rquo| |lquo| |mindegTerm| |log| |exp| |product| - |LiePolyIfCan| |trunc| |degree| / |quasiRegular| |quasiRegular?| |constant| - |constant?| |coef| |mindeg| |maxdeg| |#| |coerce| |map| |reductum| * - |RemainderList| |unexpand| |expand| Y |triangSolve| |univariateSolve| - |realSolve| |positiveSolve| |squareFree| |convert| |linearlyDependentOverZ?| - |linearDependenceOverZ| |solveLinearlyOverQ| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| - |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| + |Record| |Union| |leftScalarTimes!| |selectMultiDimensionalRoutines| + |getGoodPrime| |RemainderList| |ipow| |basis| |makeprod| + |trapezoidalo| |sinhcosh| |say| |rightScalarTimes!| + |selectNonFiniteRoutines| |badNum| |unexpand| |factorial| + |normalElement| |equivOperands| |sup| |subresultantVector| + |normalDeriv| |times!| |mix| |selectSumOfSquaresRoutines| |name| + |triangSolve| |multinomial| |minimalPolynomial| |equiv?| |imagE| + |primitivePart| |e| |ran| |power!| |doubleDisc| |selectFiniteRoutines| + |body| |univariateSolve| |permutation| |eof?| |impliesOperands| + |imagk| |pointData| |highCommonTerms| |gradient| + |selectODEIVPRoutines| |polyred| |realSolve| |stirling1| |imagj| + |parent| |mapCoef| |divergence| |selectPDERoutines| |reset| + |padicFraction| |positiveSolve| |stirling2| |genericRightDiscriminant| + |alternatingGroup| |imagi| |extractProperty| |nthCoef| |laplacian| + |selectOptimizationRoutines| |padicallyExpand| |squareFree| + |summation| |genericRightTraceForm| |abelianGroup| |octon| + |extractClosed| |binomThmExpt| |hessian| |selectIntegrationRoutines| + |write| |numberOfFractionalTerms| |linearlyDependentOverZ?| + |factorials| |genericLeftDiscriminant| |cyclicGroup| |ODESolve| + |extractIndex| |pomopo!| |nthFractionalTerm| |linearDependenceOverZ| + |mkcomm| |genericLeftTraceForm| |dihedralGroup| |replace| + |constDsolve| |extractPoint| |numer| |mapExponents| |entries| + |setchildren!| |firstNumer| |solveLinearlyOverQ| |polarCoordinates| + |genericRightNorm| |mathieu11| |showTheIFTable| |traverse| Y |denom| + |linearAssociatedLog| |key?| |node?| |firstDenom| |imaginary| + |genericRightTrace| |mathieu12| |clearTheIFTable| |defineProperty| + |linearAssociatedOrder| |symbolIfCan| |child?| |compactFraction| + |solid| |genericRightMinimalPolynomial| |mathieu22| |pi| + |linearAssociatedExp| |close| |argument| |distance| |partialFraction| + |solid?| |rightRankPolynomial| |mathieu23| |f04arf| |aQuartic| + |infinity| |createNormalElement| |constantKernel| |nodes| + |gcdPrimitive| |denominators| |genericLeftNorm| |mathieu24| |f04asf| + |radicalSolve| |setLabelValue| |display| |constantIfCan| |rename| + |symmetricGroup| |numerators| |genericLeftTrace| |f04atf| |janko2| + |radicalRoots| |remove| |getCode| |kovacic| |rename!| |convergents| + |genericLeftMinimalPolynomial| |rubiksGroup| |f04axf| |contractSolve| + |kernel| |constant| |printCode| |laplace| |mainValue| |superHeight| + |cross| |approximants| |leftRankPolynomial| |f04faf| |youngGroup| + |decomposeFunc| |last| |draw| |printStatement| |trailingCoefficient| + |mainDefiningPolynomial| |subHeight| |dot| |assoc| |reducedForm| + |generic| |lexGroebner| |f04jgf| |unvectorise| |block| + |normalizeIfCan| |mainForm| |doubleFloatFormat| |scan| + |partialQuotients| |rightUnits| |totalGroebner| |f04maf| |bubbleSort!| + |returns| |input| |polCase| |rischDE| |messagePrint| |graphCurves| + |partialDenominators| |leftUnits| |expressIdealMember| |f04mbf| + |insertionSort!| |#| |goto| |library| |distFact| |rischDEsys| |padecf| + |drawCurves| |partialNumerators| |compBound| |principalIdeal| |f04mcf| + |check| |repeatUntilLoop| |identification| |monomRDE| |pade| |scale| + |reducedContinuedFraction| |tablePow| |LagrangeInterpolation| |f04qaf| + |lprop| |whileLoop| |LyndonCoordinates| |baseRDE| |root| |connect| + |push| |solveid| |psolve| |f07adf| |llprop| |forLoop| SEGMENT + |LyndonBasis| |polyRDE| |quotientByP| |region| |interpret| |bindings| + NOT |testModulus| |wrregime| |f07aef| |lllp| |sin?| |set| + |zeroDimensional?| |monomRDEsys| |moduloP| |points| |cartesian| OR + |HenselLift| |rdregime| |f07fdf| |lllip| |zeroVector| |fglmIfCan| + |baseRDEsys| |modulus| |getGraph| |polar| AND |completeHensel| + |bsolve| |f07fef| |mesh?| |zeroSquareMatrix| |groebner| |weighted| + |digits| |putGraph| |cylindrical| |multMonom| |dmp2rfi| |s01eaf| + |mesh| |top| |identitySquareMatrix| |lexTriangular| |rdHack1| + |continuedFraction| |graphs| |spherical| |build| |se2rfi| |s13aaf| + |polygon?| |continue| |lSpaceBasis| |squareFreeLexTriangular| + |operator| |light| |graphStates| |parabolic| |leadingIndex| |pr2dmp| + |s13acf| |polygon| |finiteBasis| |belong?| |midpoint| |pastel| + |graphState| |parabolicCylindrical| |leadingExponent| |hasoln| + |s13adf| |closedCurve?| |principal?| |Ci| |dark| |midpoints| + |makeViewport2D| |direction| |cons| |paraboloidal| |GospersMethod| + |ParCondList| |s14aaf| |closedCurve| |divisor| |Si| + |getSyntaxFormsFromFile| |realZeros| |viewport2D| |createThreeSpace| + |ellipticCylindrical| |nextSubsetGray| |redpps| |s14abf| |curve?| + |properties| |useNagFunctions| |Ei| |mainCharacterization| |surface| + |getPickedPoints| |prolateSpheroidal| |firstSubsetGray| |B1solve| + |s14baf| |curve| |rationalPoints| |linGenPos| |algebraicOf| + |translate| |coordinate| |colorDef| |oblateSpheroidal| + |clipPointsDefault| |factorset| |s15adf| |point?| |nonSingularModel| + |show| |groebgen| |ReduceOrder| |partitions| |intensity| |bipolar| * + |drawToScale| |maxrank| |s15aef| |enterPointData| |ptree| + |algSplitSimple| |totolex| |setref| |conjugates| |lighting| + |bipolarCylindrical| |adaptive| |minrank| |s17acf| |composites| + |hyperelliptic| |trace| |minPol| |deref| |shuffle| |clipSurface| + |source| |toroidal| |figureUnits| |minset| |s17adf| |components| + |elliptic| |computeBasis| |ref| |shufflein| |showClipRegion| |conical| + |putColorInfo| |nextSublist| |s17aef| |numberOfComposites| ~= + |integralDerivationMatrix| |coord| |radicalEigenvectors| |sequences| + |showRegion| |modTree| |mr| |appendPoint| |overset?| |s17aff| + |numberOfComponents| |coerce| |integralRepresents| |anticoord| + |radicalEigenvector| |permutations| |hitherPlane| |multiEuclideanTree| + |constructorName| |component| |ParCond| |s17agf| |create3Space| + |construct| |integralCoordinates| |intcompBasis| |radicalEigenvalues| + |atoms| |eyeDistance| |complexZeros| |ranges| |redmat| |s17ahf| + |outputAsScript| |yCoordinates| |choosemon| |eigenMatrix| |makeResult| + |perspective| |target| |divisorCascade| |pointLists| |regime| |s17ajf| + |outputAsTex| |buildSyntax| |inverseIntegralMatrixAtInfinity| + |transform| |normalise| |is?| |zoom| |graeffe| |makeGraphImage| + |sqfree| |s17akf| |abs| |solve| |integralMatrixAtInfinity| |formula| + |pack!| |gramschmidt| |Is| |rotate| |pleskenSplit| |graphImage| + |inconsistent?| |s17dcf| |Beta| |inverseIntegralMatrix| |complexLimit| + |orthonormalBasis| |addMatchRestricted| |drawStyle| + |reciprocalPolynomial| |groebSolve| |numFunEvals| |s17def| |digamma| + |integralMatrix| |limit| |antisymmetricTensors| |insertMatch| + |outlineRender| |rootRadius| |testDim| |setAdaptive| |s17dgf| + |polygamma| |reduceBasisAtInfinity| |linearlyDependent?| + |createGenericMatrix| |addMatch| |diagonals| |schwerpunkt| + |genericPosition| |adaptive?| |s17dhf| |Gamma| |normalizeAtInfinity| + |linearDependence| |symmetricTensors| |nrows| |getMatch| |axes| + |setErrorBound| |lfunc| |setScreenResolution| |s17dlf| |besselJ| + |complementaryBasis| |solveLinear| |tensorProduct| |ncols| |failed?| + |controlPanel| |startPolynomial| |inHallBasis?| |s18acf| + |screenResolution| |sum| |besselY| |integral?| |reducedSystem| + |permutationRepresentation| |optpair| |viewpoint| |compound?| + |cycleElt| |sort| |reorder| |setMaxPoints| |s18adf| |besselI| + |integralAtInfinity?| |duplicates?| |completeEchelonBasis| + |getBadValues| |dimensions| |getOperands| |computeCycleLength| + |headAst| |maxPoints| |s18aef| |besselK| |integralBasisAtInfinity| + |mapGen| |createRandomElement| |resetBadValues| |resize| + |computeCycleEntry| |heap| |setMinPoints| |s18aff| |airyAi| + |ramified?| |mapExpon| |plusInfinity| |cyclicSubmodule| + |hasTopPredicate?| |move| |arity| |gcdprim| |minPoints| |s18dcf| + |airyBi| |clearCache| |triangularSystems| |ramifiedAtInfinity?| + |commutativeEquality| |minusInfinity| |standardBasisOfCyclicSubmodule| + |topPredicate| |modifyPointData| |coerceP| |gcdcofact| |parametric?| + |s18def| |subNode?| |rootDirectory| |setelt| |singular?| |leftMult| + |areEquivalent?| |setTopPredicate| |subspace| |gcdcofactprim| + |plotPolar| |s19aaf| |infLex?| |singularAtInfinity?| |rightMult| + |isAbsolutelyIrreducible?| |patternVariable| |makeViewport3D| + |equality| |lintgcd| |debug3D| |s19abf| |setEmpty!| |copy| + |branchPoint?| |makeUnit| |meatAxe| |withPredicates| |viewport3D| + |nary?| |hex| |numFunEvals3D| |s19acf| |setStatus!| + |branchPointAtInfinity?| |reverse!| |scanOneDimSubspaces| + |setPredicates| |viewDeltaYDefault| |unary?| |every?| |setAdaptive3D| + |s19adf| |setCondition!| |makeMulti| |retractIfCan| |expt| |retract| + |predicates| |viewDeltaXDefault| |nullary?| |match?| |any?| + |adaptive3D?| |s20acf| |setValue!| |swap| |autoCoerce| |type| + |makeTerm| |showArrayValues| |hasPredicate?| |viewZoomDefault| + |derivative| |arguments| |host| |setScreenResolution3D| |s20adf| + |empty?| |minPoly| |listOfMonoms| |showScalarValues| |optional?| + |viewPhiDefault| |constantOperator| |precision| |width| |trueEqual| + |screenResolution3D| |s21baf| |splitNodeOf!| |freeOf?| |directory| + |symmetricSquare| |solveRetract| |simplify| |multiple?| + |viewThetaDefault| |constantOpIfCan| |s21bbf| |remove!| |error| + |operators| |factor1| |mainVariable| |htrigs| |generic?| + |pointColorDefault| |integerBound| |useSingleFactorBound?| |s21bcf| + |subNodeOf?| |assert| |substring?| |mainKernel| |symmetricProduct| + |uniform01| |simplifyExp| |quoted?| |lineColorDefault| |setright!| + |numeric| |useSingleFactorBound| |s21bdf| |nodeOf?| |distribute| + |setleft!| |symmetricPower| |normal01| |simplifyLog| |inR?| + |axesColorDefault| |radical| |inc| |useEisensteinCriterion?| + |fortranCompilerName| |updateStatus!| |suffix?| + |functionIsFracPolynomial?| |isList| |unitsColorDefault| + |brillhartIrreducible?| |useEisensteinCriterion| |fortranLinkerArgs| + |extractSplittingLeaf| |problemPoints| |perfectSquare?| |asinIfCan| + |isOp| |pointSizeDefault| |brillhartTrials| |eisensteinIrreducible?| + |aspFilename| |squareMatrix| |prefix?| |zerosOf| |perfectSqrt| + |acosIfCan| |map| |satisfy?| |viewPosDefault| |noLinearFactor?| + |tryFunctionalDecomposition?| |optional| |dimensionsOf| |transpose| + |singularitiesOf| |approxSqrt| |atanIfCan| |addBadValue| + |viewSizeDefault| |insertRoot!| |tryFunctionalDecomposition| + |polynomialZeros| |generateIrredPoly| |acotIfCan| |badValues| + |viewDefaults| |binarySearchTree| |btwFact| |e01saf| |startTableGcd!| + |f2df| |complexExpand| |asecIfCan| |retractable?| |viewWriteDefault| + |nor| |beauzamyBound| |e01sbf| |stopTableGcd!| |ef2edf| + |complexIntegrate| |acscIfCan| |ListOfTerms| |viewWriteAvailable| + |nand| |bombieriNorm| |e01sef| |startTableInvSet!| |optimize| + |ocf2ocdf| |dimensionOfIrreducibleRepresentation| |sinhIfCan| + |convert| |binaryTournament| |rootBound| |e01sff| |stopTableInvSet!| + |infix?| |socf2socdf| |irreducibleRepresentation| |coshIfCan| + |infinite?| |pseudoRemainder| |any| |binaryTree| |signature| + |singleFactorBound| |e02adf| |stosePrepareSubResAlgo| |mask| BY + |df2fi| |checkRur| |tanhIfCan| |finite?| |shiftLeft| |byte| + |quadraticNorm| |null| |e02aef| |stoseInternalLastSubResultant| |init| + |edf2fi| |cAcsch| |cothIfCan| |pureLex| |shiftRight| |subtractIfCan| + |infinityNorm| |case| |e02agf| |stoseIntegralLastSubResultant| + |edf2df| |cAsech| |sechIfCan| |totalLex| |karatsubaDivide| + |setPosition| |scaleRoots| |Zero| |e02ahf| |stoseLastSubResultant| + |pattern| |expenseOfEvaluation| |cAcoth| |cschIfCan| |reverseLex| + |monicDivide| |generalizedContinuumHypothesisAssumed| |shiftRoots| + |One| |tail| |e02ajf| |stoseInvertible?sqfreg| |numberOfOperations| + |cAtanh| |asinhIfCan| |leftLcm| |divideExponents| + |generalizedContinuumHypothesisAssumed?| |degreePartition| |e02akf| + |stoseInvertibleSetsqfreg| |edf2efi| |cAcosh| |acoshIfCan| + |rightExtendedGcd| |unmakeSUP| |countable?| |factorOfDegree| |e02baf| + |stoseInvertible?reg| |dfRange| |cAsinh| |atanhIfCan| |printInfo| + |rightGcd| |makeSUP| |Aleph| |factorsOfDegree| |e02bbf| + |stoseInvertibleSetreg| |char| |message| |dflist| |cCsch| |acothIfCan| + |rightExactQuotient| |vectorise| |unravel| |pascalTriangle| |e02bcf| + |stoseInvertible?| |df2mf| |cSech| |asechIfCan| |rightRemainder| + |extend| |lift| |expr| |id| |isQuotient| |leviCivitaSymbol| + |rangePascalTriangle| |elt| |e02bdf| |stoseInvertibleSet| |plus| + |ldf2vmf| |cCoth| |acschIfCan| |rightQuotient| |truncate| |reduce| + |kroneckerDelta| |sizePascalTriangle| |e02bef| |stoseSquareFreePart| + |edf2ef| |cTanh| |pushdown| |rightLcm| |order| |table| |reindex| + |fillPascalTriangle| |e02daf| |coleman| |vedf2vef| |cCosh| |pushup| + |leftExtendedGcd| |terms| |new| |alphanumeric| |cond| |safeCeiling| + |e02dcf| |inverseColeman| |float| |df2st| |cSinh| + |reducedDiscriminant| |leftGcd| |squareFreePart| |variable| + |alphabetic| |safeFloor| |e02ddf| |listYoungTableaus| |times| |f2st| + |cAcsc| |idealSimplify| |leftExactQuotient| |BumInSepFFE| |iterators| + |height| |hexDigit| |safetyMargin| |e02def| |makeYoungTableau| + |ldf2lst| |cAsec| |definingInequation| |leftRemainder| + |multiplyExponents| |digit| |sumSquares| |e02dff| |nextColeman| + |implies| |sdf2lst| |cAcot| |definingEquations| |leftQuotient| + |laurentIfCan| |tree| |t| |status| |charClass| |euclideanNormalForm| + |e02gaf| |nextLatticePermutation| |getlo| |cAtan| |setStatus| + |monicLeftDivide| |laurentRep| |alphanumeric?| |euclideanGroebner| + |e02zaf| |nextPartition| |monom| |xor| |gethi| |cAcos| + |quasiAlgebraicSet| |monicRightDivide| |rationalPower| |lowerCase?| + |factorGroebnerBasis| |e04dgf| |numberOfImproperPartitions| + |outputMeasure| |cAsin| |radicalSimplify| |leftDivide| |dominantTerm| + |upperCase?| |groebnerFactorize| |e04fdf| |subSet| |measure2Result| + |cCsc| |denominator| |rightDivide| |limitPlus| |alphabetic?| |credPol| + |e04gcf| |unrankImproperPartitions0| |common| GE |att2Result| |cSec| + |numerator| |hermiteH| |split!| |hexDigit?| |redPol| = |e04jaf| + |unrankImproperPartitions1| GT |iflist2Result| |cCot| |quadraticForm| + |laguerreL| |setlast!| |left| |escape| |arg1| |gbasis| |e04mbf| + |subresultantSequence| LE |pdf2ef| |cTan| |back| |legendreP| + |setrest!| |ord| |right| |critT| |arg2| |reverse| < |e04naf| + |SturmHabichtSequence| LT |currentSubProgram| |pdf2df| |cCos| |front| + |writeBytes!| |cyclic?| |setfirst!| |mkIntegral| |critM| > |e04ucf| + |SturmHabichtCoefficients| |showSummary| |newSubProgram| |df2ef| + |cSin| |rotate!| |writeByteIfCan!| |complexNormalize| |cycleSplit!| + |radPoly| |conditions| |critB| <= |e04ycf| |SturmHabicht| + |clearTheSymbolTable| |fi2df| |cLog| |dequeue!| |isOpen?| |concat!| + |rootPoly| |match| |critBonD| >= |f01brf| |countRealRoots| |erf| + |showTheSymbolTable| |mat| |showAttributes| |cExp| |enqueue!| + |outputBinaryFile| |cycleTail| |loadNativeModule| |ravel| |goodPoint| + |critMTonD1| |f01bsf| |SturmHabichtMultiple| |printTypes| |neglist| + |cRationalPower| |quatern| |blankSeparate| |cycleLength| |chvar| + |reshape| |critMonD1| |f01maf| |countRealRootsMultiple| |newTypeLists| + |multiEuclidean| |cPower| |imagK| |semicolonSeparate| |cycleEntry| + |find| |redPo| + |f01mcf| |signatureAst| |extendedEuclidean| + |seriesToOutputForm| |imagJ| |commaSeparate| |depth| |invmultisect| + |clipParametric| |hMonic| - |f01qcf| |pop!| |typeLists| + |euclideanSize| |iCompose| |imagI| |pile| |multisect| |clipWithRanges| + |updatF| / |f01qdf| |push!| |externalList| |sizeLess?| + |taylorQuoByVar| |conjugate| |paren| |revert| |numberOfHues| |sPol| + |f01qef| |minordet| |simplifyPower| |iExquo| |queue| |bracket| + |generalLambert| |yellow| |update| |updatD| |f01rcf| |determinant| + |number?| |getStream| |nthRoot| |prod| |evenlambert| |iifact| + |minGbasis| |f01rdf| |diagonalProduct| |seriesSolve| |getRef| + |equation| |fractRadix| |overlabel| |oddlambert| |getOperator| + |iibinom| |lepol| |f01ref| |diagonal| |constantToUnaryFunction| + |makeSeries| |wholeRadix| |overbar| |lambert| |fortran| |nil?| + |iiperm| |prinshINFO| |f02aaf| |diagonalMatrix| |log| |tubePlot| GF2FG + |cycleRagits| |prime| |lagrange| |iipow| |prindINFO| |f02abf| + |scalarMatrix| |exponentialOrder| FG2F |prefixRagits| |quote| + |univariatePolynomial| |fprindINFO| |f02adf| |hermite| |digit?| + |completeEval| F2FG |fractRagits| |supersub| |integrate| |rightRank| + |position| |prinpolINFO| |f02aef| |completeHermite| |function| ~ + |lowerPolynomial| |explogs2trigs| |wholeRagits| |presuper| + |multiplyCoefficients| |doubleRank| |prinb| |f02aff| |smith| + |raisePolynomial| |trigs2explogs| |radix| |presub| |quoByVar| + |weakBiRank| |critpOrder| |outputList| |f02agf| |completeSmith| |open| + |swap!| |randnum| |super| |coefficients| |biRank| |makeCrit| |f02ajf| + |diophantineSystem| |iilog| |fill!| |reseed| |sub| |stFunc1| + |basisOfCommutingElements| |virtualDegree| |f02akf| |csubst| |iisin| + |minIndex| |seed| |rarrow| |stFunc2| |basisOfLeftAnnihilator| |stack| + |conditionsForIdempotents| |f02awf| |particularSolution| |iicos| + |maxIndex| |rational| |assign| |stFuncN| |basisOfRightAnnihilator| + |f02axf| |mapSolve| |iitan| |entry?| |rational?| |slash| + |fixedPointExquo| |basisOfLeftNucleus| |nilFactor| |f02bbf| + |quadratic| |iicot| |indices| |rationalIfCan| |over| |ode1| + |basisOfRightNucleus| |regularRepresentation| |f02bjf| |cubic| |dim| + |iisec| |index?| |setvalue!| |zag| |ode2| |basisOfMiddleNucleus| + |script| |traceMatrix| |f02fjf| |quartic| |iicsc| |declare| |postfix| + |ode| |basisOfNucleus| |leader| |randomLC| |f02wef| |aLinear| |iiasin| + |eulerPhi| |collect| |infix| |complexElementary| |mpsode| + |basisOfCenter| |minimize| |f02xef| |aQuadratic| |iiacos| |fibonacci| + |mantissa| |collectUnder| |double| |vconcat| |trigs| UP2UTS + |basisOfLeftNucloid| |tex| |module| |f04adf| |aCubic| |lcm| |iiatan| + |harmonic| |mainVariable?| |hconcat| UTS2UP |basisOfRightNucloid| + |rightRegularRepresentation| |iiacot| |jacobi| |mainVariables| + |rspace| LODO2FUN |basisOfCentroid| |leftRegularRepresentation| + |squareFreePrim| |internalLastSubResultant| |append| |iiasec| + |moebiusMu| |removeSquaresIfCan| |vspace| RF2UTS + |radicalOfLeftTraceForm| |rightTraceMatrix| |compdegd| + |checkPrecision| |integralLastSubResultant| |gcd| |iiacsc| + |numberOfDivisors| |unprotectedRemoveRedundantFactors| |hspace| + |magnitude| |showTypeInOutput| |leftTraceMatrix| |univcase| + |toseLastSubResultant| |false| |iisinh| |sumOfDivisors| + |removeRedundantFactors| |objectOf| |rightDiscriminant| |consnewpol| + |toseInvertible?| |lhs| |iicosh| |sumOfKthPowerDivisors| + |certainlySubVariety?| |OMputString| |stronglyReduced?| |domainOf| + |leftDiscriminant| |nsqfree| |toseInvertibleSet| |iitanh| |rhs| + |HermiteIntegrate| |OMputSymbol| |declare!| |possiblyNewVariety?| + |prefix| |reduced?| |applyRules| |represents| |intChoose| + |toseSquareFreePart| |second| |iicoth| |palgint| |probablyZeroDim?| + |OMgetApp| |normalized?| |localUnquote| |node| |test| |mergeFactors| + |coefChoose| |quotedOperators| |iisech| |palgextint| |OMgetAtp| + |selectPolynomials| |quasiComponent| |cyclicParents| |setColumn!| + |isMult| |myDegree| |rur| |iicsch| |palglimint| |OMgetAttr| + |selectOrPolynomials| |initials| |cyclicEqual?| |setRow!| |exprToXXP| + |normDeriv2| |create| |iiasinh| |palgRDE| |selectAndPolynomials| + |OMgetBind| |basicSet| |oneDimensionalArray| |exprToUPS| + |plenaryPower| |enterInCache| |iiacosh| |dec| |palgLODE| + |quasiMonicPolynomials| |OMgetBVar| |infRittWu?| |associatedSystem| + |exprToGenUPS| |c02aff| |currentCategoryFrame| |iiatanh| + |splitConstant| |univariate?| |OMgetError| |getCurve| + |uncouplingMatrices| |localAbs| |c02agf| |currentScope| |iiacoth| + |pmComplexintegrate| |segment| |univariatePolynomials| |OMgetObject| + |listLoops| |associatedEquations| |universe| |c05adf| |pushNewContour| + |iiasech| |pmintegrate| |linear?| |OMgetEndApp| |closed?| |arrayStack| + |complement| |c05nbf| |findBinding| |iiacsch| |infieldint| + |linearPolynomials| |OMgetEndAtp| |open?| |setButtonValue| + |cardinality| |c05pbf| |contours| |call| |specialTrigs| |extendedint| + |bivariate?| |OMgetEndAttr| |setClosed| |setAttributeButtonStep| + |internalIntegrate0| |c06eaf| |structuralConstants| |localReal?| |eq| + |limitedint| |bivariatePolynomials| |OMgetEndBind| |tube| + |resetAttributeButtons| |makeCos| |c06ebf| |coordinates| |void| + |rischNormalize| |iter| |integerIfCan| + |removeRoughlyRedundantFactorsInPols| |OMgetEndBVar| |unitVector| + |getButtonValue| |makeSin| |c06ecf| |bounds| |realElementary| + |internalIntegrate| |removeRoughlyRedundantFactorsInPol| + |OMgetEndError| |cosSinInfo| |decrease| |iiGamma| |c06ekf| |high| + |list| |exquo| |validExponential| |infieldIntegrate| |interReduce| + |OMgetEndObject| |loopPoints| |increase| |iiabs| |c06fpf| |low| |car| + |div| |/\\| |rootNormalize| |limitedIntegrate| |roughBasicSet| + |OMgetInteger| |generalTwoFactor| |morphism| |bringDown| |c06fqf| + |subset?| |next| |cdr| |quo| |\\/| |tanQ| |extendedIntegrate| + |crushedSet| |hash| |OMgetFloat| |generalSqFr| |balancedFactorisation| + |newReduc| |c06frf| |symmetricDifference| |setDifference| |callForm?| + |count| |varselect| |OMgetVariable| + |rewriteSetByReducingWithParticularGenerators| |twoFactor| |center| + |mapDown!| |logical?| |c06fuf| |difference| |setIntersection| |rem| + |getIdentifier| |kmax| |rewriteIdealWithQuasiMonicGenerators| + |OMgetString| |setOrder| |mapUp!| |character?| |c06gbf| |intersect| + |setUnion| |getConstant| |exp| |ksec| |squareFreeFactors| + |OMgetSymbol| |getOrder| |setleaves!| |doubleComplex?| |c06gcf| + |part?| |apply| |select!| |approximate| |vark| + |univariatePolynomialsGcds| |OMgetType| |less?| |balancedBinaryTree| + |previous| |complex?| |c06gqf| |latex| |delete!| |symbolTable| + |removeConstantTerm| |removeRoughlyRedundantFactorsInContents| + |OMencodingBinary| |userOrdered?| |sylvesterMatrix| |double?| |c06gsf| + |member?| |size| |sn| |mkPrim| |removeRedundantFactorsInContents| + |OMencodingSGML| |largest| |bezoutMatrix| |ffactor| |d01ajf| + |enumerate| |dn| |pushFortranOutputStack| |intPatternMatch| + |removeRedundantFactorsInPols| |OMencodingXML| |more?| + |bezoutResultant| |qfactor| |d01akf| |setOfMinN| |sncndn| + |popFortranOutputStack| |primintegrate| |irreducibleFactors| + |OMencodingUnknown| |setVariableOrder| |bezoutDiscriminant| |UP2ifCan| + |d01alf| |elements| |first| |rule| |categoryFrame| |outputAsFortran| + |expintegrate| |lazyIrreducibleFactors| |omError| |getVariableOrder| + |bfEntry| |anfactor| |d01amf| |replaceKthElement| |rest| + |setProperties!| |tanintegrate| |removeIrreducibleRedundantFactors| + |errorInfo| |resetVariableOrder| |bfKeys| |fortranCharacter| |d01anf| + |incrementKthElement| |substitute| |getProperties| |primextendedint| + |normalForm| |errorKind| |prime?| |lp| |inspect| + |fortranDoubleComplex| |systemCommand| |d01apf| |hostPlatform| + |float?| |removeDuplicates| |not| |setProperty!| |expextendedint| + |changeBase| |OMReadError?| |rationalFunction| |extract!| + |fortranComplex| |d01aqf| |nativeModuleExtension| |integer?| |key| + |getProperty| |primlimitedint| |companionBlocks| |OMUnknownSymbol?| + |taylorIfCan| |bag| |fortranLogical| |d01asf| |bumprow| |symbol?| + |scopes| |zero| |explimitedint| |xCoord| |OMUnknownCD?| |removeZeroes| + |binding| |fortranInteger| |d01bbf| |bumptab| |normal| |string?| + |filename| |eigenvalues| |primextintfrac| |yCoord| |OMParseError?| + |taylorRep| |position!| |fortranDouble| |d01fcf| |bumptab1| |list?| + |not?| |eigenvector| |And| |primlimintfrac| |zCoord| |OMwrite| + |factorSquareFree| |setProperties| |fortranReal| |d01gaf| |untab| + |pair?| |parse| |generalizedEigenvector| |Or| |primintfldpoly| + |rCoord| |po| |henselFact| |setProperty| |external?| |d01gbf| |bat1| + |atom?| |generalizedEigenvectors| |Not| |expintfldpoly| |thetaCoord| + |OMread| |hasHi| |deleteProperty!| |scalarTypeOf| |d02bbf| |bat| + |null?| |eigenvectors| |monomialIntegrate| |phiCoord| |OMreadFile| + |fmecg| |has?| |fortranCarriageReturn| |d02bhf| |tab1| |startTable!| + |label| |factorAndSplit| |monomialIntPoly| |color| |OMreadStr| + |commonDenominator| |comparison| |fortranLiteral| |d02cjf| |tab| + |stopTable!| |rightOne| |vector| |inverseLaplace| |hue| |OMlistCDs| + |clearDenominator| |fortranLiteralLine| |d02ejf| |lex| + |supDimElseRittWu?| |leftOne| |differentiate| |bothWays| |shade| + |OMlistSymbols| |splitDenominator| |processTemplate| |d02gaf| + |algebraicSort| |rightZero| |iprint| |nthRootIfCan| |OMsupportsCD?| + |monicRightFactorIfCan| |makeFR| |d02gbf| |moreAlgebraic?| |leftZero| + |elem?| |expIfCan| |OMsupportsSymbol?| |rightFactorIfCan| + |musserTrials| |d02kef| |subTriSet?| |notelem| |logIfCan| + |OMunhandledSymbol| |leftFactorIfCan| |flatten| |sample| + |stopMusserTrials| |d02raf| |subPolSet?| |setnext!| |logpart| + |sinIfCan| |OMreceive| |monicDecomposeIfCan| |numberOfFactors| + |d03edf| |internalSubPolSet?| |setprevious!| |ratpart| |cosIfCan| + |OMsend| |monicCompleteDecompose| |argscript| |modularFactor| |d03eef| + |internalInfRittWu?| |shanksDiscLogAlgorithm| |index| |mkAnswer| + |tanIfCan| |OMserve| |divideIfCan| |search| |d03faf| + |internalSubQuasiComponent?| |reflect| |perfectNthPower?| |cotIfCan| + |makeop| |noKaratsuba| |superscript| |antiCommutative?| |e01baf| + |slex| |subQuasiComponent?| |option| |reify| |perfectNthRoot| + |secIfCan| |opeval| |karatsubaOnce| |subscript| |commutative?| + |e01bef| |inverse| |removeSuperfluousQuasiComponents| |or| |separant| + |pair| |approxNthRoot| |cscIfCan| |evaluateInverse| |karatsuba| + |rightCharacteristicPolynomial| |e01bff| |subCase?| |isobaric?| + |nothing| |evaluate| |separate| |leftCharacteristicPolynomial| + |e01bgf| |removeSuperfluousCases| |weights| |inputBinaryFile| + |implies?| |conjug| |pseudoDivide| |rightNorm| |e01bhf| + |prepareDecompose| |differentialVariables| |increment| |orOperands| + |adjoint| |pseudoQuotient| |leftNorm| |leaves| |e01daf| |branchIfCan| + |extractBottom!| |charpol| |or?| |getDatabase| |composite| + |outerProduct| |rightTrace| |extractTop!| |solve1| |andOperands| + |numericalOptimization| |subResultantGcd| |save| |leftTrace| + |bandedHessian| |routines| |varList| |insertBottom!| + |innerEigenvectors| |and?| |goodnessOfFit| |resultant| |someBasis| + |rightTrim| |jacobian| |mainSquareFreePart| |generator| |insertTop!| + |parseString| |notOperand| |whatInfinity| |discriminant| |sort!| + |scripted?| |bandedJacobian| |leftTrim| |mainPrimitivePart| |lists| + |bottom!| |unparse| |variable?| |resetNew| |copyInto!| |duplicates| + |mainContent| |top!| |binary| |term| |iFTable| |closeComponent| + |symFunc| |sorted?| |removeDuplicates!| |primitivePart!| |dequeue| + |packageCall| |term?| |showIntensityFunctions| |modifyPoint| + |symbolTableOf| |LiePoly| |linears| |nextsubResultant2| |recolor| + |innerSolve1| |equiv| |expint| |addPointLast| |argumentListOf| + |quickSort| |ddFact| |LazardQuotient2| |drawComplex| |innerSolve| + |merge!| |diff| |addPoint2| |returnTypeOf| |heapSort| + |separateFactors| |LazardQuotient| |drawComplexVectorField| |makeEq| + |resultantEuclidean| |algDsolve| |addPoint| |printHeader| |shellSort| + |exptMod| |subResultantChain| |setRealSteps| |modularGcdPrimitive| + |denomLODE| |semiResultantEuclidean2| |merge| F |returnType!| + |outputSpacing| |meshPar2Var| |halfExtendedSubResultantGcd2| |lo| + |setImagSteps| |modularGcd| |semiResultantEuclidean1| + |indicialEquations| |deepCopy| |outputGeneral| |meshFun2Var| + |halfExtendedSubResultantGcd1| |incr| |setClipValue| |reduction| + |indiceSubResultant| |indicialEquation| |shallowCopy| |real?| + |outputFixed| |meshPar1Var| |extendedSubResultantGcd| |hi| |option?| + |signAround| |indiceSubResultantEuclidean| |denomRicDE| + |numberOfChildren| |complexForm| |outputFloating| |ptFunc| + |exactQuotient!| |range| |stop| |invmod| + |semiIndiceSubResultantEuclidean| |leadingCoefficientRicDE| |children| + |predicate| |makeObject| |exp1| |minimumExponent| |exactQuotient| + |colorFunction| |powmod| |degreeSubResultant| + |constantCoefficientRicDE| |child| |log2| |max| |maximumExponent| + |primPartElseUnitCanonical!| |curveColor| |mulmod| + |degreeSubResultantEuclidean| |changeVar| |birth| |coef| + |rationalApproximation| |rowEch| |primPartElseUnitCanonical| + |UpTriBddDenomInv| |pointColor| |submod| + |semiDegreeSubResultantEuclidean| |ratDsolve| |internal?| |relerror| + |rowEchLocal| |lazyResidueClass| |kind| |clip| |addmod| + |lastSubResultantEuclidean| |indicialEquationAtInfinity| |root?| + |complexSolve| |rowEchelonLocal| |monicModulo| |op| |clipBoolean| + |symmetricRemainder| |semiLastSubResultantEuclidean| |reduceLODE| + |leaf?| |complexRoots| |normalizedDivide| |lazyPseudoDivide| |style| + |positiveRemainder| |subResultantGcdEuclidean| |singRicDE| + |outputForm| |comment| |currentEnv| |realRoots| |maxint| + |lazyPremWithDefault| |maxrow| |toScale| |bit?| + |semiSubResultantGcdEuclidean2| |polyRicDE| |expandPower| |obj| + |leadingTerm| |binaryFunction| |lazyPquo| |tableau| + |pointColorPalette| |parameters| |algint| + |semiSubResultantGcdEuclidean1| |ricDsolve| |expandLog| |cache| + |writable?| |makeFloatFunction| |lazyPrem| |concat| + |curveColorPalette| |algintegrate| |discriminantEuclidean| + |triangulate| |cos2sec| |readable?| |unaryFunction| |pquo| |var1Steps| + |palgintegrate| |semiDiscriminantEuclidean| |solveInField| |cosh2sech| + |exists?| |compiledFunction| |prem| |union| |shift| |generate| + |var2Steps| |operation| |palginfieldint| |chainSubResultants| + |wronskianMatrix| |cot2trig| |zeroOf| |extension| |corrPoly| + |supRittWu?| |category| |space| |bitLength| |schema| + |variationOfParameters| |coth2trigh| |rootsOf| |shallowExpand| + |lifting| |RittWuCompare| |rank| |domain| |incrementBy| |tubePoints| + |bitCoef| |resultantReduit| |result| |factors| |csc2sin| |makeSketch| + |deepExpand| |lifting1| |mainMonomials| |expand| |length| |package| + |tubeRadius| |bitTruth| |resultantReduitEuclidean| |nthFactor| + |csch2sinh| |inrootof| |clearFortranOutputStack| |exprex| + |mainCoefficients| |filterWhile| |scripts| |weight| |contains?| + |semiResultantReduitEuclidean| |nthExpon| |sec2cos| |droot| + |showFortranOutputStack| |coerceL| |leastMonomial| |filterUntil| + |makeVariable| |inf| |divide| |overlap| |sech2cosh| |iroot| + |topFortranOutputStack| |coerceS| |mainMonomial| |select| + |finiteBound| |qinterval| |Lazard| |hcrf| |sin2csc| |unknown| |size?| + |setFormula!| |frobenius| |quasiMonic?| |sortConstraints| |interval| + |Lazard2| |hclf| |sinh2csch| |eq?| |linkToFortran| |computePowers| + |monic?| |sumOfSquares| |unit?| |nextsousResultant2| |lexico| + |tan2trig| |doublyTransitive?| |setLegalFortranSourceExtensions| |pow| + |deepestInitial| |splitLinear| |associates?| |resultantnaif| + |OMmakeConn| |tanh2trigh| |knownInfBasis| |fracPart| |An| + |iteratedInitials| |nil| |simpleBounds?| |unitCanonical| + |resultantEuclideannaif| |OMcloseConn| |tan2cot| |rootSplit| + |polyPart| |UnVectorise| |deepestTail| |linearMatrix| |unitNormal| + |semiResultantEuclideannaif| |OMconnInDevice| |tanh2coth| |ratDenom| + |rules| |fullPartialFraction| |Vectorise| |head| |makeRecord| |failed| + |linearPart| |lfextendedint| |pdct| |OMconnOutDevice| |cot2tan| + |ratPoly| |primeFrobenius| |setPoly| |mdeg| |nonLinearPart| + |lflimitedint| |powers| |OMconnectTCP| |coth2tanh| |rootPower| + |discreteLog| |exponent| |mvar| |typeList| |quadratic?| |lfinfieldint| + |dilog| |partition| |OMbindTCP| |removeCosSq| |rootProduct| + |decreasePrecision| |exQuo| |relativeApprox| |changeNameToObjf| + |parametersOf| |lfintegrate| |complete| |sin| |point| |OMopenFile| + |removeSinSq| |rootSimp| |increasePrecision| |moebius| |rootOf| + |fortranTypeOf| |optAttributes| |lfextlimint| |pole?| |cos| + |OMopenString| |removeCoshSq| |rootKerSimp| |bits| |rightRecip| + |allRootsOf| |empty| |Nul| |BasicMethod| |listBranches| |tan| + |OMclose| |removeSinhSq| |leftRank| |unitNormalize| |leftRecip| + |definingPolynomial| |exponents| |PollardSmallFactor| |triangular?| + |cot| |series| |OMsetEncoding| |expandTrigProducts| |unit| |leftPower| + |positive?| |symbol| |iisqrt2| |showTheFTable| + |rewriteIdealWithRemainder| |OMputApp| |fintegrate| |sec| |flagFactor| + |rightPower| |negative?| |qelt| |expression| |iisqrt3| + |clearTheFTable| |rewriteIdealWithHeadRemainder| |OMputAtp| + |coefficient| |csc| |sqfrFactor| |derivationCoordinates| |zero?| + |integer| |iiexp| |fTable| |remainder| |OMputAttr| |coHeight| |asin| + |primeFactor| |one?| |augment| |xRange| |palgint0| |li| + |headRemainder| |OMputBind| |extendIfCan| |min| |acos| |nthFlag| + |splitSquarefree| |lastSubResultant| |yRange| |powerSum| |palgextint0| + |categories| |roughUnitIdeal?| |OMputBVar| |algebraicVariables| |atan| + |level| |nthExponent| |normalDenom| |lastSubResultantElseSplit| + |zRange| |elementary| |palglimint0| |roughEqualIdeals?| |OMputError| + |zeroSetSplitIntoTriangularSystems| |acot| |irreducibleFactor| |map!| + |totalfract| |invertibleSet| |alternating| |palgRDE0| |roughSubIdeal?| + |OMputObject| |zeroSetSplit| |asec| |qsetelt!| |pushdterm| + |invertible?| |cyclic| |palgLODE0| |roughBase?| |OMputEndApp| + |reduceByQuasiMonic| |acsc| |rationalPoint?| |random| |pushucoef| + |invertibleElseSplit?| |dihedral| |chineseRemainder| |trivialIdeal?| + |OMputEndAtp| |collectQuasiMonic| |sinh| |absolutelyIrreducible?| + |keys| |pushuconst| |purelyAlgebraicLeadingMonomial?| |tower| |cap| + |divisors| |collectUpper| |OMputEndAttr| |removeZero| |cosh| |genus| + |numberOfMonomials| |algebraicCoefficients?| |cup| |OMputEndBind| + |initiallyReduce| |tanh| |getZechTable| |members| + |purelyTranscendental?| |true| |wreath| |factorList| |setMaxPoints3D| + |OMputEndBVar| |headReduce| |coth| |createZechTable| |multiset| + |purelyAlgebraic?| |acsch| |and| |SFunction| |listConjugateBases| + |maxPoints3D| |OMputEndError| |stronglyReduce| |sech| + |createMultiplicationTable| |mergeDifference| |prepareSubResAlgo| + |skewSFunction| |matrixGcd| |setMinPoints3D| |OMputEndObject| + |rewriteSetWithReduction| |debug| |csch| |createMultiplicationMatrix| + |brace| |complexNumeric| |cyclotomicDecomposition| |divideIfCan!| + |minPoints3D| |OMputInteger| |autoReduced?| D |asinh| + |createLowComplexityTable| |directSum| |exponential1| + |cyclotomicFactorization| |leastPower| |tValues| |OMputFloat| + |initiallyReduced?| |acosh| |box| |createLowComplexityNormalBasis| + |solveLinearPolynomialEquationByFractions| |chiSquare1| |kernels| + |rangeIsFinite| |idealiser| |tRange| |OMputVariable| |headReduced?| + |atanh| |representationType| |hasSolution?| |exponential| |univariate| + |functionIsContinuousAtEndPoints| |idealiserMatrix| |plot| |acoth| + |createPrimitiveElement| |parts| |value| |linSolve| |chiSquare| + |listOfLists| |functionIsOscillatory| |moduleSum| |pointPlot| + |restorePrecision| |trim| |asech| ** |tableForDiscreteLogarithm| + |LyndonWordsList| |factorFraction| |tanSum| |changeName| + |mapUnivariate| |calcRanges| |antiCommutator| |split| + |factorsOfCyclicGroupSize| |LyndonWordsList1| |componentUpperBound| + |tanAn| |factor| |exprHasWeightCosWXorSinWX| |mapUnivariateIfCan| + |fixPredicate| |commutator| |upperCase!| |multiple| |subst| + |sizeMultiplication| |lyndonIfCan| |blue| |tanNa| + |exprHasAlgebraicWeight| |sqrt| |datalist| EQ |mapMatrixIfCan| + |patternMatch| |associator| |upperCase| |applyQuote| + |getMultiplicationMatrix| |lyndon| |green| |condition| |initTable!| + |PDESolve| |var1StepsDefault| |real| |exprHasLogarithmicWeights| + |mapBivariate| |patternMatchTimes| |complexEigenvalues| |lowerCase!| + |complex| |getMultiplicationTable| |lyndon?| |red| |printInfo!| + |leftFactor| |var2StepsDefault| |imag| |combineFeatureCompatibility| + |fullDisplay| |bernoulli| |complexEigenvectors| |lowerCase| |print| + |primitive?| |numberOfComputedEntries| |whitePoint| |startStats!| + |rightFactorCandidate| |tubePointsDefault| |directProduct| + |sparsityIF| |relationsIdeal| |chebyshevT| |normalizedAssociate| + |KrullNumber| |ruleset| |argumentList!| |numberOfIrreduciblePoly| + |rst| |uniform| |printStats!| |measure| |tubeRadiusDefault| + |stiffnessAndStabilityFactor| |saturate| |chebyshevU| |normalize| + |numberOfVariables| |third| |endSubProgram| |numberOfPrimitivePoly| + |frst| |binomial| |clearTable!| |coerceImages| |dimension| |destruct| + |stiffnessAndStabilityOfODEIF| |matrix| |groebner?| |cyclotomic| + |outputArgs| |algebraicDecompose| |numberOfNormalPoly| |lazyEvaluate| + |poisson| |objects| |usingTable?| |fixedPoints| |crest| + |LowTriBddDenomInv| |systemSizeIF| |groebnerIdeal| |euler| + |normInvertible?| |transcendentalDecompose| |suchThat| + |createIrreduciblePoly| |lazy?| |geometric| |base| |printingInfo?| + |bright| |odd?| |cfirst| |expenseOfEvaluationIF| |ideal| + |fixedDivisor| |normFactors| |internalDecompose| |createPrimitivePoly| + |explicitlyEmpty?| |ridHack1| |makingStats?| |even?| |sts2stst| + |accuracyIF| |leadingIdeal| |npcoef| |laguerre| |cyclicEntries| + |decompose| |createNormalPoly| |explicitEntries?| |interpolate| + |extractIfCan| |numberOfCycles| |clikeUniv| |monomial| + |intermediateResultsIF| |backOldPos| |listexp| |legendre| |cyclicCopy| + |upDateBranches| |createNormalPrimitivePoly| |matrixDimensions| + |insert!| |nullSpace| |cyclePartition| |weierstrass| |multivariate| + |subscriptedVariables| |generalPosition| |dmpToHdmp| + |characteristicPolynomial| |preprocess| |createPrimitiveNormalPoly| + |matrixConcat3D| |interpretString| |nullity| |coerceListOfPairs| |qqq| + |variables| |central?| |quotient| |hdmpToDmp| |realEigenvalues| + |internalZeroSetSplit| |nextIrreduciblePoly| |setelt!| + |stripCommentsAndBlanks| |rowEchelon| |coercePreimagesImages| + |integralBasis| |insert| |elliptic?| |zeroDim?| |pToHdmp| + |realEigenvectors| |internalAugment| |nextPrimitivePoly| |delete| + |identityMatrix| |setPrologue!| |column| |listRepresentation| + |localIntegralBasis| |doubleResultant| |inRadical?| |hdmpToP| + |halfExtendedResultant2| |possiblyInfinite?| |nextNormalPoly| + |zeroMatrix| |setTex!| |row| |permanent| |qualifier| |distdfact| |in?| + |dmpToP| |halfExtendedResultant1| |explicitlyFinite?| + |nextNormalPrimitivePoly| |compile| |mappingAst| |setEpilogue!| + |maxColIndex| |cycles| |mainExpression| |separateDegrees| |element?| + |pToDmp| |extendedResultant| |nextItem| |nextPrimitiveNormalPoly| + |nullary| |prologue| |minColIndex| |cycle| |changeWeightLevel| + |taylor| |trace2PowMod| |zeroDimPrime?| |sylvesterSequence| + |subResultantsChain| |infiniteProduct| |leastAffineMultiple| + |fixedPoint| |epilogue| |maxRowIndex| |initializeGroupForWordProblem| + |characteristicSerie| |laurent| |tracePowMod| |zeroDimPrimary?| + |sturmSequence| |delta| |lazyPseudoQuotient| |evenInfiniteProduct| + |reducedQPowers| |recur| |endOfFile?| |minRowIndex| |movedPoints| + |characteristicSet| |puiseux| |irreducible?| |primaryDecomp| + |boundOfCauchy| |lazyPseudoRemainder| |oddInfiniteProduct| |linear| + |eval| |rootOfIrreduciblePoly| |const| |readIfCan!| |antisymmetric?| + |wordInGenerators| |medialSet| |decimal| |contract| + |sturmVariationsOf| |bernoulliB| |generalInfiniteProduct| |property| + |write!| |curry| |readLineIfCan!| |symmetric?| + |wordInStrongGenerators| |Hausdorff| |inv| |innerint| |leadingSupport| + |lazyVariations| |eulerE| |showAll?| |polynomial| |read!| |diag| + |readLine!| |diagonal?| |orbits| |Frobenius| |ground?| + |exteriorDifferential| |shrinkable| |content| |numericIfCan| + |showAllElements| |iomode| |curryRight| |writeLine!| |square?| |orbit| + |transcendenceDegree| |ground| |totalDifferential| |physicalLength!| + |entry| |totalDegree| |complexNumericIfCan| |delay| |units| |close!| + |curryLeft| |sign| |rectangularMatrix| |permutationGroup| + |extensionDegree| |leadingMonomial| |homogeneous?| |physicalLength| + |minimumDegree| |FormatArabic| |findCycle| |reopen!| |log10| + |constantRight| |nonQsign| |characteristic| |wordsForStrongGenerators| + |inGroundField?| |leadingCoefficient| |leadingBasisTerm| + |flexibleArray| |lambda| |monomials| |ScanArabic| |repeating?| + |bitand| |rightUnit| |constantLeft| |round| |strongGenerators| + |transcendent?| |primitiveMonomials| |ignore?| |elseBranch| |isPlus| + |FormatRoman| |repeating| |bitior| |leftUnit| |twist| |fractionPart| + |generators| |algebraic?| |reductum| |computeInt| |thenBranch| + |isTimes| |ScanRoman| |recip| |rightMinimalPolynomial| |setsubMatrix!| + |wholePart| |bivariateSLPEBR| |sh| |checkForZero| |generalizedInverse| + |isExpt| |ScanFloatIgnoreSpaces| |integers| |code| |initial| + |leftMinimalPolynomial| |subMatrix| |floor| + |solveLinearPolynomialEquationByRecursion| |mirror| |logGamma| + |imports| |isPower| |ScanFloatIgnoreSpacesIfCan| |oddintegers| + |associatorDependence| |swapColumns!| |ceiling| |factorByRecursion| + |monomial?| |hypergeometric0F1| |sequence| |rroot| + |numericalIntegration| |int| |lieAlgebra?| |swapRows!| |norm| + |factorSquareFreeByRecursion| |rquo| |rotatez| |output| |iterationVar| + |qroot| |rk4| |mapmult| |jordanAlgebra?| |vertConcat| |mightHaveRoots| + |randomR| |lquo| |rotatey| |readBytes!| |froot| |rk4a| |deriv| + |noncommutativeJordanAlgebra?| |horizConcat| |refine| + |factorSFBRlcUnit| |options| |mindegTerm| |rotatex| |readByteIfCan!| + |nthr| |rk4qc| |gderiv| |jordanAdmissible?| |comp| |squareTop| + |middle| |charthRoot| |product| |identity| |setFieldInfo| |port| + |rk4f| |compose| |lieAdmissible?| |elRow1!| |roman| |conditionP| + |LiePolyIfCan| |dictionary| |pol| |firstUncouplingMatrix| |aromberg| + |addiag| |cn| |jacobiIdentity?| |elRow2!| |recoverAfterFail| + |solveLinearPolynomialEquation| |string| |trunc| |dioSolve| |xn| + |integral| |asimpson| |lazyIntegrate| |powerAssociative?| |elColumn2!| + |showTheRoutinesTable| |factorSquareFreePolynomial| |degree| |newLine| + |dAndcExp| |primitiveElement| |atrapezoidal| |nlde| |dom| + |alternative?| |fractionFreeGauss!| |deleteRoutine!| + |factorPolynomial| |quasiRegular| |copies| |repSq| |nextPrime| + |romberg| |powern| |flexible?| |invertIfCan| |getExplanations| + |squareFreePolynomial| |quasiRegular?| |sayLength| |expPot| + |prevPrime| |simpson| |mapdiv| |rightAlternative?| |copy!| + |getMeasure| |gcdPolynomial| |constant?| |qPot| |primes| |trapezoidal| + |lazyGintegrate| |leftAlternative?| |plus!| |changeMeasure| |torsion?| + |mindeg| |iidsum| |lookup| |selectsecond| |rombergo| |power| + |antiAssociative?| |minus!| |changeThreshhold| |torsionIfCan| |maxdeg| + |iidprod| |normal?| |selectfirst| |simpsono| |sincos| |title| + |associative?| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-402 (-552))) -1523 (|has| |#1| (-344)) (|has| |#1| (-358))) ((-38 |#1|) . T) ((-38 $) -1523 (|has| |#1| (-544)) (|has| |#1| (-344)) (|has| |#1| (-358)) (|has| |#1| (-302))) ((-35) |has| |#1| (-1171)) ((-94) |has| |#1| (-1171)) ((-101) . T) ((-111 #0# #0#) -1523 (|has| |#1| (-344)) (|has| |#1| (-358))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-130) . T) ((-143) -1523 (|has| |#1| (-344)) (|has| |#1| (-143))) ((-145) |has| |#1| (-145)) ((-597 (-839)) . T) ((-170) . T) ((-598 (-167 (-221))) |has| |#1| (-998)) ((-598 (-167 (-374))) |has| |#1| (-998)) ((-598 (-528)) |has| |#1| (-598 (-528))) ((-598 (-868 (-374))) |has| |#1| (-598 (-868 (-374)))) ((-598 (-868 (-552))) |has| |#1| (-598 (-868 (-552)))) ((-598 #1=(-1145 |#1|)) . T) ((-227 |#1|) . 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T) ((-304 |#2|) -12 (|has| |#2| (-304 |#2|)) (|has| |#2| (-1073))) ((-363) |has| |#2| (-363)) ((-372 |#2|) |has| |#2| (-1025)) ((-406 |#2|) |has| |#2| (-1073)) ((-483 |#2|) . T) ((-588 #0# |#2|) . T) ((-507 |#2| |#2|) -12 (|has| |#2| (-304 |#2|)) (|has| |#2| (-1073))) ((-628 |#2|) -1523 (|has| |#2| (-1025)) (|has| |#2| (-358)) (|has| |#2| (-170))) ((-628 $) -1523 (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-170))) ((-621 (-552)) -12 (|has| |#2| (-621 (-552))) (|has| |#2| (-1025))) ((-621 |#2|) |has| |#2| (-1025)) ((-698 |#2|) -1523 (|has| |#2| (-358)) (|has| |#2| (-170))) ((-707) -1523 (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-707)) (|has| |#2| (-170))) ((-771) |has| |#2| (-825)) ((-772) -1523 (|has| |#2| (-825)) (|has| |#2| (-773))) ((-773) |has| |#2| (-773)) ((-774) -1523 (|has| |#2| (-825)) (|has| |#2| (-773))) ((-775) -1523 (|has| |#2| (-825)) (|has| |#2| (-773))) ((-825) |has| |#2| (-825)) ((-827) -1523 (|has| |#2| (-825)) (|has| |#2| (-773))) ((-876 (-1149)) -12 (|has| |#2| (-876 (-1149))) (|has| |#2| (-1025))) ((-1014 (-402 (-552))) -12 (|has| |#2| (-1014 (-402 (-552)))) (|has| |#2| (-1073))) ((-1014 (-552)) -12 (|has| |#2| (-1014 (-552))) (|has| |#2| (-1073))) ((-1014 |#2|) |has| |#2| (-1073)) ((-1031 |#2|) -1523 (|has| |#2| (-1025)) (|has| |#2| (-358)) (|has| |#2| (-170))) ((-1031 $) |has| |#2| (-170)) ((-1025) -1523 (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-170))) ((-1032) -1523 (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-170))) ((-1085) -1523 (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-707)) (|has| |#2| (-170))) ((-1073) -1523 (|has| |#2| (-1073)) (|has| |#2| (-1025)) (|has| |#2| (-825)) (|has| |#2| (-773)) (|has| |#2| (-707)) (|has| |#2| (-363)) (|has| |#2| (-358)) (|has| |#2| (-170)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1186) . T) ((-1239 |#2|) |has| |#2| (-358))) +((-1454 (((-236 |#1| |#3|) (-1 |#3| |#2| |#3|) (-236 |#1| |#2|) |#3|) 21)) (-2163 ((|#3| (-1 |#3| |#2| |#3|) (-236 |#1| |#2|) |#3|) 23)) (-1996 (((-236 |#1| |#3|) (-1 |#3| |#2|) (-236 |#1| |#2|)) 18))) +(((-235 |#1| |#2| |#3|) (-10 -7 (-15 -1454 ((-236 |#1| |#3|) (-1 |#3| |#2| |#3|) (-236 |#1| |#2|) |#3|)) (-15 -2163 (|#3| (-1 |#3| |#2| |#3|) (-236 |#1| |#2|) |#3|)) (-15 -1996 ((-236 |#1| |#3|) (-1 |#3| |#2|) (-236 |#1| |#2|)))) (-751) (-1186) (-1186)) (T -235)) +((-1996 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-236 *5 *6)) (-14 *5 (-751)) (-4 *6 (-1186)) (-4 *7 (-1186)) (-5 *2 (-236 *5 *7)) (-5 *1 (-235 *5 *6 *7)))) (-2163 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-236 *5 *6)) (-14 *5 (-751)) (-4 *6 (-1186)) (-4 *2 (-1186)) (-5 *1 (-235 *5 *6 *2)))) (-1454 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-236 *6 *7)) (-14 *6 (-751)) (-4 *7 (-1186)) (-4 *5 (-1186)) (-5 *2 (-236 *6 *5)) (-5 *1 (-235 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-372 |#1|) . T) ((-407 |#1|) . T) ((-446) -3891 (|has| |#1| (-886)) (|has| |#1| (-446))) ((-507 |#2| |#1|) |has| |#1| (-229)) ((-507 |#2| $) |has| |#1| (-229)) ((-507 |#3| |#1|) . T) ((-507 |#3| $) . T) ((-507 $ $) . T) ((-545) -3891 (|has| |#1| (-886)) (|has| |#1| (-545)) (|has| |#1| (-446))) ((-628 #1#) |has| |#1| (-38 (-402 (-538)))) ((-628 |#1|) . T) ((-628 $) . T) ((-621 (-538)) |has| |#1| (-621 (-538))) ((-621 |#1|) . T) ((-698 #1#) |has| |#1| (-38 (-402 (-538)))) ((-698 |#1|) |has| |#1| (-170)) ((-698 $) -3891 (|has| |#1| (-886)) (|has| |#1| (-545)) (|has| |#1| (-446))) ((-707) . T) ((-827) |has| |#1| (-827)) ((-876 (-1149)) |has| |#1| (-876 (-1149))) ((-876 |#3|) . T) ((-862 (-373)) -12 (|has| |#1| (-862 (-373))) (|has| |#3| (-862 (-373)))) ((-862 (-538)) -12 (|has| |#1| (-862 (-538))) (|has| |#3| (-862 (-538)))) ((-926 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-47 |#1| #0=(-552)) . T) ((-25) . T) ((-38 #1=(-402 (-552))) -1523 (|has| |#1| (-358)) (|has| |#1| (-38 (-402 (-552))))) ((-38 |#1|) |has| |#1| (-170)) ((-38 |#2|) |has| |#1| (-358)) ((-38 $) -1523 (|has| |#1| (-544)) (|has| |#1| (-358))) ((-35) |has| |#1| (-38 (-402 (-552)))) ((-94) |has| |#1| (-38 (-402 (-552)))) ((-101) . T) ((-111 #1# #1#) -1523 (|has| |#1| (-358)) (|has| |#1| (-38 (-402 (-552))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-358)) ((-111 $ $) -1523 (|has| |#1| (-544)) (|has| |#1| (-358)) (|has| |#1| (-170))) ((-130) . T) ((-143) -1523 (-12 (|has| |#1| (-358)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -1523 (-12 (|has| |#1| (-358)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-597 (-839)) . 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3021531) (-1213 3013146 3013225 3013404 "UPXS2" 3013631 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1212 3005120 3012261 3012543 "UPXS" 3012922 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1211 3003777 3004029 3004379 "UPSQFREE" 3004864 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1210 2997695 3000704 3000759 "UPSCAT" 3001920 NIL UPSCAT (NIL T T) -9 NIL 3002694) (-1209 2996899 2997106 2997433 "UPSCAT-" 2997438 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1208 2996526 2996569 2996702 "UPOLYC2" 2996850 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1207 2982650 2990613 2990656 "UPOLYC" 2992757 NIL UPOLYC (NIL T) -9 NIL 2993978) (-1206 2974015 2976428 2979563 "UPOLYC-" 2979568 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1205 2973354 2973461 2973625 "UPMP" 2973904 NIL UPMP (NIL T T) -7 NIL NIL) (-1204 2972907 2972988 2973127 "UPDIVP" 2973267 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1203 2971475 2971724 2972040 "UPDECOMP" 2972656 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1202 2970710 2970822 2971007 "UPCDEN" 2971359 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1201 2970229 2970298 2970447 "UP2" 2970635 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1200 2961726 2969795 2969933 "UP" 2970139 NIL UP (NIL NIL T) -8 NIL NIL) (-1199 2960941 2961068 2961273 "UNISEG2" 2961569 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1198 2959458 2960145 2960422 "UNISEG" 2960699 NIL UNISEG (NIL T) -8 NIL NIL) (-1197 2958518 2958698 2958924 "UNIFACT" 2959274 NIL UNIFACT (NIL T) -7 NIL NIL) (-1196 2946576 2958422 2958494 "ULSCONS" 2958499 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1195 2929396 2941315 2941377 "ULSCCAT" 2942097 NIL ULSCCAT (NIL T T) -9 NIL 2942394) (-1194 2928482 2928715 2929091 "ULSCCAT-" 2929096 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1193 2918545 2924975 2925018 "ULSCAT" 2925881 NIL ULSCAT (NIL T) -9 NIL 2926611) (-1192 2917975 2918054 2918233 "ULS2" 2918460 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1191 2901960 2917152 2917403 "ULS" 2917782 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1190 2900398 2901321 2901351 "UFD" 2901563 T UFD (NIL) -9 NIL 2901677) (-1189 2900192 2900238 2900333 "UFD-" 2900338 NIL UFD- (NIL T) -8 NIL NIL) (-1188 2899274 2899457 2899673 "UDVO" 2899998 T UDVO (NIL) -7 NIL NIL) (-1187 2897090 2897499 2897970 "UDPO" 2898838 NIL UDPO (NIL T) -7 NIL NIL) (-1186 2896877 2897045 2897076 "TYPEAST" 2897081 T TYPEAST (NIL) -8 NIL NIL) (-1185 2896810 2896815 2896845 "TYPE" 2896850 T TYPE (NIL) -9 NIL NIL) (-1184 2895781 2895983 2896223 "TWOFACT" 2896604 NIL TWOFACT (NIL T) -7 NIL NIL) (-1183 2894719 2895056 2895319 "TUPLE" 2895553 NIL TUPLE (NIL T) -8 NIL NIL) (-1182 2892410 2892929 2893468 "TUBETOOL" 2894202 T TUBETOOL (NIL) -7 NIL NIL) (-1181 2891259 2891464 2891705 "TUBE" 2892203 NIL TUBE (NIL T) -8 NIL NIL) (-1180 2879926 2884018 2884115 "TSETCAT" 2889384 NIL TSETCAT (NIL T T T T) -9 NIL 2890915) (-1179 2874660 2876258 2878149 "TSETCAT-" 2878154 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1178 2869424 2873632 2873915 "TS" 2874412 NIL TS (NIL T) -8 NIL NIL) (-1177 2863687 2864533 2865475 "TRMANIP" 2868560 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1176 2863128 2863191 2863354 "TRIMAT" 2863619 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1175 2860924 2861161 2861525 "TRIGMNIP" 2862877 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1174 2860444 2860557 2860587 "TRIGCAT" 2860800 T TRIGCAT (NIL) -9 NIL NIL) (-1173 2860113 2860192 2860333 "TRIGCAT-" 2860338 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1172 2857013 2858973 2859253 "TREE" 2859868 NIL TREE (NIL T) -8 NIL NIL) (-1171 2856287 2856815 2856845 "TRANFUN" 2856880 T TRANFUN (NIL) -9 NIL 2856946) (-1170 2855566 2855757 2856037 "TRANFUN-" 2856042 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1169 2855370 2855402 2855463 "TOPSP" 2855527 T TOPSP (NIL) -7 NIL NIL) (-1168 2854718 2854833 2854987 "TOOLSIGN" 2855251 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1167 2853379 2853895 2854134 "TEXTFILE" 2854501 T TEXTFILE (NIL) -8 NIL NIL) (-1166 2853160 2853191 2853263 "TEX1" 2853342 NIL TEX1 (NIL T) -7 NIL NIL) (-1165 2851025 2851539 2851977 "TEX" 2852744 T TEX (NIL) -8 NIL NIL) (-1164 2850673 2850736 2850826 "TEMUTL" 2850957 T TEMUTL (NIL) -7 NIL NIL) (-1163 2848827 2849107 2849432 "TBCMPPK" 2850396 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1162 2840717 2846987 2847043 "TBAGG" 2847443 NIL TBAGG (NIL T T) -9 NIL 2847654) (-1161 2835787 2837275 2839029 "TBAGG-" 2839034 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1160 2835171 2835278 2835423 "TANEXP" 2835676 NIL TANEXP (NIL T) -7 NIL NIL) (-1159 2834583 2834682 2834820 "TABLEAU" 2835068 NIL TABLEAU (NIL T) -8 NIL NIL) (-1158 2828086 2834440 2834533 "TABLE" 2834538 NIL TABLE (NIL T T) -8 NIL NIL) (-1157 2822694 2823914 2825162 "TABLBUMP" 2826872 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1156 2822122 2822222 2822350 "SYSTEM" 2822588 T SYSTEM (NIL) -7 NIL NIL) (-1155 2818585 2819280 2820063 "SYSSOLP" 2821373 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1154 2814877 2815584 2816318 "SYNTAX" 2817873 T SYNTAX (NIL) -8 NIL NIL) (-1153 2812035 2812637 2813269 "SYMTAB" 2814267 T SYMTAB (NIL) -8 NIL NIL) (-1152 2807308 2808204 2809181 "SYMS" 2811080 T SYMS (NIL) -8 NIL NIL) (-1151 2804590 2806769 2806999 "SYMPOLY" 2807116 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1150 2804107 2804182 2804305 "SYMFUNC" 2804502 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1149 2800084 2801344 2802166 "SYMBOL" 2803307 T SYMBOL (NIL) -8 NIL NIL) (-1148 2793623 2795312 2797032 "SWITCH" 2798386 T SWITCH (NIL) -8 NIL NIL) (-1147 2786893 2792444 2792747 "SUTS" 2793378 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1146 2778866 2786008 2786290 "SUPXS" 2786669 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1145 2778025 2778152 2778369 "SUPFRACF" 2778734 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1144 2777646 2777705 2777818 "SUP2" 2777960 NIL SUP2 (NIL T T) -7 NIL NIL) (-1143 2769215 2777264 2777390 "SUP" 2777555 NIL SUP (NIL T) -8 NIL NIL) (-1142 2767628 2767902 2768265 "SUMRF" 2768914 NIL SUMRF (NIL T) -7 NIL NIL) (-1141 2766942 2767008 2767207 "SUMFS" 2767549 NIL SUMFS (NIL T T) -7 NIL NIL) (-1140 2750967 2766119 2766370 "SULS" 2766749 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1139 2750596 2750789 2750859 "SUCHTAST" 2750919 T SUCHTAST (NIL) -8 NIL NIL) (-1138 2749918 2750121 2750261 "SUCH" 2750504 NIL SUCH (NIL T T) -8 NIL NIL) (-1137 2743812 2744824 2745783 "SUBSPACE" 2749006 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1136 2743242 2743332 2743496 "SUBRESP" 2743700 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1135 2737415 2738535 2739682 "STTFNC" 2742142 NIL STTFNC (NIL T) -7 NIL NIL) (-1134 2730784 2732080 2733391 "STTF" 2736151 NIL STTF (NIL T) -7 NIL NIL) (-1133 2722099 2723966 2725760 "STTAYLOR" 2729025 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1132 2715345 2721963 2722046 "STRTBL" 2722051 NIL STRTBL (NIL T) -8 NIL NIL) (-1131 2710736 2715300 2715331 "STRING" 2715336 T STRING (NIL) -8 NIL NIL) (-1130 2705624 2710109 2710139 "STRICAT" 2710198 T STRICAT (NIL) -9 NIL 2710260) (-1129 2705134 2705211 2705355 "STREAM3" 2705541 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1128 2704116 2704299 2704534 "STREAM2" 2704947 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1127 2703804 2703856 2703949 "STREAM1" 2704058 NIL STREAM1 (NIL T) -7 NIL NIL) (-1126 2696519 2701327 2701947 "STREAM" 2703219 NIL STREAM (NIL T) -8 NIL NIL) (-1125 2695535 2695716 2695947 "STINPROD" 2696335 NIL STINPROD (NIL T) -7 NIL NIL) (-1124 2695113 2695297 2695327 "STEP" 2695407 T STEP (NIL) -9 NIL 2695485) (-1123 2688658 2695012 2695089 "STBL" 2695094 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1122 2683835 2687880 2687923 "STAGG" 2688076 NIL STAGG (NIL T) -9 NIL 2688165) (-1121 2681543 2682143 2683013 "STAGG-" 2683018 NIL STAGG- (NIL T T) -8 NIL NIL) (-1120 2679738 2681313 2681405 "STACK" 2681486 NIL STACK (NIL T) -8 NIL NIL) (-1119 2672490 2677879 2678335 "SREGSET" 2679368 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1118 2664916 2666284 2667797 "SRDCMPK" 2671096 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1117 2657883 2662356 2662386 "SRAGG" 2663689 T SRAGG (NIL) -9 NIL 2664297) (-1116 2656900 2657155 2657534 "SRAGG-" 2657539 NIL SRAGG- (NIL T) -8 NIL NIL) (-1115 2651399 2655847 2656268 "SQMATRIX" 2656526 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1114 2645152 2648119 2648845 "SPLTREE" 2650745 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1113 2641142 2641808 2642454 "SPLNODE" 2644578 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1112 2640189 2640422 2640452 "SPFCAT" 2640896 T SPFCAT (NIL) -9 NIL NIL) (-1111 2638926 2639136 2639400 "SPECOUT" 2639947 T SPECOUT (NIL) -7 NIL NIL) (-1110 2630615 2632359 2632389 "SPADXPT" 2636781 T SPADXPT (NIL) -9 NIL 2638815) (-1109 2630376 2630416 2630485 "SPADPRSR" 2630568 T SPADPRSR (NIL) -7 NIL NIL) (-1108 2628559 2630331 2630362 "SPADAST" 2630367 T SPADAST (NIL) -8 NIL NIL) (-1107 2620530 2622277 2622320 "SPACEC" 2626693 NIL SPACEC (NIL T) -9 NIL 2628509) (-1106 2618701 2620462 2620511 "SPACE3" 2620516 NIL SPACE3 (NIL T) -8 NIL NIL) (-1105 2617453 2617624 2617915 "SORTPAK" 2618506 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1104 2615503 2615806 2616225 "SOLVETRA" 2617117 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1103 2614514 2614736 2615010 "SOLVESER" 2615276 NIL SOLVESER (NIL T) -7 NIL NIL) (-1102 2609734 2610615 2611617 "SOLVERAD" 2613566 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1101 2605549 2606158 2606887 "SOLVEFOR" 2609101 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1100 2599873 2604898 2604995 "SNTSCAT" 2605000 NIL SNTSCAT (NIL T T T T) -9 NIL 2605070) (-1099 2594016 2598196 2598587 "SMTS" 2599563 NIL SMTS (NIL T T T) -8 NIL NIL) (-1098 2588492 2593904 2593981 "SMP" 2593986 NIL SMP (NIL T T) -8 NIL NIL) (-1097 2586651 2586952 2587350 "SMITH" 2588189 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1096 2579632 2583783 2583886 "SMATCAT" 2585240 NIL SMATCAT (NIL NIL T T T) -9 NIL 2585790) (-1095 2576593 2577409 2578580 "SMATCAT-" 2578585 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1094 2574306 2575829 2575872 "SKAGG" 2576133 NIL SKAGG (NIL T) -9 NIL 2576268) (-1093 2570424 2573410 2573688 "SINT" 2574050 T SINT (NIL) -8 NIL NIL) (-1092 2570196 2570234 2570300 "SIMPAN" 2570380 T SIMPAN (NIL) -7 NIL NIL) (-1091 2569055 2569269 2569537 "SIGNRF" 2569962 NIL SIGNRF (NIL T) -7 NIL NIL) (-1090 2567881 2568025 2568309 "SIGNEF" 2568891 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1089 2567214 2567464 2567588 "SIGAST" 2567779 T SIGAST (NIL) -8 NIL NIL) (-1088 2566521 2566749 2566889 "SIG" 2567096 T SIG (NIL) -8 NIL NIL) (-1087 2564211 2564665 2565171 "SHP" 2566062 NIL SHP (NIL T NIL) -7 NIL NIL) (-1086 2558124 2564112 2564188 "SHDP" 2564193 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1085 2557723 2557889 2557919 "SGROUP" 2558012 T SGROUP (NIL) -9 NIL 2558074) (-1084 2557581 2557607 2557680 "SGROUP-" 2557685 NIL SGROUP- (NIL T) -8 NIL NIL) (-1083 2554417 2555114 2555837 "SGCF" 2556880 T SGCF (NIL) -7 NIL NIL) (-1082 2548839 2553864 2553961 "SFRTCAT" 2553966 NIL SFRTCAT (NIL T T T T) -9 NIL 2554005) (-1081 2542263 2543278 2544414 "SFRGCD" 2547822 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1080 2535391 2536462 2537648 "SFQCMPK" 2541196 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1079 2535013 2535102 2535212 "SFORT" 2535332 NIL SFORT (NIL T T) -8 NIL NIL) (-1078 2534158 2534853 2534974 "SEXOF" 2534979 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1077 2528934 2529623 2529718 "SEXCAT" 2533489 NIL SEXCAT (NIL T T T T T) -9 NIL 2534108) (-1076 2528068 2528815 2528883 "SEX" 2528888 T SEX (NIL) -8 NIL NIL) (-1075 2526325 2526785 2527088 "SETMN" 2527811 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1074 2525931 2526057 2526087 "SETCAT" 2526204 T SETCAT (NIL) -9 NIL 2526289) (-1073 2525711 2525763 2525862 "SETCAT-" 2525867 NIL SETCAT- (NIL T) -8 NIL NIL) (-1072 2522098 2524172 2524215 "SETAGG" 2525085 NIL SETAGG (NIL T) -9 NIL 2525425) (-1071 2521556 2521672 2521909 "SETAGG-" 2521914 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1070 2518736 2521490 2521538 "SET" 2521543 NIL SET (NIL T) -8 NIL NIL) (-1069 2518206 2518432 2518533 "SEQAST" 2518657 T SEQAST (NIL) -8 NIL NIL) (-1068 2517410 2517703 2517764 "SEGXCAT" 2518050 NIL SEGXCAT (NIL T T) -9 NIL 2518170) (-1067 2516317 2516530 2516573 "SEGCAT" 2517155 NIL SEGCAT (NIL T) -9 NIL 2517393) (-1066 2515938 2515997 2516110 "SEGBIND2" 2516252 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1065 2514987 2515317 2515517 "SEGBIND" 2515773 NIL SEGBIND (NIL T) -8 NIL NIL) (-1064 2514588 2514788 2514865 "SEGAST" 2514932 T SEGAST (NIL) -8 NIL NIL) (-1063 2513807 2513933 2514137 "SEG2" 2514432 NIL SEG2 (NIL T T) -7 NIL NIL) (-1062 2512863 2513473 2513655 "SEG" 2513660 NIL SEG (NIL T) -8 NIL NIL) (-1061 2512300 2512798 2512845 "SDVAR" 2512850 NIL SDVAR (NIL T) -8 NIL NIL) (-1060 2504631 2512070 2512200 "SDPOL" 2512205 NIL SDPOL (NIL T) -8 NIL NIL) (-1059 2503224 2503490 2503809 "SCPKG" 2504346 NIL SCPKG (NIL T) -7 NIL NIL) (-1058 2502360 2502540 2502740 "SCOPE" 2503046 T SCOPE (NIL) -8 NIL NIL) (-1057 2501581 2501714 2501893 "SCACHE" 2502215 NIL SCACHE (NIL T) -7 NIL NIL) (-1056 2501290 2501450 2501480 "SASTCAT" 2501485 T SASTCAT (NIL) -9 NIL 2501498) (-1055 2500729 2501050 2501135 "SAOS" 2501227 T SAOS (NIL) -8 NIL NIL) (-1054 2500294 2500329 2500502 "SAERFFC" 2500688 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1053 2499887 2499922 2500081 "SAEFACT" 2500253 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1052 2493870 2499784 2499864 "SAE" 2499869 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1051 2492191 2492505 2492906 "RURPK" 2493536 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1050 2490827 2491106 2491418 "RULESET" 2492025 NIL RULESET (NIL T T T) -8 NIL NIL) (-1049 2490466 2490621 2490704 "RULECOLD" 2490779 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1048 2487653 2488156 2488621 "RULE" 2490147 NIL RULE (NIL T T T) -8 NIL NIL) (-1047 2487151 2487370 2487464 "RSTRCAST" 2487581 T RSTRCAST (NIL) -8 NIL NIL) (-1046 2482000 2482794 2483714 "RSETGCD" 2486350 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1045 2471284 2476309 2476406 "RSETCAT" 2480525 NIL RSETCAT (NIL T T T T) -9 NIL 2481622) (-1044 2469211 2469750 2470574 "RSETCAT-" 2470579 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1043 2461598 2462973 2464493 "RSDCMPK" 2467810 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1042 2459603 2460044 2460118 "RRCC" 2461204 NIL RRCC (NIL T T) -9 NIL 2461548) (-1041 2458954 2459128 2459407 "RRCC-" 2459412 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1040 2458424 2458650 2458751 "RPTAST" 2458875 T RPTAST (NIL) -8 NIL NIL) (-1039 2432683 2442237 2442304 "RPOLCAT" 2452968 NIL RPOLCAT (NIL T T T) -9 NIL 2456127) (-1038 2424219 2426545 2429655 "RPOLCAT-" 2429660 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1037 2415268 2422430 2422912 "ROUTINE" 2423759 T ROUTINE (NIL) -8 NIL NIL) (-1036 2412028 2414819 2414968 "ROMAN" 2415141 T ROMAN (NIL) -8 NIL NIL) (-1035 2410305 2410888 2411148 "ROIRC" 2411833 NIL ROIRC (NIL T T) -8 NIL NIL) (-1034 2406760 2408995 2409025 "RNS" 2409329 T RNS (NIL) -9 NIL 2409601) (-1033 2405269 2405652 2406186 "RNS-" 2406261 NIL RNS- (NIL T) -8 NIL NIL) (-1032 2404718 2405100 2405130 "RNG" 2405135 T RNG (NIL) -9 NIL 2405156) (-1031 2404110 2404472 2404515 "RMODULE" 2404577 NIL RMODULE (NIL T) -9 NIL 2404619) (-1030 2402946 2403040 2403376 "RMCAT2" 2404011 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1029 2399651 2402120 2402445 "RMATRIX" 2402680 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1028 2392593 2394827 2394942 "RMATCAT" 2398301 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2399283) (-1027 2391968 2392115 2392422 "RMATCAT-" 2392427 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1026 2391535 2391610 2391738 "RINTERP" 2391887 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1025 2390623 2391143 2391173 "RING" 2391285 T RING (NIL) -9 NIL 2391380) (-1024 2390415 2390459 2390556 "RING-" 2390561 NIL RING- (NIL T) -8 NIL NIL) (-1023 2389256 2389493 2389751 "RIDIST" 2390179 T RIDIST (NIL) -7 NIL NIL) (-1022 2380599 2388724 2388930 "RGCHAIN" 2389104 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1021 2379975 2380355 2380396 "RGBCSPC" 2380454 NIL RGBCSPC (NIL T) -9 NIL 2380506) (-1020 2379159 2379514 2379555 "RGBCMDL" 2379787 NIL RGBCMDL (NIL T) -9 NIL 2379901) (-1019 2378805 2378868 2378971 "RFFACTOR" 2379090 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1018 2378530 2378565 2378662 "RFFACT" 2378764 NIL RFFACT (NIL T) -7 NIL NIL) (-1017 2376647 2377011 2377393 "RFDIST" 2378170 T RFDIST (NIL) -7 NIL NIL) (-1016 2373641 2374255 2374925 "RF" 2376011 NIL RF (NIL T) -7 NIL NIL) (-1015 2373094 2373186 2373349 "RETSOL" 2373543 NIL RETSOL (NIL T T) -7 NIL NIL) (-1014 2372682 2372762 2372805 "RETRACT" 2372998 NIL RETRACT (NIL T) -9 NIL NIL) (-1013 2372531 2372556 2372643 "RETRACT-" 2372648 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1012 2372160 2372353 2372423 "RETAST" 2372483 T RETAST (NIL) -8 NIL NIL) (-1011 2365016 2371813 2371940 "RESULT" 2372055 T RESULT (NIL) -8 NIL NIL) (-1010 2363642 2364285 2364484 "RESRING" 2364919 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1009 2363278 2363327 2363425 "RESLATC" 2363579 NIL RESLATC (NIL T) -7 NIL NIL) (-1008 2362984 2363018 2363125 "REPSQ" 2363237 NIL REPSQ (NIL T) -7 NIL NIL) (-1007 2362682 2362716 2362827 "REPDB" 2362943 NIL REPDB (NIL T) -7 NIL NIL) (-1006 2356592 2357971 2359194 "REP2" 2361494 NIL REP2 (NIL T) -7 NIL NIL) (-1005 2352969 2353650 2354458 "REP1" 2355819 NIL REP1 (NIL T) -7 NIL NIL) (-1004 2350391 2350971 2351573 "REP" 2352389 T REP (NIL) -7 NIL NIL) (-1003 2343144 2348532 2348988 "REGSET" 2350021 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1002 2341957 2342292 2342542 "REF" 2342929 NIL REF (NIL T) -8 NIL NIL) (-1001 2341334 2341437 2341604 "REDORDER" 2341841 NIL REDORDER (NIL T T) -7 NIL NIL) (-1000 2337376 2340553 2340778 "RECLOS" 2341163 NIL RECLOS (NIL T) -8 NIL NIL) (-999 2336433 2336614 2336827 "REALSOLV" 2337183 T REALSOLV (NIL) -7 NIL NIL) (-998 2332924 2333726 2334608 "REAL0Q" 2335598 NIL REAL0Q (NIL T) -7 NIL NIL) (-997 2328535 2329523 2330582 "REAL0" 2331905 NIL REAL0 (NIL T) -7 NIL NIL) (-996 2328383 2328424 2328452 "REAL" 2328457 T REAL (NIL) -9 NIL 2328492) (-995 2327885 2328104 2328196 "RDUCEAST" 2328311 T RDUCEAST (NIL) -8 NIL NIL) (-994 2327293 2327365 2327570 "RDIV" 2327807 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-993 2326366 2326540 2326751 "RDIST" 2327115 NIL RDIST (NIL T) -7 NIL NIL) (-992 2324967 2325254 2325624 "RDETRS" 2326074 NIL RDETRS (NIL T T) -7 NIL NIL) (-991 2322784 2323238 2323774 "RDETR" 2324509 NIL RDETR (NIL T T) -7 NIL NIL) (-990 2321398 2321676 2322078 "RDEEFS" 2322500 NIL RDEEFS (NIL T T) -7 NIL NIL) (-989 2319896 2320202 2320632 "RDEEF" 2321086 NIL RDEEF (NIL T T) -7 NIL NIL) (-988 2314242 2317104 2317132 "RCFIELD" 2318409 T RCFIELD (NIL) -9 NIL 2319139) (-987 2312311 2312815 2313508 "RCFIELD-" 2313581 NIL RCFIELD- (NIL T) -8 NIL NIL) (-986 2308642 2310427 2310468 "RCAGG" 2311539 NIL RCAGG (NIL T) -9 NIL 2312004) (-985 2308273 2308367 2308527 "RCAGG-" 2308532 NIL RCAGG- (NIL T T) -8 NIL NIL) (-984 2307613 2307725 2307888 "RATRET" 2308157 NIL RATRET (NIL T) -7 NIL NIL) (-983 2307170 2307237 2307356 "RATFACT" 2307541 NIL RATFACT (NIL T) -7 NIL NIL) (-982 2306485 2306605 2306755 "RANDSRC" 2307040 T RANDSRC (NIL) -7 NIL NIL) (-981 2306222 2306266 2306337 "RADUTIL" 2306434 T RADUTIL (NIL) -7 NIL NIL) (-980 2299308 2304965 2305282 "RADIX" 2305937 NIL RADIX (NIL NIL) -8 NIL NIL) (-979 2290975 2299152 2299280 "RADFF" 2299285 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-978 2290627 2290702 2290730 "RADCAT" 2290887 T RADCAT (NIL) -9 NIL NIL) (-977 2290412 2290460 2290557 "RADCAT-" 2290562 NIL RADCAT- (NIL T) -8 NIL NIL) (-976 2288563 2290187 2290276 "QUEUE" 2290356 NIL QUEUE (NIL T) -8 NIL NIL) (-975 2288201 2288244 2288371 "QUATCT2" 2288514 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-974 2282068 2285362 2285402 "QUATCAT" 2286182 NIL QUATCAT (NIL T) -9 NIL 2286948) (-973 2278233 2279263 2280643 "QUATCAT-" 2280737 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-972 2274816 2278170 2278215 "QUAT" 2278220 NIL QUAT (NIL T) -8 NIL NIL) (-971 2272336 2273900 2273941 "QUAGG" 2274316 NIL QUAGG (NIL T) -9 NIL 2274491) (-970 2271968 2272161 2272229 "QQUTAST" 2272288 T QQUTAST (NIL) -8 NIL NIL) (-969 2270893 2271366 2271538 "QFORM" 2271840 NIL QFORM (NIL NIL T) -8 NIL NIL) (-968 2270531 2270574 2270701 "QFCAT2" 2270844 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-967 2261880 2267067 2267107 "QFCAT" 2267765 NIL QFCAT (NIL T) -9 NIL 2268764) (-966 2257488 2258677 2260256 "QFCAT-" 2260350 NIL QFCAT- (NIL T T) -8 NIL NIL) (-965 2256948 2257058 2257188 "QEQUAT" 2257378 T QEQUAT (NIL) -8 NIL NIL) (-964 2250096 2251167 2252351 "QCMPACK" 2255881 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-963 2249341 2249515 2249747 "QALGSET2" 2249916 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-962 2246923 2247342 2247768 "QALGSET" 2248998 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-961 2245614 2245837 2246154 "PWFFINTB" 2246696 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-960 2243813 2243981 2244335 "PUSHVAR" 2245428 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-959 2239731 2240785 2240826 "PTRANFN" 2242710 NIL PTRANFN (NIL T) -9 NIL NIL) (-958 2238133 2238424 2238746 "PTPACK" 2239442 NIL PTPACK (NIL T) -7 NIL NIL) (-957 2237765 2237822 2237931 "PTFUNC2" 2238070 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-956 2232231 2236576 2236617 "PTCAT" 2236990 NIL PTCAT (NIL T) -9 NIL 2237152) (-955 2231889 2231924 2232048 "PSQFR" 2232190 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-954 2230484 2230782 2231116 "PSEUDLIN" 2231587 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-953 2217253 2219618 2221942 "PSETPK" 2228244 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-952 2210297 2213011 2213107 "PSETCAT" 2216128 NIL PSETCAT (NIL T T T T) -9 NIL 2216942) (-951 2208133 2208767 2209588 "PSETCAT-" 2209593 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-950 2207482 2207647 2207675 "PSCURVE" 2207943 T PSCURVE (NIL) -9 NIL 2208110) (-949 2203963 2205445 2205510 "PSCAT" 2206354 NIL PSCAT (NIL T T T) -9 NIL 2206594) (-948 2203026 2203242 2203642 "PSCAT-" 2203647 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-947 2201678 2202311 2202525 "PRTITION" 2202832 T PRTITION (NIL) -8 NIL NIL) (-946 2201180 2201399 2201491 "PRTDAST" 2201606 T PRTDAST (NIL) -8 NIL NIL) (-945 2190278 2192484 2194672 "PRS" 2199042 NIL PRS (NIL T T) -7 NIL NIL) (-944 2188136 2189628 2189668 "PRQAGG" 2189851 NIL PRQAGG (NIL T) -9 NIL 2189953) (-943 2187522 2187751 2187779 "PROPLOG" 2187964 T PROPLOG (NIL) -9 NIL 2188086) (-942 2184692 2185336 2185800 "PROPFRML" 2187090 NIL PROPFRML (NIL T) -8 NIL NIL) (-941 2184152 2184262 2184392 "PROPERTY" 2184582 T PROPERTY (NIL) -8 NIL NIL) (-940 2178237 2182318 2183138 "PRODUCT" 2183378 NIL PRODUCT (NIL T T) -8 NIL NIL) (-939 2178033 2178065 2178124 "PRINT" 2178198 T PRINT (NIL) -7 NIL NIL) (-938 2177373 2177490 2177642 "PRIMES" 2177913 NIL PRIMES (NIL T) -7 NIL NIL) (-937 2175438 2175839 2176305 "PRIMELT" 2176952 NIL PRIMELT (NIL T) -7 NIL NIL) (-936 2175167 2175216 2175244 "PRIMCAT" 2175368 T PRIMCAT (NIL) -9 NIL NIL) (-935 2174174 2174352 2174580 "PRIMARR2" 2174985 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-934 2170335 2174112 2174157 "PRIMARR" 2174162 NIL PRIMARR (NIL T) -8 NIL NIL) (-933 2169978 2170034 2170145 "PREASSOC" 2170273 NIL PREASSOC (NIL T T) -7 NIL NIL) (-932 2167298 2169436 2169670 "PR" 2169789 NIL PR (NIL T T) -8 NIL NIL) (-931 2166773 2166906 2166934 "PPCURVE" 2167139 T PPCURVE (NIL) -9 NIL 2167275) (-930 2166395 2166568 2166651 "PORTNUM" 2166710 T PORTNUM (NIL) -8 NIL NIL) (-929 2163754 2164153 2164745 "POLYROOT" 2165976 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-928 2163137 2163195 2163429 "POLYLIFT" 2163690 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-927 2159412 2159861 2160490 "POLYCATQ" 2162682 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-926 2146465 2151807 2151872 "POLYCAT" 2155386 NIL POLYCAT (NIL T T T) -9 NIL 2157314) (-925 2139972 2141814 2144179 "POLYCAT-" 2144184 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-924 2139559 2139627 2139747 "POLY2UP" 2139898 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-923 2139191 2139248 2139357 "POLY2" 2139496 NIL POLY2 (NIL T T) -7 NIL NIL) (-922 2133167 2138795 2138955 "POLY" 2139064 NIL POLY (NIL T) -8 NIL NIL) (-921 2131852 2132091 2132367 "POLUTIL" 2132941 NIL POLUTIL (NIL T T) -7 NIL NIL) (-920 2130207 2130484 2130815 "POLTOPOL" 2131574 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-919 2125725 2130143 2130189 "POINT" 2130194 NIL POINT (NIL T) -8 NIL NIL) (-918 2123912 2124269 2124644 "PNTHEORY" 2125370 T PNTHEORY (NIL) -7 NIL NIL) (-917 2122331 2122628 2123040 "PMTOOLS" 2123610 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-916 2121924 2122002 2122119 "PMSYM" 2122247 NIL PMSYM (NIL T) -7 NIL NIL) (-915 2121434 2121503 2121677 "PMQFCAT" 2121849 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-914 2120830 2120916 2121077 "PMPREDFS" 2121335 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-913 2120185 2120295 2120451 "PMPRED" 2120707 NIL PMPRED (NIL T) -7 NIL NIL) (-912 2118828 2119036 2119421 "PMPLCAT" 2119947 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-911 2118360 2118439 2118591 "PMLSAGG" 2118743 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-910 2117835 2117911 2118092 "PMKERNEL" 2118278 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-909 2117452 2117527 2117640 "PMINS" 2117754 NIL PMINS (NIL T) -7 NIL NIL) (-908 2116880 2116949 2117165 "PMFS" 2117377 NIL PMFS (NIL T T T) -7 NIL NIL) (-907 2116108 2116226 2116431 "PMDOWN" 2116757 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-906 2115382 2115493 2115656 "PMASSFS" 2115994 NIL PMASSFS (NIL T T) -7 NIL NIL) (-905 2114545 2114704 2114886 "PMASS" 2115220 T PMASS (NIL) -7 NIL NIL) (-904 2114200 2114268 2114362 "PLOTTOOL" 2114471 T PLOTTOOL (NIL) -7 NIL NIL) (-903 2110014 2111048 2111969 "PLOT3D" 2113299 T PLOT3D (NIL) -8 NIL NIL) (-902 2108926 2109103 2109338 "PLOT1" 2109818 NIL PLOT1 (NIL T) -7 NIL NIL) (-901 2103548 2104737 2105885 "PLOT" 2107798 T PLOT (NIL) -8 NIL NIL) (-900 2078942 2083614 2088465 "PLEQN" 2098814 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-899 2078635 2078682 2078785 "PINTERPA" 2078889 NIL PINTERPA (NIL T T) -7 NIL NIL) (-898 2077953 2078075 2078255 "PINTERP" 2078500 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-897 2076385 2077326 2077354 "PID" 2077536 T PID (NIL) -9 NIL 2077670) (-896 2076110 2076147 2076235 "PICOERCE" 2076342 NIL PICOERCE (NIL T) -7 NIL NIL) (-895 2075395 2075916 2076003 "PI" 2076043 T PI (NIL) -8 NIL NIL) (-894 2074715 2074854 2075030 "PGROEB" 2075251 NIL PGROEB (NIL T) -7 NIL NIL) (-893 2070302 2071116 2072021 "PGE" 2073830 T PGE (NIL) -7 NIL NIL) (-892 2068426 2068672 2069038 "PGCD" 2070019 NIL PGCD (NIL T T T T) -7 NIL NIL) (-891 2067764 2067867 2068028 "PFRPAC" 2068310 NIL PFRPAC (NIL T) -7 NIL NIL) (-890 2064446 2066312 2066665 "PFR" 2067443 NIL PFR (NIL T) -8 NIL NIL) (-889 2062835 2063079 2063404 "PFOTOOLS" 2064193 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-888 2061368 2061607 2061958 "PFOQ" 2062592 NIL PFOQ (NIL T T T) -7 NIL NIL) (-887 2059841 2060053 2060416 "PFO" 2061152 NIL PFO (NIL T T T T T) -7 NIL NIL) (-886 2057310 2058547 2058575 "PFECAT" 2059160 T PFECAT (NIL) -9 NIL 2059544) (-885 2056755 2056909 2057123 "PFECAT-" 2057128 NIL PFECAT- (NIL T) -8 NIL NIL) (-884 2055359 2055610 2055911 "PFBRU" 2056504 NIL PFBRU (NIL T T) -7 NIL NIL) (-883 2053226 2053577 2054009 "PFBR" 2055010 NIL PFBR (NIL T T T T) -7 NIL NIL) (-882 2049816 2053115 2053184 "PF" 2053189 NIL PF (NIL NIL) -8 NIL NIL) (-881 2045082 2046023 2046893 "PERMGRP" 2048979 NIL PERMGRP (NIL T) -8 NIL NIL) (-880 2043214 2044145 2044186 "PERMCAT" 2044632 NIL PERMCAT (NIL T) -9 NIL 2044937) (-879 2042867 2042908 2043032 "PERMAN" 2043167 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-878 2038783 2040243 2040919 "PERM" 2042224 NIL PERM (NIL T) -8 NIL NIL) (-877 2036225 2038352 2038483 "PENDTREE" 2038685 NIL PENDTREE (NIL T) -8 NIL NIL) (-876 2034338 2035072 2035113 "PDRING" 2035770 NIL PDRING (NIL T) -9 NIL 2036056) (-875 2033441 2033659 2034021 "PDRING-" 2034026 NIL PDRING- (NIL T T) -8 NIL NIL) (-874 2030582 2031333 2032024 "PDEPROB" 2032770 T PDEPROB (NIL) -8 NIL NIL) (-873 2028129 2028631 2029186 "PDEPACK" 2030047 T PDEPACK (NIL) -7 NIL NIL) (-872 2027041 2027231 2027482 "PDECOMP" 2027928 NIL PDECOMP (NIL T T) -7 NIL NIL) (-871 2024646 2025463 2025491 "PDECAT" 2026278 T PDECAT (NIL) -9 NIL 2026991) (-870 2024397 2024430 2024520 "PCOMP" 2024607 NIL PCOMP (NIL T T) -7 NIL NIL) (-869 2022602 2023198 2023495 "PBWLB" 2024126 NIL PBWLB (NIL T) -8 NIL NIL) (-868 2022234 2022291 2022400 "PATTERN2" 2022539 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-867 2019991 2020379 2020836 "PATTERN1" 2021823 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-866 2012497 2014064 2015402 "PATTERN" 2018674 NIL PATTERN (NIL T) -8 NIL NIL) (-865 2012061 2012128 2012260 "PATRES2" 2012424 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-864 2009456 2010010 2010491 "PATRES" 2011626 NIL PATRES (NIL T T) -8 NIL NIL) (-863 2007339 2007744 2008151 "PATMATCH" 2009123 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-862 2006875 2007058 2007099 "PATMAB" 2007206 NIL PATMAB (NIL T) -9 NIL 2007289) (-861 2005420 2005729 2005987 "PATLRES" 2006680 NIL PATLRES (NIL T T T) -8 NIL NIL) (-860 2004966 2005089 2005130 "PATAB" 2005135 NIL PATAB (NIL T) -9 NIL 2005307) (-859 2002447 2002979 2003552 "PARTPERM" 2004413 T PARTPERM (NIL) -7 NIL NIL) (-858 2002068 2002131 2002233 "PARSURF" 2002378 NIL PARSURF (NIL T) -8 NIL NIL) (-857 2001700 2001757 2001866 "PARSU2" 2002005 NIL PARSU2 (NIL T T) -7 NIL NIL) (-856 2001464 2001504 2001571 "PARSER" 2001653 T PARSER (NIL) -7 NIL NIL) (-855 2001085 2001148 2001250 "PARSCURV" 2001395 NIL PARSCURV (NIL T) -8 NIL NIL) (-854 2000717 2000774 2000883 "PARSC2" 2001022 NIL PARSC2 (NIL T T) -7 NIL NIL) (-853 2000356 2000414 2000511 "PARPCURV" 2000653 NIL PARPCURV (NIL T) -8 NIL NIL) (-852 1999988 2000045 2000154 "PARPC2" 2000293 NIL PARPC2 (NIL T T) -7 NIL NIL) (-851 1999508 1999594 1999713 "PAN2EXPR" 1999889 T PAN2EXPR (NIL) -7 NIL NIL) (-850 1998314 1998629 1998857 "PALETTE" 1999300 T PALETTE (NIL) -8 NIL NIL) (-849 1996782 1997319 1997679 "PAIR" 1998000 NIL PAIR (NIL T T) -8 NIL NIL) (-848 1990711 1996041 1996235 "PADICRC" 1996637 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-847 1983998 1990057 1990241 "PADICRAT" 1990559 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-846 1981245 1982773 1982813 "PADICCT" 1983394 NIL PADICCT (NIL NIL) -9 NIL 1983676) (-845 1979597 1981182 1981227 "PADIC" 1981232 NIL PADIC (NIL NIL) -8 NIL NIL) (-844 1978554 1978754 1979022 "PADEPAC" 1979384 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-843 1977766 1977899 1978105 "PADE" 1978416 NIL PADE (NIL T T T) -7 NIL NIL) (-842 1975816 1976602 1976919 "OWP" 1977533 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-841 1974925 1975421 1975593 "OVAR" 1975684 NIL OVAR (NIL NIL) -8 NIL NIL) (-840 1963832 1966034 1968234 "OUTFORM" 1972745 T OUTFORM (NIL) -8 NIL NIL) (-839 1963253 1963429 1963556 "OUTBFILE" 1963725 T OUTBFILE (NIL) -8 NIL NIL) (-838 1962890 1962973 1963001 "OUTBCON" 1963152 T OUTBCON (NIL) -9 NIL 1963237) (-837 1962730 1962765 1962841 "OUTBCON-" 1962846 NIL OUTBCON- (NIL T) -8 NIL NIL) (-836 1961994 1962115 1962276 "OUT" 1962589 T OUT (NIL) -7 NIL NIL) (-835 1961402 1961723 1961812 "OSI" 1961925 T OSI (NIL) -8 NIL NIL) (-834 1960958 1961270 1961298 "OSGROUP" 1961303 T OSGROUP (NIL) -9 NIL 1961325) (-833 1959703 1959930 1960215 "ORTHPOL" 1960705 NIL ORTHPOL (NIL T) -7 NIL NIL) (-832 1957127 1959362 1959501 "OREUP" 1959646 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-831 1954579 1956818 1956945 "ORESUP" 1957069 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-830 1952107 1952607 1953168 "OREPCTO" 1954068 NIL OREPCTO (NIL T T) -7 NIL NIL) (-829 1946025 1948185 1948226 "OREPCAT" 1950574 NIL OREPCAT (NIL T) -9 NIL 1951678) (-828 1943193 1943968 1945019 "OREPCAT-" 1945024 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-827 1942370 1942642 1942670 "ORDSET" 1942979 T ORDSET (NIL) -9 NIL 1943143) (-826 1941889 1942011 1942204 "ORDSET-" 1942209 NIL ORDSET- (NIL T) -8 NIL NIL) (-825 1940543 1941300 1941328 "ORDRING" 1941530 T ORDRING (NIL) -9 NIL 1941655) (-824 1940188 1940282 1940426 "ORDRING-" 1940431 NIL ORDRING- (NIL T) -8 NIL NIL) (-823 1939594 1940031 1940059 "ORDMON" 1940064 T ORDMON (NIL) -9 NIL 1940085) (-822 1938756 1938903 1939098 "ORDFUNS" 1939443 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-821 1938267 1938626 1938654 "ORDFIN" 1938659 T ORDFIN (NIL) -9 NIL 1938680) (-820 1937533 1937660 1937846 "ORDCOMP2" 1938127 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-819 1934132 1936119 1936528 "ORDCOMP" 1937157 NIL ORDCOMP (NIL T) -8 NIL NIL) (-818 1930639 1931522 1932359 "OPTPROB" 1933315 T OPTPROB (NIL) -8 NIL NIL) (-817 1927441 1928080 1928784 "OPTPACK" 1929955 T OPTPACK (NIL) -7 NIL NIL) (-816 1925154 1925894 1925922 "OPTCAT" 1926741 T OPTCAT (NIL) -9 NIL 1927391) (-815 1924922 1924961 1925027 "OPQUERY" 1925108 T OPQUERY (NIL) -7 NIL NIL) (-814 1922090 1923233 1923737 "OP" 1924451 NIL OP (NIL T) -8 NIL NIL) (-813 1921395 1921510 1921684 "ONECOMP2" 1921962 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-812 1918247 1920192 1920561 "ONECOMP" 1921059 NIL ONECOMP (NIL T) -8 NIL NIL) (-811 1917666 1917772 1917902 "OMSERVER" 1918137 T OMSERVER (NIL) -7 NIL NIL) (-810 1914554 1917106 1917146 "OMSAGG" 1917207 NIL OMSAGG (NIL T) -9 NIL 1917271) (-809 1913177 1913440 1913722 "OMPKG" 1914292 T OMPKG (NIL) -7 NIL NIL) (-808 1911759 1912726 1912895 "OMLO" 1913058 NIL OMLO (NIL T T) -8 NIL NIL) (-807 1910684 1910831 1911058 "OMEXPR" 1911585 NIL OMEXPR (NIL T) -7 NIL NIL) (-806 1909862 1910105 1910265 "OMERRK" 1910544 T OMERRK (NIL) -8 NIL NIL) (-805 1909180 1909408 1909544 "OMERR" 1909746 T OMERR (NIL) -8 NIL NIL) (-804 1908658 1908857 1908965 "OMENC" 1909092 T OMENC (NIL) -8 NIL NIL) (-803 1902553 1903738 1904909 "OMDEV" 1907507 T OMDEV (NIL) -8 NIL NIL) (-802 1901622 1901793 1901987 "OMCONN" 1902379 T OMCONN (NIL) -8 NIL NIL) (-801 1901052 1901155 1901183 "OM" 1901482 T OM (NIL) -9 NIL NIL) (-800 1899708 1900650 1900678 "OINTDOM" 1900683 T OINTDOM (NIL) -9 NIL 1900704) (-799 1895514 1896698 1897414 "OFMONOID" 1899024 NIL OFMONOID (NIL T) -8 NIL NIL) (-798 1894952 1895451 1895496 "ODVAR" 1895501 NIL ODVAR (NIL T) -8 NIL NIL) (-797 1892164 1894449 1894634 "ODR" 1894827 NIL ODR (NIL T T NIL) -8 NIL NIL) (-796 1884549 1891940 1892066 "ODPOL" 1892071 NIL ODPOL (NIL T) -8 NIL NIL) (-795 1878432 1884421 1884526 "ODP" 1884531 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-794 1877198 1877413 1877688 "ODETOOLS" 1878206 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-793 1874167 1874823 1875539 "ODESYS" 1876531 NIL ODESYS (NIL T T) -7 NIL NIL) (-792 1869049 1869957 1870982 "ODERTRIC" 1873242 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-791 1868475 1868557 1868751 "ODERED" 1868961 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-790 1865371 1865917 1866592 "ODERAT" 1867900 NIL ODERAT (NIL T T) -7 NIL NIL) (-789 1862331 1862795 1863392 "ODEPRRIC" 1864900 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-788 1860200 1860769 1861278 "ODEPROB" 1861842 T ODEPROB (NIL) -8 NIL NIL) (-787 1856722 1857205 1857852 "ODEPRIM" 1859679 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-786 1855971 1856073 1856333 "ODEPAL" 1856614 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-785 1852133 1852924 1853788 "ODEPACK" 1855127 T ODEPACK (NIL) -7 NIL NIL) (-784 1851166 1851273 1851502 "ODEINT" 1852022 NIL ODEINT (NIL T T) -7 NIL NIL) (-783 1845267 1846692 1848139 "ODEIFTBL" 1849739 T ODEIFTBL (NIL) -8 NIL NIL) (-782 1840616 1841398 1842353 "ODEEF" 1844430 NIL ODEEF (NIL T T) -7 NIL NIL) (-781 1839951 1840040 1840270 "ODECONST" 1840521 NIL ODECONST (NIL T T T) -7 NIL NIL) (-780 1838102 1838737 1838765 "ODECAT" 1839370 T ODECAT (NIL) -9 NIL 1839901) (-779 1837740 1837783 1837910 "OCTCT2" 1838053 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-778 1834659 1837452 1837571 "OCT" 1837653 NIL OCT (NIL T) -8 NIL NIL) (-777 1834037 1834479 1834507 "OCAMON" 1834512 T OCAMON (NIL) -9 NIL 1834533) (-776 1828905 1831298 1831338 "OC" 1832435 NIL OC (NIL T) -9 NIL 1833293) (-775 1826153 1826894 1827877 "OC-" 1827971 NIL OC- (NIL T T) -8 NIL NIL) (-774 1825710 1826025 1826053 "OASGP" 1826058 T OASGP (NIL) -9 NIL 1826078) (-773 1824997 1825460 1825488 "OAMONS" 1825528 T OAMONS (NIL) -9 NIL 1825571) (-772 1824437 1824844 1824872 "OAMON" 1824877 T OAMON (NIL) -9 NIL 1824897) (-771 1823741 1824233 1824261 "OAGROUP" 1824266 T OAGROUP (NIL) -9 NIL 1824286) (-770 1823431 1823481 1823569 "NUMTUBE" 1823685 NIL NUMTUBE (NIL T) -7 NIL NIL) (-769 1817004 1818522 1820058 "NUMQUAD" 1821915 T NUMQUAD (NIL) -7 NIL NIL) (-768 1812760 1813748 1814773 "NUMODE" 1815999 T NUMODE (NIL) -7 NIL NIL) (-767 1810141 1810995 1811023 "NUMINT" 1811946 T NUMINT (NIL) -9 NIL 1812710) (-766 1809089 1809286 1809504 "NUMFMT" 1809943 T NUMFMT (NIL) -7 NIL NIL) (-765 1795448 1798393 1800925 "NUMERIC" 1806596 NIL NUMERIC (NIL T) -7 NIL NIL) (-764 1789872 1794897 1794992 "NTSCAT" 1794997 NIL NTSCAT (NIL T T T T) -9 NIL 1795036) (-763 1789066 1789231 1789424 "NTPOLFN" 1789711 NIL NTPOLFN (NIL T) -7 NIL NIL) (-762 1788698 1788755 1788864 "NSUP2" 1789003 NIL NSUP2 (NIL T T) -7 NIL NIL) (-761 1776583 1785523 1786335 "NSUP" 1787919 NIL NSUP (NIL T) -8 NIL NIL) (-760 1766628 1776357 1776490 "NSMP" 1776495 NIL NSMP (NIL T T) -8 NIL NIL) (-759 1765060 1765361 1765718 "NREP" 1766316 NIL NREP (NIL T) -7 NIL NIL) (-758 1763651 1763903 1764261 "NPCOEF" 1764803 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-757 1762717 1762832 1763048 "NORMRETR" 1763532 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-756 1760758 1761048 1761457 "NORMPK" 1762425 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-755 1760443 1760471 1760595 "NORMMA" 1760724 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-754 1760232 1760261 1760330 "NONE1" 1760407 NIL NONE1 (NIL T) -7 NIL NIL) (-753 1760059 1760189 1760218 "NONE" 1760223 T NONE (NIL) -8 NIL NIL) (-752 1759542 1759604 1759790 "NODE1" 1759991 NIL NODE1 (NIL T T) -7 NIL NIL) (-751 1757882 1758705 1758960 "NNI" 1759307 T NNI (NIL) -8 NIL NIL) (-750 1756302 1756615 1756979 "NLINSOL" 1757550 NIL NLINSOL (NIL T) -7 NIL NIL) (-749 1752469 1753437 1754359 "NIPROB" 1755400 T NIPROB (NIL) -8 NIL NIL) (-748 1751226 1751460 1751762 "NFINTBAS" 1752231 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-747 1749934 1750165 1750446 "NCODIV" 1750994 NIL NCODIV (NIL T T) -7 NIL NIL) (-746 1749696 1749733 1749808 "NCNTFRAC" 1749891 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-745 1747876 1748240 1748660 "NCEP" 1749321 NIL NCEP (NIL T) -7 NIL NIL) (-744 1746794 1747526 1747554 "NASRING" 1747664 T NASRING (NIL) -9 NIL 1747738) (-743 1746589 1746633 1746727 "NASRING-" 1746732 NIL NASRING- (NIL T) -8 NIL NIL) (-742 1745742 1746241 1746269 "NARNG" 1746386 T NARNG (NIL) -9 NIL 1746477) (-741 1745434 1745501 1745635 "NARNG-" 1745640 NIL NARNG- (NIL T) -8 NIL NIL) (-740 1744313 1744520 1744755 "NAGSP" 1745219 T NAGSP (NIL) -7 NIL NIL) (-739 1735585 1737269 1738942 "NAGS" 1742660 T NAGS (NIL) -7 NIL NIL) (-738 1734133 1734441 1734772 "NAGF07" 1735274 T NAGF07 (NIL) -7 NIL NIL) (-737 1728671 1729962 1731269 "NAGF04" 1732846 T NAGF04 (NIL) -7 NIL NIL) (-736 1721639 1723253 1724886 "NAGF02" 1727058 T NAGF02 (NIL) -7 NIL NIL) (-735 1716863 1717963 1719080 "NAGF01" 1720542 T NAGF01 (NIL) -7 NIL NIL) (-734 1710491 1712057 1713642 "NAGE04" 1715298 T NAGE04 (NIL) -7 NIL NIL) (-733 1701660 1703781 1705911 "NAGE02" 1708381 T NAGE02 (NIL) -7 NIL NIL) (-732 1697613 1698560 1699524 "NAGE01" 1700716 T NAGE01 (NIL) -7 NIL NIL) (-731 1695408 1695942 1696500 "NAGD03" 1697075 T NAGD03 (NIL) -7 NIL NIL) (-730 1687158 1689086 1691040 "NAGD02" 1693474 T NAGD02 (NIL) -7 NIL NIL) (-729 1680969 1682394 1683834 "NAGD01" 1685738 T NAGD01 (NIL) -7 NIL NIL) (-728 1677178 1678000 1678837 "NAGC06" 1680152 T NAGC06 (NIL) -7 NIL NIL) (-727 1675643 1675975 1676331 "NAGC05" 1676842 T NAGC05 (NIL) -7 NIL NIL) (-726 1675019 1675138 1675282 "NAGC02" 1675519 T NAGC02 (NIL) -7 NIL NIL) (-725 1674079 1674636 1674676 "NAALG" 1674755 NIL NAALG (NIL T) -9 NIL 1674816) (-724 1673914 1673943 1674033 "NAALG-" 1674038 NIL NAALG- (NIL T T) -8 NIL NIL) (-723 1667864 1668972 1670159 "MULTSQFR" 1672810 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-722 1667183 1667258 1667442 "MULTFACT" 1667776 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-721 1660406 1664271 1664324 "MTSCAT" 1665394 NIL MTSCAT (NIL T T) -9 NIL 1665908) (-720 1660118 1660172 1660264 "MTHING" 1660346 NIL MTHING (NIL T) -7 NIL NIL) (-719 1659910 1659943 1660003 "MSYSCMD" 1660078 T MSYSCMD (NIL) -7 NIL NIL) (-718 1657005 1659471 1659512 "MSETAGG" 1659517 NIL MSETAGG (NIL T) -9 NIL 1659551) (-717 1653117 1655760 1656080 "MSET" 1656718 NIL MSET (NIL T) -8 NIL NIL) (-716 1649002 1650496 1651241 "MRING" 1652417 NIL MRING (NIL T T) -8 NIL NIL) (-715 1648568 1648635 1648766 "MRF2" 1648929 NIL MRF2 (NIL T T T) -7 NIL NIL) (-714 1648186 1648221 1648365 "MRATFAC" 1648527 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-713 1645798 1646093 1646524 "MPRFF" 1647891 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-712 1639884 1645652 1645749 "MPOLY" 1645754 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-711 1639374 1639409 1639617 "MPCPF" 1639843 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-710 1638888 1638931 1639115 "MPC3" 1639325 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-709 1638083 1638164 1638385 "MPC2" 1638803 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-708 1636384 1636721 1637111 "MONOTOOL" 1637743 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-707 1635635 1635926 1635954 "MONOID" 1636173 T MONOID (NIL) -9 NIL 1636320) (-706 1635181 1635300 1635481 "MONOID-" 1635486 NIL MONOID- (NIL T) -8 NIL NIL) (-705 1626240 1632137 1632196 "MONOGEN" 1632870 NIL MONOGEN (NIL T T) -9 NIL 1633326) (-704 1623479 1624207 1625200 "MONOGEN-" 1625319 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-703 1622338 1622758 1622786 "MONADWU" 1623178 T MONADWU (NIL) -9 NIL 1623416) (-702 1621710 1621869 1622117 "MONADWU-" 1622122 NIL MONADWU- (NIL T) -8 NIL NIL) (-701 1621095 1621313 1621341 "MONAD" 1621548 T MONAD (NIL) -9 NIL 1621660) (-700 1620780 1620858 1620990 "MONAD-" 1620995 NIL MONAD- (NIL T) -8 NIL NIL) (-699 1619096 1619693 1619972 "MOEBIUS" 1620533 NIL MOEBIUS (NIL T) -8 NIL NIL) (-698 1618488 1618866 1618906 "MODULE" 1618911 NIL MODULE (NIL T) -9 NIL 1618937) (-697 1618056 1618152 1618342 "MODULE-" 1618347 NIL MODULE- (NIL T T) -8 NIL NIL) (-696 1615815 1616464 1616791 "MODRING" 1617880 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-695 1612803 1613920 1614441 "MODOP" 1615344 NIL MODOP (NIL T T) -8 NIL NIL) (-694 1610990 1611442 1611783 "MODMONOM" 1612602 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-693 1600738 1609182 1609605 "MODMON" 1610618 NIL MODMON (NIL T T) -8 NIL NIL) (-692 1597955 1599606 1599882 "MODFIELD" 1600613 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-691 1596959 1597236 1597426 "MMLFORM" 1597785 T MMLFORM (NIL) -8 NIL NIL) (-690 1596485 1596528 1596707 "MMAP" 1596910 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-689 1594754 1595487 1595528 "MLO" 1595951 NIL MLO (NIL T) -9 NIL 1596193) (-688 1592121 1592636 1593238 "MLIFT" 1594235 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-687 1591512 1591596 1591750 "MKUCFUNC" 1592032 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-686 1591111 1591181 1591304 "MKRECORD" 1591435 NIL MKRECORD (NIL T T) -7 NIL NIL) (-685 1590159 1590320 1590548 "MKFUNC" 1590922 NIL MKFUNC (NIL T) -7 NIL NIL) (-684 1589547 1589651 1589807 "MKFLCFN" 1590042 NIL MKFLCFN (NIL T) -7 NIL NIL) (-683 1588973 1589340 1589429 "MKCHSET" 1589491 NIL MKCHSET (NIL T) -8 NIL NIL) (-682 1588250 1588352 1588537 "MKBCFUNC" 1588866 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-681 1584994 1587804 1587940 "MINT" 1588134 T MINT (NIL) -8 NIL NIL) (-680 1583806 1584049 1584326 "MHROWRED" 1584749 NIL MHROWRED (NIL T) -7 NIL NIL) (-679 1579241 1582341 1582746 "MFLOAT" 1583421 T MFLOAT (NIL) -8 NIL NIL) (-678 1578598 1578674 1578845 "MFINFACT" 1579153 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-677 1574933 1575776 1576655 "MESH" 1577739 T MESH (NIL) -7 NIL NIL) (-676 1573323 1573635 1573988 "MDDFACT" 1574620 NIL MDDFACT (NIL T) -7 NIL NIL) (-675 1570165 1572482 1572523 "MDAGG" 1572778 NIL MDAGG (NIL T) -9 NIL 1572921) (-674 1559963 1569458 1569665 "MCMPLX" 1569978 T MCMPLX (NIL) -8 NIL NIL) (-673 1559104 1559250 1559450 "MCDEN" 1559812 NIL MCDEN (NIL T T) -7 NIL NIL) (-672 1556994 1557264 1557644 "MCALCFN" 1558834 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-671 1555905 1556078 1556319 "MAYBE" 1556792 NIL MAYBE (NIL T) -8 NIL NIL) (-670 1553517 1554040 1554602 "MATSTOR" 1555376 NIL MATSTOR (NIL T) -7 NIL NIL) (-669 1549522 1552889 1553137 "MATRIX" 1553302 NIL MATRIX (NIL T) -8 NIL NIL) (-668 1545291 1545995 1546731 "MATLIN" 1548879 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-667 1543885 1544038 1544371 "MATCAT2" 1545126 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-666 1534033 1537174 1537251 "MATCAT" 1542134 NIL MATCAT (NIL T T T) -9 NIL 1543551) (-665 1530397 1531410 1532766 "MATCAT-" 1532771 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-664 1528509 1528833 1529217 "MAPPKG3" 1530072 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-663 1527490 1527663 1527885 "MAPPKG2" 1528333 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-662 1525989 1526273 1526600 "MAPPKG1" 1527196 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-661 1525095 1525395 1525572 "MAPPAST" 1525832 T MAPPAST (NIL) -8 NIL NIL) (-660 1524706 1524764 1524887 "MAPHACK3" 1525031 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-659 1524298 1524359 1524473 "MAPHACK2" 1524638 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-658 1523736 1523839 1523981 "MAPHACK1" 1524189 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-657 1521842 1522436 1522740 "MAGMA" 1523464 NIL MAGMA (NIL T) -8 NIL NIL) (-656 1521348 1521566 1521657 "MACROAST" 1521771 T MACROAST (NIL) -8 NIL NIL) (-655 1517815 1519587 1520048 "M3D" 1520920 NIL M3D (NIL T) -8 NIL NIL) (-654 1511972 1516185 1516226 "LZSTAGG" 1517008 NIL LZSTAGG (NIL T) -9 NIL 1517303) (-653 1507945 1509103 1510560 "LZSTAGG-" 1510565 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-652 1505059 1505836 1506323 "LWORD" 1507490 NIL LWORD (NIL T) -8 NIL NIL) (-651 1504662 1504863 1504938 "LSTAST" 1505004 T LSTAST (NIL) -8 NIL NIL) (-650 1497894 1504433 1504567 "LSQM" 1504572 NIL LSQM (NIL NIL T) -8 NIL NIL) (-649 1497118 1497257 1497485 "LSPP" 1497749 NIL LSPP (NIL T T T T) -7 NIL NIL) (-648 1493960 1494617 1495330 "LSMP1" 1496437 NIL LSMP1 (NIL T) -7 NIL NIL) (-647 1491795 1492089 1492538 "LSMP" 1493656 NIL LSMP (NIL T T T T) -7 NIL NIL) (-646 1485723 1490963 1491004 "LSAGG" 1491066 NIL LSAGG (NIL T) -9 NIL 1491144) (-645 1482418 1483342 1484555 "LSAGG-" 1484560 NIL LSAGG- (NIL T T) -8 NIL NIL) (-644 1480044 1481562 1481811 "LPOLY" 1482213 NIL LPOLY (NIL T T) -8 NIL NIL) (-643 1479626 1479711 1479834 "LPEFRAC" 1479953 NIL LPEFRAC (NIL T) -7 NIL NIL) (-642 1479278 1479390 1479418 "LOGIC" 1479529 T LOGIC (NIL) -9 NIL 1479610) (-641 1479140 1479163 1479234 "LOGIC-" 1479239 NIL LOGIC- (NIL T) -8 NIL NIL) (-640 1478333 1478473 1478666 "LODOOPS" 1478996 NIL LODOOPS (NIL T T) -7 NIL NIL) (-639 1476871 1477106 1477459 "LODOF" 1478080 NIL LODOF (NIL T T) -7 NIL NIL) (-638 1473328 1475711 1475752 "LODOCAT" 1476190 NIL LODOCAT (NIL T) -9 NIL 1476401) (-637 1473061 1473119 1473246 "LODOCAT-" 1473251 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-636 1470430 1472902 1473020 "LODO2" 1473025 NIL LODO2 (NIL T T) -8 NIL NIL) (-635 1467914 1470367 1470412 "LODO1" 1470417 NIL LODO1 (NIL T) -8 NIL NIL) (-634 1465386 1467830 1467896 "LODO" 1467901 NIL LODO (NIL T NIL) -8 NIL NIL) (-633 1464246 1464411 1464723 "LODEEF" 1465209 NIL LODEEF (NIL T T T) -7 NIL NIL) (-632 1462593 1463340 1463593 "LO" 1464078 NIL LO (NIL T T T) -8 NIL NIL) (-631 1457879 1460723 1460764 "LNAGG" 1461711 NIL LNAGG (NIL T) -9 NIL 1462155) (-630 1457026 1457240 1457582 "LNAGG-" 1457587 NIL LNAGG- (NIL T T) -8 NIL NIL) (-629 1453189 1453951 1454590 "LMOPS" 1456441 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-628 1452584 1452946 1452987 "LMODULE" 1453048 NIL LMODULE (NIL T) -9 NIL 1453090) (-627 1449830 1452229 1452352 "LMDICT" 1452494 NIL LMDICT (NIL T) -8 NIL NIL) (-626 1449556 1449738 1449798 "LITERAL" 1449803 NIL LITERAL (NIL T) -8 NIL NIL) (-625 1449081 1449155 1449294 "LIST3" 1449476 NIL LIST3 (NIL T T T) -7 NIL NIL) (-624 1447215 1447527 1447926 "LIST2MAP" 1448728 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-623 1446222 1446400 1446628 "LIST2" 1447033 NIL LIST2 (NIL T T) -7 NIL NIL) (-622 1439451 1445168 1445466 "LIST" 1445957 NIL LIST (NIL T) -8 NIL NIL) (-621 1438201 1438837 1438878 "LINEXP" 1439133 NIL LINEXP (NIL T) -9 NIL 1439282) (-620 1436848 1437108 1437405 "LINDEP" 1437953 NIL LINDEP (NIL T T) -7 NIL NIL) (-619 1433686 1434386 1435144 "LIMITRF" 1436122 NIL LIMITRF (NIL T) -7 NIL NIL) (-618 1431985 1432273 1432682 "LIMITPS" 1433388 NIL LIMITPS (NIL T T) -7 NIL NIL) (-617 1431034 1431477 1431517 "LIECAT" 1431657 NIL LIECAT (NIL T) -9 NIL 1431808) (-616 1430875 1430902 1430990 "LIECAT-" 1430995 NIL LIECAT- (NIL T T) -8 NIL NIL) (-615 1425362 1430386 1430614 "LIE" 1430696 NIL LIE (NIL T T) -8 NIL NIL) (-614 1417976 1424811 1424976 "LIB" 1425217 T LIB (NIL) -8 NIL NIL) (-613 1413613 1414494 1415429 "LGROBP" 1417093 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-612 1412453 1413145 1413173 "LFCAT" 1413380 T LFCAT (NIL) -9 NIL 1413519) (-611 1410319 1410593 1410955 "LF" 1412174 NIL LF (NIL T T) -7 NIL NIL) (-610 1407223 1407851 1408539 "LEXTRIPK" 1409683 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-609 1403994 1404793 1405296 "LEXP" 1406803 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-608 1403497 1403715 1403807 "LETAST" 1403922 T LETAST (NIL) -8 NIL NIL) (-607 1401895 1402208 1402609 "LEADCDET" 1403179 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-606 1401085 1401159 1401388 "LAZM3PK" 1401816 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-605 1396055 1399162 1399700 "LAUPOL" 1400597 NIL LAUPOL (NIL T T) -8 NIL NIL) (-604 1395620 1395664 1395832 "LAPLACE" 1396005 NIL LAPLACE (NIL T T) -7 NIL NIL) (-603 1394721 1395271 1395312 "LALG" 1395374 NIL LALG (NIL T) -9 NIL 1395433) (-602 1394435 1394494 1394630 "LALG-" 1394635 NIL LALG- (NIL T T) -8 NIL NIL) (-601 1392409 1393536 1393787 "LA" 1394268 NIL LA (NIL T T T) -8 NIL NIL) (-600 1391209 1391626 1391855 "KTVLOGIC" 1392200 T KTVLOGIC (NIL) -8 NIL NIL) (-599 1390113 1390300 1390599 "KOVACIC" 1391009 NIL KOVACIC (NIL T T) -7 NIL NIL) (-598 1389948 1389972 1390013 "KONVERT" 1390075 NIL KONVERT (NIL T) -9 NIL NIL) (-597 1389783 1389807 1389848 "KOERCE" 1389910 NIL KOERCE (NIL T) -9 NIL NIL) (-596 1389285 1389366 1389496 "KERNEL2" 1389697 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-595 1387019 1387779 1388172 "KERNEL" 1388924 NIL KERNEL (NIL T) -8 NIL NIL) (-594 1380870 1385558 1385612 "KDAGG" 1385989 NIL KDAGG (NIL T T) -9 NIL 1386195) (-593 1380399 1380523 1380728 "KDAGG-" 1380733 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-592 1373576 1380060 1380215 "KAFILE" 1380277 NIL KAFILE (NIL T) -8 NIL NIL) (-591 1368063 1373087 1373315 "JORDAN" 1373397 NIL JORDAN (NIL T T) -8 NIL NIL) (-590 1367469 1367712 1367833 "JOINAST" 1367962 T JOINAST (NIL) -8 NIL NIL) (-589 1367198 1367257 1367344 "JAVACODE" 1367402 T JAVACODE (NIL) -8 NIL NIL) (-588 1363497 1365403 1365457 "IXAGG" 1366386 NIL IXAGG (NIL T T) -9 NIL 1366845) (-587 1362416 1362722 1363141 "IXAGG-" 1363146 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-586 1357996 1362338 1362397 "IVECTOR" 1362402 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-585 1356762 1356999 1357265 "ITUPLE" 1357763 NIL ITUPLE (NIL T) -8 NIL NIL) (-584 1355198 1355375 1355681 "ITRIGMNP" 1356584 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-583 1353943 1354147 1354430 "ITFUN3" 1354974 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-582 1353575 1353632 1353741 "ITFUN2" 1353880 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-581 1351412 1352437 1352736 "ITAYLOR" 1353309 NIL ITAYLOR (NIL T) -8 NIL NIL) (-580 1340394 1345549 1346712 "ISUPS" 1350282 NIL ISUPS (NIL T) -8 NIL NIL) (-579 1339498 1339638 1339874 "ISUMP" 1340241 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-578 1334762 1339299 1339378 "ISTRING" 1339451 NIL ISTRING (NIL NIL) -8 NIL NIL) (-577 1334265 1334483 1334575 "ISAST" 1334690 T ISAST (NIL) -8 NIL NIL) (-576 1333475 1333556 1333772 "IRURPK" 1334179 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-575 1332411 1332612 1332852 "IRSN" 1333255 T IRSN (NIL) -7 NIL NIL) (-574 1330440 1330795 1331231 "IRRF2F" 1332049 NIL IRRF2F (NIL T) -7 NIL NIL) (-573 1330187 1330225 1330301 "IRREDFFX" 1330396 NIL IRREDFFX (NIL T) -7 NIL NIL) (-572 1328802 1329061 1329360 "IROOT" 1329920 NIL IROOT (NIL T) -7 NIL NIL) (-571 1327874 1327987 1328208 "IR2F" 1328685 NIL IR2F (NIL T T) -7 NIL NIL) (-570 1325487 1325982 1326548 "IR2" 1327352 NIL IR2 (NIL T T) -7 NIL NIL) (-569 1322119 1323171 1323863 "IR" 1324827 NIL IR (NIL T) -8 NIL NIL) (-568 1321910 1321944 1322004 "IPRNTPK" 1322079 T IPRNTPK (NIL) -7 NIL NIL) (-567 1318531 1321799 1321868 "IPF" 1321873 NIL IPF (NIL NIL) -8 NIL NIL) (-566 1316896 1318456 1318513 "IPADIC" 1318518 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-565 1316396 1316600 1316710 "IOMODE" 1316806 T IOMODE (NIL) -8 NIL NIL) (-564 1316160 1316300 1316328 "IOBCON" 1316333 T IOBCON (NIL) -9 NIL 1316354) (-563 1315657 1315715 1315905 "INVLAPLA" 1316096 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-562 1305354 1307695 1310069 "INTTR" 1313333 NIL INTTR (NIL T T) -7 NIL NIL) (-561 1301698 1302440 1303304 "INTTOOLS" 1304539 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-560 1301284 1301375 1301492 "INTSLPE" 1301601 T INTSLPE (NIL) -7 NIL NIL) (-559 1299279 1301207 1301266 "INTRVL" 1301271 NIL INTRVL (NIL T) -8 NIL NIL) (-558 1296881 1297393 1297968 "INTRF" 1298764 NIL INTRF (NIL T) -7 NIL NIL) (-557 1296292 1296389 1296531 "INTRET" 1296779 NIL INTRET (NIL T) -7 NIL NIL) (-556 1294289 1294678 1295148 "INTRAT" 1295900 NIL INTRAT (NIL T T) -7 NIL NIL) (-555 1291517 1292100 1292726 "INTPM" 1293774 NIL INTPM (NIL T T) -7 NIL NIL) (-554 1288243 1288835 1289573 "INTPAF" 1290910 NIL INTPAF (NIL T T T) -7 NIL NIL) (-553 1283422 1284384 1285435 "INTPACK" 1287212 T INTPACK (NIL) -7 NIL NIL) (-552 1282674 1282826 1283034 "INTHERTR" 1283264 NIL INTHERTR (NIL T T) -7 NIL NIL) (-551 1282113 1282193 1282381 "INTHERAL" 1282588 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-550 1279959 1280402 1280859 "INTHEORY" 1281676 T INTHEORY (NIL) -7 NIL NIL) (-549 1271325 1272928 1274689 "INTG0" 1278329 NIL INTG0 (NIL T T T) -7 NIL NIL) (-548 1257598 1260963 1264348 "INTFTBL" 1267960 T INTFTBL (NIL) -8 NIL NIL) (-547 1256847 1256985 1257158 "INTFACT" 1257457 NIL INTFACT (NIL T) -7 NIL NIL) (-546 1254238 1254682 1255244 "INTEF" 1256403 NIL INTEF (NIL T T) -7 NIL NIL) (-545 1252740 1253445 1253473 "INTDOM" 1253774 T INTDOM (NIL) -9 NIL 1253981) (-544 1252109 1252283 1252525 "INTDOM-" 1252530 NIL INTDOM- (NIL T) -8 NIL NIL) (-543 1248642 1250528 1250582 "INTCAT" 1251381 NIL INTCAT (NIL T) -9 NIL 1251701) (-542 1248115 1248217 1248345 "INTBIT" 1248534 T INTBIT (NIL) -7 NIL NIL) (-541 1246786 1246940 1247254 "INTALG" 1247960 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-540 1246243 1246333 1246503 "INTAF" 1246690 NIL INTAF (NIL T T) -7 NIL NIL) (-539 1239699 1246053 1246193 "INTABL" 1246198 NIL INTABL (NIL T T T) -8 NIL NIL) (-538 1236613 1239428 1239555 "INT" 1239592 T INT (NIL) -8 NIL NIL) (-537 1231670 1234339 1234367 "INS" 1235301 T INS (NIL) -9 NIL 1235965) (-536 1228910 1229681 1230655 "INS-" 1230728 NIL INS- (NIL T) -8 NIL NIL) (-535 1227758 1227963 1228239 "INPSIGN" 1228685 NIL INPSIGN (NIL T T) -7 NIL NIL) (-534 1226876 1226993 1227190 "INPRODPF" 1227638 NIL INPRODPF (NIL T T) -7 NIL NIL) (-533 1225770 1225887 1226124 "INPRODFF" 1226756 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-532 1224770 1224922 1225182 "INNMFACT" 1225606 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-531 1223967 1224064 1224252 "INMODGCD" 1224669 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-530 1222476 1222720 1223044 "INFSP" 1223712 NIL INFSP (NIL T T T) -7 NIL NIL) (-529 1221660 1221777 1221960 "INFPROD0" 1222356 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-528 1221270 1221330 1221428 "INFORM1" 1221595 NIL INFORM1 (NIL T) -7 NIL NIL) (-527 1218152 1219335 1219850 "INFORM" 1220763 T INFORM (NIL) -8 NIL NIL) (-526 1217675 1217764 1217878 "INFINITY" 1218058 T INFINITY (NIL) -7 NIL NIL) (-525 1216292 1216541 1216862 "INEP" 1217423 NIL INEP (NIL T T T) -7 NIL NIL) (-524 1215568 1216189 1216254 "INDE" 1216259 NIL INDE (NIL T) -8 NIL NIL) (-523 1215132 1215200 1215317 "INCRMAPS" 1215495 NIL INCRMAPS (NIL T) -7 NIL NIL) (-522 1214435 1214628 1214778 "INBFILE" 1215002 T INBFILE (NIL) -8 NIL NIL) (-521 1209746 1210671 1211615 "INBFF" 1213523 NIL INBFF (NIL T) -7 NIL NIL) (-520 1209415 1209491 1209519 "INBCON" 1209652 T INBCON (NIL) -9 NIL 1209730) (-519 1209255 1209290 1209366 "INBCON-" 1209371 NIL INBCON- (NIL T) -8 NIL NIL) (-518 1208757 1208976 1209068 "INAST" 1209183 T INAST (NIL) -8 NIL NIL) (-517 1208211 1208436 1208542 "IMPTAST" 1208671 T IMPTAST (NIL) -8 NIL NIL) (-516 1204704 1208055 1208159 "IMATRIX" 1208164 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-515 1203416 1203539 1203854 "IMATQF" 1204560 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-514 1201636 1201863 1202200 "IMATLIN" 1203172 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-513 1196264 1201560 1201618 "ILIST" 1201623 NIL ILIST (NIL T NIL) -8 NIL NIL) (-512 1194217 1196124 1196237 "IIARRAY2" 1196242 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-511 1189652 1194128 1194192 "IFF" 1194197 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-510 1189026 1189269 1189385 "IFAST" 1189556 T IFAST (NIL) -8 NIL NIL) (-509 1184069 1188318 1188506 "IFARRAY" 1188883 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-508 1183276 1183973 1184046 "IFAMON" 1184051 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-507 1182860 1182925 1182979 "IEVALAB" 1183186 NIL IEVALAB (NIL T T) -9 NIL NIL) (-506 1182535 1182603 1182763 "IEVALAB-" 1182768 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-505 1181812 1182424 1182499 "IDPOAMS" 1182504 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-504 1181146 1181701 1181776 "IDPOAM" 1181781 NIL IDPOAM (NIL T T) -8 NIL NIL) (-503 1180804 1181060 1181123 "IDPO" 1181128 NIL IDPO (NIL T T) -8 NIL NIL) (-502 1179889 1180139 1180192 "IDPC" 1180605 NIL IDPC (NIL T T) -9 NIL 1180754) (-501 1179385 1179781 1179854 "IDPAM" 1179859 NIL IDPAM (NIL T T) -8 NIL NIL) (-500 1178788 1179277 1179350 "IDPAG" 1179355 NIL IDPAG (NIL T T) -8 NIL NIL) (-499 1178518 1178703 1178753 "IDENT" 1178758 T IDENT (NIL) -8 NIL NIL) (-498 1174773 1175621 1176516 "IDECOMP" 1177675 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-497 1167646 1168696 1169743 "IDEAL" 1173809 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-496 1166810 1166922 1167121 "ICDEN" 1167530 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-495 1165909 1166290 1166437 "ICARD" 1166683 T ICARD (NIL) -8 NIL NIL) (-494 1163969 1164282 1164687 "IBPTOOLS" 1165586 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-493 1159603 1163589 1163702 "IBITS" 1163888 NIL IBITS (NIL NIL) -8 NIL NIL) (-492 1156326 1156902 1157597 "IBATOOL" 1159020 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-491 1154106 1154567 1155100 "IBACHIN" 1155861 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-490 1151983 1153952 1154055 "IARRAY2" 1154060 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-489 1148136 1151909 1151966 "IARRAY1" 1151971 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-488 1142140 1146550 1147030 "IAN" 1147676 T IAN (NIL) -8 NIL NIL) (-487 1141651 1141708 1141881 "IALGFACT" 1142077 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-486 1141179 1141292 1141320 "HYPCAT" 1141527 T HYPCAT (NIL) -9 NIL NIL) (-485 1140717 1140834 1141020 "HYPCAT-" 1141025 NIL HYPCAT- (NIL T) -8 NIL NIL) (-484 1140339 1140512 1140595 "HOSTNAME" 1140654 T HOSTNAME (NIL) -8 NIL NIL) (-483 1137018 1138349 1138390 "HOAGG" 1139371 NIL HOAGG (NIL T) -9 NIL 1140050) (-482 1135612 1136011 1136537 "HOAGG-" 1136542 NIL HOAGG- (NIL T T) -8 NIL NIL) (-481 1129521 1135053 1135219 "HEXADEC" 1135466 T HEXADEC (NIL) -8 NIL NIL) (-480 1128269 1128491 1128754 "HEUGCD" 1129298 NIL HEUGCD (NIL T) -7 NIL NIL) (-479 1127372 1128106 1128236 "HELLFDIV" 1128241 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-478 1125600 1127149 1127237 "HEAP" 1127316 NIL HEAP (NIL T) -8 NIL NIL) (-477 1124891 1125152 1125286 "HEADAST" 1125486 T HEADAST (NIL) -8 NIL NIL) (-476 1118818 1124806 1124868 "HDP" 1124873 NIL HDP (NIL NIL T) -8 NIL NIL) (-475 1112600 1118453 1118605 "HDMP" 1118719 NIL HDMP (NIL NIL T) -8 NIL NIL) (-474 1111925 1112064 1112228 "HB" 1112456 T HB (NIL) -7 NIL NIL) (-473 1105424 1111771 1111875 "HASHTBL" 1111880 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-472 1104927 1105145 1105237 "HASAST" 1105352 T HASAST (NIL) -8 NIL NIL) (-471 1102745 1104551 1104732 "HACKPI" 1104766 T HACKPI (NIL) -8 NIL NIL) (-470 1098467 1102598 1102711 "GTSET" 1102716 NIL GTSET (NIL T T T T) -8 NIL NIL) (-469 1091995 1098345 1098443 "GSTBL" 1098448 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-468 1084310 1091026 1091291 "GSERIES" 1091786 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-467 1083477 1083868 1083896 "GROUP" 1084099 T GROUP (NIL) -9 NIL 1084233) (-466 1082843 1083002 1083253 "GROUP-" 1083258 NIL GROUP- (NIL T) -8 NIL NIL) (-465 1081212 1081531 1081918 "GROEBSOL" 1082520 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-464 1080152 1080414 1080465 "GRMOD" 1080994 NIL GRMOD (NIL T T) -9 NIL 1081162) (-463 1079920 1079956 1080084 "GRMOD-" 1080089 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-462 1075245 1076274 1077274 "GRIMAGE" 1078940 T GRIMAGE (NIL) -8 NIL NIL) (-461 1073712 1073972 1074296 "GRDEF" 1074941 T GRDEF (NIL) -7 NIL NIL) (-460 1073156 1073272 1073413 "GRAY" 1073591 T GRAY (NIL) -7 NIL NIL) (-459 1072387 1072767 1072818 "GRALG" 1072971 NIL GRALG (NIL T T) -9 NIL 1073064) (-458 1072048 1072121 1072284 "GRALG-" 1072289 NIL GRALG- (NIL T T T) -8 NIL NIL) (-457 1068852 1071633 1071811 "GPOLSET" 1071955 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-456 1068206 1068263 1068521 "GOSPER" 1068789 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-455 1063965 1064644 1065170 "GMODPOL" 1067905 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-454 1062970 1063154 1063392 "GHENSEL" 1063777 NIL GHENSEL (NIL T T) -7 NIL NIL) (-453 1057021 1057864 1058891 "GENUPS" 1062054 NIL GENUPS (NIL T T) -7 NIL NIL) (-452 1056718 1056769 1056858 "GENUFACT" 1056964 NIL GENUFACT (NIL T) -7 NIL NIL) (-451 1056130 1056207 1056372 "GENPGCD" 1056636 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-450 1055604 1055639 1055852 "GENMFACT" 1056089 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-449 1054172 1054427 1054734 "GENEEZ" 1055347 NIL GENEEZ (NIL T T) -7 NIL NIL) (-448 1048116 1053783 1053945 "GDMP" 1054095 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-447 1037515 1041887 1042993 "GCNAALG" 1047099 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-446 1035977 1036805 1036833 "GCDDOM" 1037088 T GCDDOM (NIL) -9 NIL 1037245) (-445 1035447 1035574 1035789 "GCDDOM-" 1035794 NIL GCDDOM- (NIL T) -8 NIL NIL) (-444 1024067 1026393 1028785 "GBINTERN" 1033138 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-443 1021904 1022196 1022617 "GBF" 1023742 NIL GBF (NIL T T T T) -7 NIL NIL) (-442 1020685 1020850 1021117 "GBEUCLID" 1021720 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-441 1019357 1019542 1019846 "GB" 1020464 NIL GB (NIL T T T T) -7 NIL NIL) (-440 1018706 1018831 1018980 "GAUSSFAC" 1019228 T GAUSSFAC (NIL) -7 NIL NIL) (-439 1017073 1017375 1017689 "GALUTIL" 1018425 NIL GALUTIL (NIL T) -7 NIL NIL) (-438 1015381 1015655 1015979 "GALPOLYU" 1016800 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-437 1012746 1013036 1013443 "GALFACTU" 1015078 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-436 1004552 1006051 1007659 "GALFACT" 1011178 NIL GALFACT (NIL T) -7 NIL NIL) (-435 1001940 1002598 1002626 "FVFUN" 1003782 T FVFUN (NIL) -9 NIL 1004502) (-434 1001206 1001388 1001416 "FVC" 1001707 T FVC (NIL) -9 NIL 1001890) (-433 1000848 1001003 1001084 "FUNCTION" 1001158 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-432 999666 1000149 1000352 "FTEM" 1000665 T FTEM (NIL) -8 NIL NIL) (-431 997348 997896 998382 "FT" 999200 T FT (NIL) -8 NIL NIL) (-430 995604 995893 996297 "FSUPFACT" 997039 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-429 994001 994290 994622 "FST" 995292 T FST (NIL) -8 NIL NIL) (-428 993172 993278 993473 "FSRED" 993883 NIL FSRED (NIL T T) -7 NIL NIL) (-427 991851 992106 992460 "FSPRMELT" 992887 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-426 988936 989374 989873 "FSPECF" 991414 NIL FSPECF (NIL T T) -7 NIL NIL) (-425 988450 988504 988681 "FSINT" 988877 NIL FSINT (NIL T T) -7 NIL NIL) (-424 986777 987443 987746 "FSERIES" 988229 NIL FSERIES (NIL T T) -8 NIL NIL) (-423 985791 985907 986138 "FSCINT" 986657 NIL FSCINT (NIL T T) -7 NIL NIL) (-422 984833 984976 985203 "FSAGG2" 985644 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-421 981067 983777 983818 "FSAGG" 984188 NIL FSAGG (NIL T) -9 NIL 984447) (-420 978829 979430 980226 "FSAGG-" 980321 NIL FSAGG- (NIL T T) -8 NIL NIL) (-419 976484 976763 977317 "FS2UPS" 978547 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-418 975341 975512 975821 "FS2EXPXP" 976309 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-417 974923 974966 975121 "FS2" 975292 NIL FS2 (NIL T T T T) -7 NIL NIL) (-416 957394 965807 965847 "FS" 969695 NIL FS (NIL T) -9 NIL 971984) (-415 946125 949088 953117 "FS-" 953414 NIL FS- (NIL T T) -8 NIL NIL) (-414 945551 945666 945818 "FRUTIL" 946005 NIL FRUTIL (NIL T) -7 NIL NIL) (-413 940658 943269 943309 "FRNAALG" 944705 NIL FRNAALG (NIL T) -9 NIL 945312) (-412 936387 937441 938699 "FRNAALG-" 939449 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-411 936025 936068 936195 "FRNAAF2" 936338 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-410 934432 934879 935174 "FRMOD" 935837 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-409 933627 933714 934003 "FRIDEAL2" 934339 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-408 931406 932010 932327 "FRIDEAL" 933418 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-407 930655 931062 931103 "FRETRCT" 931108 NIL FRETRCT (NIL T) -9 NIL 931284) (-406 929788 930012 930356 "FRETRCT-" 930361 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-405 927038 928214 928273 "FRAMALG" 929155 NIL FRAMALG (NIL T T) -9 NIL 929447) (-404 925172 925627 926257 "FRAMALG-" 926480 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-403 924808 924865 924972 "FRAC2" 925109 NIL FRAC2 (NIL T T) -7 NIL NIL) (-402 918789 924283 924559 "FRAC" 924564 NIL FRAC (NIL T) -8 NIL NIL) (-401 918425 918482 918589 "FR2" 918726 NIL FR2 (NIL T T) -7 NIL NIL) (-400 910001 914005 915334 "FR" 917128 NIL FR (NIL T) -8 NIL NIL) (-399 904735 907579 907607 "FPS" 908726 T FPS (NIL) -9 NIL 909283) (-398 904184 904293 904457 "FPS-" 904603 NIL FPS- (NIL T) -8 NIL NIL) (-397 901692 903325 903353 "FPC" 903578 T FPC (NIL) -9 NIL 903720) (-396 901485 901525 901622 "FPC-" 901627 NIL FPC- (NIL T) -8 NIL NIL) (-395 900363 900973 901014 "FPATMAB" 901019 NIL FPATMAB (NIL T) -9 NIL 901171) (-394 898063 898539 898965 "FPARFRAC" 900000 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-393 893495 893994 894676 "FORTRAN" 897495 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-392 891171 891733 891761 "FORTFN" 892821 T FORTFN (NIL) -9 NIL 893445) (-391 890935 890985 891013 "FORTCAT" 891072 T FORTCAT (NIL) -9 NIL 891134) (-390 888651 889151 889690 "FORT" 890416 T FORT (NIL) -7 NIL NIL) (-389 888439 888469 888538 "FORMULA1" 888615 NIL FORMULA1 (NIL T) -7 NIL NIL) (-388 886499 886982 887381 "FORMULA" 888060 T FORMULA (NIL) -8 NIL NIL) (-387 886022 886074 886247 "FORDER" 886441 NIL FORDER (NIL T T T T) -7 NIL NIL) (-386 885118 885282 885475 "FOP" 885849 T FOP (NIL) -7 NIL NIL) (-385 883726 884398 884572 "FNLA" 885000 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-384 882394 882783 882811 "FNCAT" 883383 T FNCAT (NIL) -9 NIL 883676) (-383 881960 882353 882381 "FNAME" 882386 T FNAME (NIL) -8 NIL NIL) (-382 880658 881587 881615 "FMTC" 881620 T FMTC (NIL) -9 NIL 881656) (-381 877020 878181 878810 "FMONOID" 880062 NIL FMONOID (NIL T) -8 NIL NIL) (-380 874444 875090 875118 "FMFUN" 876262 T FMFUN (NIL) -9 NIL 876970) (-379 871656 872490 872544 "FMCAT" 873739 NIL FMCAT (NIL T T) -9 NIL 874234) (-378 870925 871106 871134 "FMC" 871424 T FMC (NIL) -9 NIL 871606) (-377 869818 870691 870791 "FM1" 870870 NIL FM1 (NIL T T) -8 NIL NIL) (-376 869037 869560 869709 "FM" 869714 NIL FM (NIL T T) -8 NIL NIL) (-375 866811 867227 867721 "FLOATRP" 868588 NIL FLOATRP (NIL T) -7 NIL NIL) (-374 864249 864749 865327 "FLOATCP" 866278 NIL FLOATCP (NIL T) -7 NIL NIL) (-373 857804 861905 862535 "FLOAT" 863639 T FLOAT (NIL) -8 NIL NIL) (-372 856633 857437 857478 "FLINEXP" 857483 NIL FLINEXP (NIL T) -9 NIL 857576) (-371 855787 856022 856350 "FLINEXP-" 856355 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-370 854863 855007 855231 "FLASORT" 855639 NIL FLASORT (NIL T T) -7 NIL NIL) (-369 852080 852922 852974 "FLALG" 854201 NIL FLALG (NIL T T) -9 NIL 854668) (-368 851122 851265 851492 "FLAGG2" 851933 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-367 844906 848608 848649 "FLAGG" 849911 NIL FLAGG (NIL T) -9 NIL 850563) (-366 843632 843971 844461 "FLAGG-" 844466 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 840645 841619 841678 "FINRALG" 842806 NIL FINRALG (NIL T T) -9 NIL 843314) (-364 839805 840034 840373 "FINRALG-" 840378 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-363 839211 839424 839452 "FINITE" 839648 T FINITE (NIL) -9 NIL 839755) (-362 831669 833830 833870 "FINAALG" 837537 NIL FINAALG (NIL T) -9 NIL 838990) (-361 827010 828051 829195 "FINAALG-" 830574 NIL FINAALG- (NIL T T) -8 NIL NIL) (-360 825694 826006 826060 "FILECAT" 826744 NIL FILECAT (NIL T T) -9 NIL 826960) (-359 825089 825449 825552 "FILE" 825624 NIL FILE (NIL T) -8 NIL NIL) (-358 823011 824503 824531 "FIELD" 824571 T FIELD (NIL) -9 NIL 824651) (-357 821631 822016 822527 "FIELD-" 822532 NIL FIELD- (NIL T) -8 NIL NIL) (-356 819509 820266 820613 "FGROUP" 821317 NIL FGROUP (NIL T) -8 NIL NIL) (-355 818599 818763 818983 "FGLMICPK" 819341 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-354 814468 818524 818581 "FFX" 818586 NIL FFX (NIL T NIL) -8 NIL NIL) (-353 814069 814130 814265 "FFSLPE" 814401 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-352 813573 813609 813818 "FFPOLY2" 814027 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-351 809566 810345 811141 "FFPOLY" 812809 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 805454 809485 809548 "FFP" 809553 NIL FFP (NIL T NIL) -8 NIL NIL) (-349 800617 804797 804987 "FFNBX" 805308 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-348 795593 799752 800010 "FFNBP" 800471 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-347 790263 794877 795088 "FFNB" 795426 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-346 789095 789293 789608 "FFINTBAS" 790060 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-345 785381 787554 787582 "FFIELDC" 788202 T FFIELDC (NIL) -9 NIL 788578) (-344 784044 784414 784911 "FFIELDC-" 784916 NIL FFIELDC- (NIL T) -8 NIL NIL) (-343 783614 783659 783783 "FFHOM" 783986 NIL FFHOM (NIL T T T) -7 NIL NIL) (-342 781312 781796 782313 "FFF" 783129 NIL FFF (NIL T) -7 NIL NIL) (-341 776967 781054 781155 "FFCGX" 781255 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-340 772636 776699 776806 "FFCGP" 776910 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-339 767856 772363 772471 "FFCG" 772572 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-338 767267 767310 767545 "FFCAT2" 767807 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-337 749334 758361 758447 "FFCAT" 763612 NIL FFCAT (NIL T T T) -9 NIL 765063) (-336 744532 745579 746893 "FFCAT-" 748123 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-335 739967 744443 744507 "FF" 744512 NIL FF (NIL NIL NIL) -8 NIL NIL) (-334 729181 732939 734159 "FEXPR" 738819 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-333 728181 728616 728657 "FEVALAB" 728741 NIL FEVALAB (NIL T) -9 NIL 729002) (-332 727340 727550 727888 "FEVALAB-" 727893 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-331 724406 725121 725236 "FDIVCAT" 726804 NIL FDIVCAT (NIL T T T T) -9 NIL 727241) (-330 724168 724195 724365 "FDIVCAT-" 724370 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-329 723388 723475 723752 "FDIV2" 724075 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-328 721981 722771 722974 "FDIV" 723287 NIL FDIV (NIL T T T T) -8 NIL NIL) (-327 720667 720926 721215 "FCPAK1" 721712 T FCPAK1 (NIL) -7 NIL NIL) (-326 719795 720167 720308 "FCOMP" 720558 NIL FCOMP (NIL T) -8 NIL NIL) (-325 703430 706844 710405 "FC" 716254 T FC (NIL) -8 NIL NIL) (-324 696085 700064 700104 "FAXF" 701906 NIL FAXF (NIL T) -9 NIL 702598) (-323 693364 694019 694844 "FAXF-" 695309 NIL FAXF- (NIL T T) -8 NIL NIL) (-322 688464 692740 692916 "FARRAY" 693221 NIL FARRAY (NIL T) -8 NIL NIL) (-321 683878 685903 685956 "FAMR" 686979 NIL FAMR (NIL T T) -9 NIL 687439) (-320 682768 683070 683505 "FAMR-" 683510 NIL FAMR- (NIL T T T) -8 NIL NIL) (-319 681964 682690 682743 "FAMONOID" 682748 NIL FAMONOID (NIL T) -8 NIL NIL) (-318 679794 680478 680531 "FAMONC" 681472 NIL FAMONC (NIL T T) -9 NIL 681858) (-317 678486 679548 679685 "FAGROUP" 679690 NIL FAGROUP (NIL T) -8 NIL NIL) (-316 676281 676600 677003 "FACUTIL" 678167 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-315 675380 675565 675787 "FACTFUNC" 676091 NIL FACTFUNC (NIL T) -7 NIL NIL) (-314 667787 674631 674843 "EXPUPXS" 675236 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-313 665270 665810 666396 "EXPRTUBE" 667221 T EXPRTUBE (NIL) -7 NIL NIL) (-312 661464 662056 662793 "EXPRODE" 664609 NIL EXPRODE (NIL T T) -7 NIL NIL) (-311 655871 656458 657271 "EXPR2UPS" 660762 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-310 655507 655564 655671 "EXPR2" 655808 NIL EXPR2 (NIL T T) -7 NIL NIL) (-309 640942 654162 654590 "EXPR" 655111 NIL EXPR (NIL T) -8 NIL NIL) (-308 632375 640074 640371 "EXPEXPAN" 640779 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-307 631882 632099 632190 "EXITAST" 632304 T EXITAST (NIL) -8 NIL NIL) (-306 631709 631839 631868 "EXIT" 631873 T EXIT (NIL) -8 NIL NIL) (-305 631336 631398 631511 "EVALCYC" 631641 NIL EVALCYC (NIL T) -7 NIL NIL) (-304 630877 630995 631036 "EVALAB" 631206 NIL EVALAB (NIL T) -9 NIL 631310) (-303 630358 630480 630701 "EVALAB-" 630706 NIL EVALAB- (NIL T T) -8 NIL NIL) (-302 627861 629129 629157 "EUCDOM" 629712 T EUCDOM (NIL) -9 NIL 630062) (-301 626266 626708 627298 "EUCDOM-" 627303 NIL EUCDOM- (NIL T) -8 NIL NIL) (-300 625898 625955 626064 "ESTOOLS2" 626203 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-299 625649 625691 625771 "ESTOOLS1" 625850 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-298 613189 615947 618697 "ESTOOLS" 622919 T ESTOOLS (NIL) -7 NIL NIL) (-297 612934 612966 613048 "ESCONT1" 613151 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-296 609309 610069 610849 "ESCONT" 612174 T ESCONT (NIL) -7 NIL NIL) (-295 608984 609034 609134 "ES2" 609253 NIL ES2 (NIL T T) -7 NIL NIL) (-294 608614 608672 608781 "ES1" 608920 NIL ES1 (NIL T T) -7 NIL NIL) (-293 602539 604267 604295 "ES" 607063 T ES (NIL) -9 NIL 608472) (-292 597486 598773 600590 "ES-" 600754 NIL ES- (NIL T) -8 NIL NIL) (-291 596702 596831 597007 "ERROR" 597330 T ERROR (NIL) -7 NIL NIL) (-290 590207 596561 596652 "EQTBL" 596657 NIL EQTBL (NIL T T) -8 NIL NIL) (-289 589839 589896 590005 "EQ2" 590144 NIL EQ2 (NIL T T) -7 NIL NIL) (-288 582396 585153 586602 "EQ" 588423 NIL -3890 (NIL T) -8 NIL NIL) (-287 577688 578734 579827 "EP" 581335 NIL EP (NIL T) -7 NIL NIL) (-286 576270 576571 576888 "ENV" 577391 T ENV (NIL) -8 NIL NIL) (-285 575469 575989 576017 "ENTIRER" 576022 T ENTIRER (NIL) -9 NIL 576068) (-284 572027 573478 573848 "EMR" 575268 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-283 571171 571356 571410 "ELTAGG" 571790 NIL ELTAGG (NIL T T) -9 NIL 572001) (-282 570890 570952 571093 "ELTAGG-" 571098 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-281 570679 570708 570762 "ELTAB" 570846 NIL ELTAB (NIL T T) -9 NIL NIL) (-280 569805 569951 570150 "ELFUTS" 570530 NIL ELFUTS (NIL T T) -7 NIL NIL) (-279 569547 569603 569631 "ELEMFUN" 569736 T ELEMFUN (NIL) -9 NIL NIL) (-278 569417 569438 569506 "ELEMFUN-" 569511 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-277 564308 567517 567558 "ELAGG" 568498 NIL ELAGG (NIL T) -9 NIL 568961) (-276 562593 563027 563690 "ELAGG-" 563695 NIL ELAGG- (NIL T T) -8 NIL NIL) (-275 561250 561530 561825 "ELABEXPR" 562318 T ELABEXPR (NIL) -8 NIL NIL) (-274 554243 555917 556744 "EFUPXS" 560526 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-273 547820 549494 550304 "EFULS" 553519 NIL EFULS (NIL T T T) -8 NIL NIL) (-272 545242 545600 546079 "EFSTRUC" 547452 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-271 534314 535879 537439 "EF" 543757 NIL EF (NIL T T) -7 NIL NIL) (-270 533415 533799 533948 "EAB" 534185 T EAB (NIL) -8 NIL NIL) (-269 532624 533374 533402 "E04UCFA" 533407 T E04UCFA (NIL) -8 NIL NIL) (-268 531833 532583 532611 "E04NAFA" 532616 T E04NAFA (NIL) -8 NIL NIL) (-267 531042 531792 531820 "E04MBFA" 531825 T E04MBFA (NIL) -8 NIL NIL) (-266 530251 531001 531029 "E04JAFA" 531034 T E04JAFA (NIL) -8 NIL NIL) (-265 529462 530210 530238 "E04GCFA" 530243 T E04GCFA (NIL) -8 NIL NIL) (-264 528673 529421 529449 "E04FDFA" 529454 T E04FDFA (NIL) -8 NIL NIL) (-263 527882 528632 528660 "E04DGFA" 528665 T E04DGFA (NIL) -8 NIL NIL) (-262 522060 523407 524771 "E04AGNT" 526538 T E04AGNT (NIL) -7 NIL NIL) (-261 520784 521264 521304 "DVARCAT" 521779 NIL DVARCAT (NIL T) -9 NIL 521978) (-260 519988 520200 520514 "DVARCAT-" 520519 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-259 512929 519787 519916 "DSMP" 519921 NIL DSMP (NIL T T T) -8 NIL NIL) (-258 512594 512653 512751 "DROPT1" 512864 NIL DROPT1 (NIL T) -7 NIL NIL) (-257 507709 508835 509972 "DROPT0" 511477 T DROPT0 (NIL) -7 NIL NIL) (-256 502519 503654 504722 "DROPT" 506661 T DROPT (NIL) -8 NIL NIL) (-255 500864 501189 501575 "DRAWPT" 502153 T DRAWPT (NIL) -7 NIL NIL) (-254 500497 500550 500668 "DRAWHACK" 500805 NIL DRAWHACK (NIL T) -7 NIL NIL) (-253 499228 499497 499788 "DRAWCX" 500226 T DRAWCX (NIL) -7 NIL NIL) (-252 498744 498812 498963 "DRAWCURV" 499154 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-251 489215 491174 493289 "DRAWCFUN" 496649 T DRAWCFUN (NIL) -7 NIL NIL) (-250 483802 484725 485804 "DRAW" 488189 NIL DRAW (NIL T) -7 NIL NIL) (-249 480615 482497 482538 "DQAGG" 483167 NIL DQAGG (NIL T) -9 NIL 483440) (-248 469170 475831 475914 "DPOLCAT" 477766 NIL DPOLCAT (NIL T T T T) -9 NIL 478311) (-247 464060 465389 467330 "DPOLCAT-" 467335 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-246 457222 463921 464019 "DPMO" 464024 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-245 450287 457002 457169 "DPMM" 457174 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-244 449707 449910 450024 "DOMAIN" 450193 T DOMAIN (NIL) -8 NIL NIL) (-243 443489 449342 449494 "DMP" 449608 NIL DMP (NIL NIL T) -8 NIL NIL) (-242 443089 443145 443289 "DLP" 443427 NIL DLP (NIL T) -7 NIL NIL) (-241 436735 442190 442417 "DLIST" 442894 NIL DLIST (NIL T) -8 NIL NIL) (-240 433582 435590 435631 "DLAGG" 436181 NIL DLAGG (NIL T) -9 NIL 436410) (-239 432432 433062 433090 "DIVRING" 433182 T DIVRING (NIL) -9 NIL 433265) (-238 431669 431859 432159 "DIVRING-" 432164 NIL DIVRING- (NIL T) -8 NIL NIL) (-237 429771 430128 430534 "DISPLAY" 431283 T DISPLAY (NIL) -7 NIL NIL) (-236 428619 428822 429087 "DIRPROD2" 429564 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-235 422568 428533 428596 "DIRPROD" 428601 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 412113 418058 418111 "DIRPCAT" 418521 NIL DIRPCAT (NIL NIL T) -9 NIL 419361) (-233 409439 410081 410962 "DIRPCAT-" 411299 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-232 408726 408886 409072 "DIOSP" 409273 T DIOSP (NIL) -7 NIL NIL) (-231 405428 407638 407679 "DIOPS" 408113 NIL DIOPS (NIL T) -9 NIL 408342) (-230 404977 405091 405282 "DIOPS-" 405287 NIL DIOPS- (NIL T T) -8 NIL NIL) (-229 403889 404483 404511 "DIFRING" 404698 T DIFRING (NIL) -9 NIL 404808) (-228 403535 403612 403764 "DIFRING-" 403769 NIL DIFRING- (NIL T) -8 NIL NIL) (-227 401360 402598 402639 "DIFEXT" 403002 NIL DIFEXT (NIL T) -9 NIL 403296) (-226 399645 400073 400739 "DIFEXT-" 400744 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-225 396967 399177 399218 "DIAGG" 399223 NIL DIAGG (NIL T) -9 NIL 399243) (-224 396351 396508 396760 "DIAGG-" 396765 NIL DIAGG- (NIL T T) -8 NIL NIL) (-223 391815 395310 395587 "DHMATRIX" 396120 NIL DHMATRIX (NIL T) -8 NIL NIL) (-222 387427 388336 389346 "DFSFUN" 390825 T DFSFUN (NIL) -7 NIL NIL) (-221 382547 386358 386670 "DFLOAT" 387135 T DFLOAT (NIL) -8 NIL NIL) (-220 380775 381056 381452 "DFINTTLS" 382255 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-219 377840 378796 379196 "DERHAM" 380441 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-218 375689 377615 377704 "DEQUEUE" 377784 NIL DEQUEUE (NIL T) -8 NIL NIL) (-217 374904 375037 375233 "DEGRED" 375551 NIL DEGRED (NIL T T) -7 NIL NIL) (-216 371479 372179 372987 "DEFINTRF" 374177 NIL DEFINTRF (NIL T) -7 NIL NIL) (-215 369118 369559 370130 "DEFINTEF" 371026 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-214 368495 368738 368853 "DEFAST" 369023 T DEFAST (NIL) -8 NIL NIL) (-213 362404 367936 368102 "DECIMAL" 368349 T DECIMAL (NIL) -8 NIL NIL) (-212 359916 360374 360880 "DDFACT" 361948 NIL DDFACT (NIL T T) -7 NIL NIL) (-211 359512 359555 359706 "DBLRESP" 359867 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-210 357222 357556 357925 "DBASE" 359270 NIL DBASE (NIL T) -8 NIL NIL) (-209 356491 356702 356848 "DATABUF" 357121 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-208 355624 356450 356478 "D03FAFA" 356483 T D03FAFA (NIL) -8 NIL NIL) (-207 354758 355583 355611 "D03EEFA" 355616 T D03EEFA (NIL) -8 NIL NIL) (-206 352708 353174 353663 "D03AGNT" 354289 T D03AGNT (NIL) -7 NIL NIL) (-205 352024 352667 352695 "D02EJFA" 352700 T D02EJFA (NIL) -8 NIL NIL) (-204 351340 351983 352011 "D02CJFA" 352016 T D02CJFA (NIL) -8 NIL NIL) (-203 350656 351299 351327 "D02BHFA" 351332 T D02BHFA (NIL) -8 NIL NIL) (-202 349972 350615 350643 "D02BBFA" 350648 T D02BBFA (NIL) -8 NIL NIL) (-201 343170 344758 346364 "D02AGNT" 348386 T D02AGNT (NIL) -7 NIL NIL) (-200 340939 341461 342007 "D01WGTS" 342644 T D01WGTS (NIL) -7 NIL NIL) (-199 340034 340898 340926 "D01TRNS" 340931 T D01TRNS (NIL) -8 NIL NIL) (-198 339129 339993 340021 "D01GBFA" 340026 T D01GBFA (NIL) -8 NIL NIL) (-197 338224 339088 339116 "D01FCFA" 339121 T D01FCFA (NIL) -8 NIL NIL) (-196 337319 338183 338211 "D01ASFA" 338216 T D01ASFA (NIL) -8 NIL NIL) (-195 336414 337278 337306 "D01AQFA" 337311 T D01AQFA (NIL) -8 NIL NIL) (-194 335509 336373 336401 "D01APFA" 336406 T D01APFA (NIL) -8 NIL NIL) (-193 334604 335468 335496 "D01ANFA" 335501 T D01ANFA (NIL) -8 NIL NIL) (-192 333699 334563 334591 "D01AMFA" 334596 T D01AMFA (NIL) -8 NIL NIL) (-191 332794 333658 333686 "D01ALFA" 333691 T D01ALFA (NIL) -8 NIL NIL) (-190 331889 332753 332781 "D01AKFA" 332786 T D01AKFA (NIL) -8 NIL NIL) (-189 330984 331848 331876 "D01AJFA" 331881 T D01AJFA (NIL) -8 NIL NIL) (-188 324281 325832 327393 "D01AGNT" 329443 T D01AGNT (NIL) -7 NIL NIL) (-187 323618 323746 323898 "CYCLOTOM" 324149 T CYCLOTOM (NIL) -7 NIL NIL) (-186 320353 321066 321793 "CYCLES" 322911 T CYCLES (NIL) -7 NIL NIL) (-185 319665 319799 319970 "CVMP" 320214 NIL CVMP (NIL T) -7 NIL NIL) (-184 317436 317694 318070 "CTRIGMNP" 319393 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-183 316972 317167 317268 "CTORKIND" 317355 T CTORKIND (NIL) -8 NIL NIL) (-182 316483 316672 316771 "CTORCALL" 316893 T CTORCALL (NIL) -8 NIL NIL) (-181 315898 316106 316220 "CTOR" 316389 T CTOR (NIL) -8 NIL NIL) (-180 315272 315371 315524 "CSTTOOLS" 315795 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 311071 311728 312486 "CRFP" 314584 NIL CRFP (NIL T T) -7 NIL NIL) (-178 310573 310792 310884 "CRCEAST" 310999 T CRCEAST (NIL) -8 NIL NIL) (-177 309620 309805 310033 "CRAPACK" 310377 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 309004 309105 309309 "CPMATCH" 309496 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 308729 308757 308863 "CPIMA" 308970 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 305093 305765 306483 "COORDSYS" 308064 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 304477 304606 304756 "CONTOUR" 304963 T CONTOUR (NIL) -8 NIL NIL) (-172 300405 302480 302972 "CONTFRAC" 304017 NIL CONTFRAC (NIL T) -8 NIL NIL) (-171 300285 300306 300334 "CONDUIT" 300371 T CONDUIT (NIL) -9 NIL NIL) (-170 299478 299998 300026 "COMRING" 300031 T COMRING (NIL) -9 NIL 300083) (-169 298559 298836 299020 "COMPPROP" 299314 T COMPPROP (NIL) -8 NIL NIL) (-168 298220 298255 298383 "COMPLPAT" 298518 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 297856 297913 298020 "COMPLEX2" 298157 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-166 287933 297665 297774 "COMPLEX" 297779 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 287651 287686 287784 "COMPFACT" 287892 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 272058 282265 282305 "COMPCAT" 283309 NIL COMPCAT (NIL T) -9 NIL 284704) (-163 261594 264511 268131 "COMPCAT-" 268487 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 261323 261351 261454 "COMMUPC" 261560 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 261118 261151 261210 "COMMONOP" 261284 T COMMONOP (NIL) -7 NIL NIL) (-160 260722 260922 260997 "COMMAAST" 261063 T COMMAAST (NIL) -8 NIL NIL) (-159 260305 260473 260560 "COMM" 260655 T COMM (NIL) -8 NIL NIL) (-158 259554 259748 259776 "COMBOPC" 260114 T COMBOPC (NIL) -9 NIL 260289) (-157 258450 258660 258902 "COMBINAT" 259344 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 254648 255221 255861 "COMBF" 257872 NIL COMBF (NIL T T) -7 NIL NIL) (-155 253434 253764 253999 "COLOR" 254433 T COLOR (NIL) -8 NIL NIL) (-154 252937 253155 253247 "COLONAST" 253362 T COLONAST (NIL) -8 NIL NIL) (-153 252577 252624 252749 "CMPLXRT" 252884 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 252052 252277 252376 "CLLCTAST" 252498 T CLLCTAST (NIL) -8 NIL NIL) (-151 247554 248582 249662 "CLIP" 250992 T CLIP (NIL) -7 NIL NIL) (-150 245936 246660 246899 "CLIF" 247381 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242158 244082 244123 "CLAGG" 245052 NIL CLAGG (NIL T) -9 NIL 245588) (-148 240580 241037 241620 "CLAGG-" 241625 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240124 240209 240349 "CINTSLPE" 240489 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 237625 238096 238644 "CHVAR" 239652 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 236888 237408 237436 "CHARZ" 237441 T CHARZ (NIL) -9 NIL 237456) (-144 236642 236682 236760 "CHARPOL" 236842 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 235789 236342 236370 "CHARNZ" 236417 T CHARNZ (NIL) -9 NIL 236473) (-142 233814 234479 234814 "CHAR" 235474 T CHAR (NIL) -8 NIL NIL) (-141 233540 233601 233629 "CFCAT" 233740 T CFCAT (NIL) -9 NIL NIL) (-140 232785 232896 233078 "CDEN" 233424 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 228777 231938 232218 "CCLASS" 232525 T CCLASS (NIL) -8 NIL NIL) (-138 228696 228722 228757 "CATEGORY" 228762 T -10 (NIL) -8 NIL NIL) (-137 228170 228396 228495 "CATAST" 228617 T CATAST (NIL) -8 NIL NIL) (-136 227673 227891 227983 "CASEAST" 228098 T CASEAST (NIL) -8 NIL NIL) (-135 226781 226929 227150 "CARTEN2" 227520 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-134 221833 222810 223563 "CARTEN" 226084 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 220175 220983 221240 "CARD" 221596 T CARD (NIL) -8 NIL NIL) (-132 219778 219979 220054 "CAPSLAST" 220120 T CAPSLAST (NIL) -8 NIL NIL) (-131 219150 219478 219506 "CACHSET" 219638 T CACHSET (NIL) -9 NIL 219715) (-130 218646 218942 218970 "CABMON" 219020 T CABMON (NIL) -9 NIL 219076) (-129 214594 218593 218627 "BYTEARY" 218632 T BYTEARY (NIL) -8 NIL NIL) (-128 213521 213949 214145 "BYTE" 214418 T BYTE (NIL) -8 NIL NIL) (-127 211080 213213 213320 "BTREE" 213447 NIL BTREE (NIL T) -8 NIL NIL) (-126 208580 210728 210850 "BTOURN" 210990 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206000 208051 208092 "BTCAT" 208160 NIL BTCAT (NIL T) -9 NIL 208237) (-124 205667 205747 205896 "BTCAT-" 205901 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 200959 204810 204838 "BTAGG" 205060 T BTAGG (NIL) -9 NIL 205221) (-122 200449 200574 200780 "BTAGG-" 200785 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197495 199727 199942 "BSTREE" 200266 NIL BSTREE (NIL T) -8 NIL NIL) (-120 196633 196759 196943 "BRILL" 197351 NIL BRILL (NIL T) -7 NIL NIL) (-119 193335 195361 195402 "BRAGG" 196051 NIL BRAGG (NIL T) -9 NIL 196308) (-118 191867 192272 192826 "BRAGG-" 192831 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185154 191213 191397 "BPADICRT" 191715 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183506 185091 185136 "BPADIC" 185141 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183204 183234 183348 "BOUNDZRO" 183470 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 180825 181269 181789 "BOP1" 182717 NIL BOP1 (NIL T) -7 NIL NIL) (-113 176340 177431 178298 "BOP" 179978 T BOP (NIL) -8 NIL NIL) (-112 175078 175764 175957 "BOOLEAN" 176167 T BOOLEAN (NIL) -8 NIL NIL) (-111 174440 174818 174872 "BMODULE" 174877 NIL BMODULE (NIL T T) -9 NIL 174942) (-110 170270 174238 174311 "BITS" 174387 T BITS (NIL) -8 NIL NIL) (-109 169367 169802 169954 "BINFILE" 170138 T BINFILE (NIL) -8 NIL NIL) (-108 168779 168901 169043 "BINDING" 169245 T BINDING (NIL) -8 NIL NIL) (-107 162692 168223 168388 "BINARY" 168634 T BINARY (NIL) -8 NIL NIL) (-106 160519 161947 161988 "BGAGG" 162248 NIL BGAGG (NIL T) -9 NIL 162385) (-105 160350 160382 160473 "BGAGG-" 160478 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159448 159734 159939 "BFUNCT" 160165 T BFUNCT (NIL) -8 NIL NIL) (-103 158132 158313 158601 "BEZOUT" 159272 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 154651 156984 157314 "BBTREE" 157835 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154385 154438 154466 "BASTYPE" 154585 T BASTYPE (NIL) -9 NIL NIL) (-100 154237 154266 154339 "BASTYPE-" 154344 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 153675 153751 153901 "BALFACT" 154148 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 152558 153090 153276 "AUTOMOR" 153520 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152284 152289 152315 "ATTREG" 152320 T ATTREG (NIL) -9 NIL NIL) (-96 150563 150981 151333 "ATTRBUT" 151950 T ATTRBUT (NIL) -8 NIL NIL) (-95 150198 150391 150457 "ATTRAST" 150515 T ATTRAST (NIL) -8 NIL NIL) (-94 149734 149847 149873 "ATRIG" 150074 T ATRIG (NIL) -9 NIL NIL) (-93 149543 149584 149671 "ATRIG-" 149676 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149165 149325 149351 "ASTCAT" 149409 T ASTCAT (NIL) -9 NIL 149472) (-91 148892 148951 149070 "ASTCAT-" 149075 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147089 148668 148756 "ASTACK" 148835 NIL ASTACK (NIL T) -8 NIL NIL) (-89 145594 145891 146256 "ASSOCEQ" 146771 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 144648 145253 145377 "ASP9" 145501 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 143539 144253 144395 "ASP80" 144537 NIL ASP80 (NIL NIL) -8 NIL NIL) (-86 143303 143487 143526 "ASP8" 143531 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 142279 142980 143098 "ASP78" 143216 NIL ASP78 (NIL NIL) -8 NIL NIL) (-84 141270 141959 142076 "ASP77" 142193 NIL ASP77 (NIL NIL) -8 NIL NIL) (-83 140204 140908 141039 "ASP74" 141170 NIL ASP74 (NIL NIL) -8 NIL NIL) (-82 139126 139839 139971 "ASP73" 140103 NIL ASP73 (NIL NIL) -8 NIL NIL) (-81 138047 138761 138893 "ASP7" 139025 NIL ASP7 (NIL NIL) -8 NIL NIL) (-80 137024 137724 137842 "ASP6" 137960 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 135994 136701 136819 "ASP55" 136937 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 134966 135668 135787 "ASP50" 135906 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134076 134667 134777 "ASP49" 134887 NIL ASP49 (NIL NIL) -8 NIL NIL) (-76 132883 133615 133783 "ASP42" 133965 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-75 131682 132416 132586 "ASP41" 132770 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-74 130792 131383 131493 "ASP4" 131603 NIL ASP4 (NIL NIL) -8 NIL NIL) (-73 129764 130469 130587 "ASP35" 130705 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129529 129712 129751 "ASP34" 129756 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129266 129333 129409 "ASP33" 129484 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128183 128901 129033 "ASP31" 129165 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 127948 128131 128170 "ASP30" 128175 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127683 127752 127828 "ASP29" 127903 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127448 127631 127670 "ASP28" 127675 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127213 127396 127435 "ASP27" 127440 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126319 126911 127022 "ASP24" 127133 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125257 125960 126090 "ASP20" 126220 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124223 124931 125050 "ASP19" 125169 NIL ASP19 (NIL NIL) -8 NIL NIL) (-62 123960 124027 124103 "ASP12" 124178 NIL ASP12 (NIL NIL) -8 NIL NIL) (-61 122834 123559 123703 "ASP10" 123847 NIL ASP10 (NIL NIL) -8 NIL NIL) (-60 121944 122535 122645 "ASP1" 122755 NIL ASP1 (NIL NIL) -8 NIL NIL) (-59 119843 121788 121879 "ARRAY2" 121884 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 118875 119048 119269 "ARRAY12" 119666 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-57 114691 118523 118637 "ARRAY1" 118792 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 109050 110921 110996 "ARR2CAT" 113626 NIL ARR2CAT (NIL T T T) -9 NIL 114384) (-55 106484 107228 108182 "ARR2CAT-" 108187 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105232 105384 105690 "APPRULE" 106320 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 104883 104931 105050 "APPLYORE" 105178 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104161 104284 104441 "ANY1" 104757 NIL ANY1 (NIL T) -7 NIL NIL) (-51 103135 103426 103621 "ANY" 103984 T ANY (NIL) -8 NIL NIL) (-50 100700 101572 101899 "ANTISYM" 102859 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100215 100404 100501 "ANON" 100621 T ANON (NIL) -8 NIL NIL) (-48 94358 98756 99209 "AN" 99780 T AN (NIL) -8 NIL NIL) (-47 90739 92093 92144 "AMR" 92892 NIL AMR (NIL T T) -9 NIL 93492) (-46 89851 90072 90435 "AMR-" 90440 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74407 89768 89829 "ALIST" 89834 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71276 74001 74170 "ALGSC" 74325 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 67832 68386 68993 "ALGPKG" 70716 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67109 67210 67394 "ALGMFACT" 67718 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62848 63533 64188 "ALGMANIP" 66632 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54265 62474 62624 "ALGFF" 62781 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) 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NIL 2720023) (-1129 2708100 2712910 2713530 "STREAM" 2714802 NIL STREAM (NIL T) -8 NIL NIL) (-1128 2707610 2707687 2707831 "STREAM3" 2708017 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1127 2706592 2706775 2707010 "STREAM2" 2707423 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1126 2706280 2706332 2706425 "STREAM1" 2706534 NIL STREAM1 (NIL T) -7 NIL NIL) (-1125 2705296 2705477 2705708 "STINPROD" 2706096 NIL STINPROD (NIL T) -7 NIL NIL) (-1124 2704874 2705058 2705088 "STEP" 2705168 T STEP (NIL) -9 NIL 2705246) (-1123 2698417 2704773 2704850 "STBL" 2704855 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1122 2693592 2697639 2697682 "STAGG" 2697835 NIL STAGG (NIL T) -9 NIL 2697924) (-1121 2691294 2691896 2692768 "STAGG-" 2692773 NIL STAGG- (NIL T T) -8 NIL NIL) (-1120 2689489 2691064 2691156 "STACK" 2691237 NIL STACK (NIL T) -8 NIL NIL) (-1119 2682214 2687630 2688086 "SREGSET" 2689119 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1118 2674640 2676008 2677521 "SRDCMPK" 2680820 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1117 2667607 2672080 2672110 "SRAGG" 2673413 T SRAGG (NIL) -9 NIL 2674021) (-1116 2666624 2666879 2667258 "SRAGG-" 2667263 NIL SRAGG- (NIL T) -8 NIL NIL) (-1115 2661119 2665571 2665992 "SQMATRIX" 2666250 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1114 2654871 2657839 2658565 "SPLTREE" 2660465 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1113 2650861 2651527 2652173 "SPLNODE" 2654297 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1112 2649908 2650141 2650171 "SPFCAT" 2650615 T SPFCAT (NIL) -9 NIL NIL) (-1111 2648645 2648855 2649119 "SPECOUT" 2649666 T SPECOUT (NIL) -7 NIL NIL) (-1110 2640334 2642078 2642108 "SPADXPT" 2646500 T SPADXPT (NIL) -9 NIL 2648534) (-1109 2640095 2640135 2640204 "SPADPRSR" 2640287 T SPADPRSR (NIL) -7 NIL NIL) (-1108 2638278 2640050 2640081 "SPADAST" 2640086 T SPADAST (NIL) -8 NIL NIL) (-1107 2630249 2631996 2632039 "SPACEC" 2636412 NIL SPACEC (NIL T) -9 NIL 2638228) (-1106 2628420 2630181 2630230 "SPACE3" 2630235 NIL SPACE3 (NIL T) -8 NIL NIL) (-1105 2627172 2627343 2627634 "SORTPAK" 2628225 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1104 2625222 2625525 2625944 "SOLVETRA" 2626836 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1103 2624233 2624455 2624729 "SOLVESER" 2624995 NIL SOLVESER (NIL T) -7 NIL NIL) (-1102 2619453 2620334 2621336 "SOLVERAD" 2623285 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1101 2615268 2615877 2616606 "SOLVEFOR" 2618820 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1100 2609565 2614617 2614714 "SNTSCAT" 2614719 NIL SNTSCAT (NIL T T T T) -9 NIL 2614789) (-1099 2603708 2607888 2608279 "SMTS" 2609255 NIL SMTS (NIL T T T) -8 NIL NIL) (-1098 2598158 2603596 2603673 "SMP" 2603678 NIL SMP (NIL T T) -8 NIL NIL) (-1097 2596317 2596618 2597016 "SMITH" 2597855 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1096 2589300 2593455 2593558 "SMATCAT" 2594909 NIL SMATCAT (NIL NIL T T T) -9 NIL 2595459) (-1095 2586240 2587063 2588241 "SMATCAT-" 2588246 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1094 2583953 2585476 2585519 "SKAGG" 2585780 NIL SKAGG (NIL T) -9 NIL 2585915) (-1093 2580069 2583057 2583335 "SINT" 2583697 T SINT (NIL) -8 NIL NIL) (-1092 2579841 2579879 2579945 "SIMPAN" 2580025 T SIMPAN (NIL) -7 NIL NIL) (-1091 2579148 2579376 2579516 "SIG" 2579723 T SIG (NIL) -8 NIL NIL) (-1090 2577986 2578207 2578482 "SIGNRF" 2578907 NIL SIGNRF (NIL T) -7 NIL NIL) (-1089 2576791 2576942 2577233 "SIGNEF" 2577815 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1088 2576124 2576374 2576498 "SIGAST" 2576689 T SIGAST (NIL) -8 NIL NIL) (-1087 2573814 2574268 2574774 "SHP" 2575665 NIL SHP (NIL T NIL) -7 NIL NIL) (-1086 2567720 2573715 2573791 "SHDP" 2573796 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1085 2567319 2567485 2567515 "SGROUP" 2567608 T SGROUP (NIL) -9 NIL 2567670) (-1084 2567177 2567203 2567276 "SGROUP-" 2567281 NIL SGROUP- (NIL T) -8 NIL NIL) (-1083 2564013 2564710 2565433 "SGCF" 2566476 T SGCF (NIL) -7 NIL NIL) (-1082 2558408 2563460 2563557 "SFRTCAT" 2563562 NIL SFRTCAT (NIL T T T T) -9 NIL 2563601) (-1081 2551832 2552847 2553983 "SFRGCD" 2557391 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1080 2544960 2546031 2547217 "SFQCMPK" 2550765 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1079 2544582 2544671 2544781 "SFORT" 2544901 NIL SFORT (NIL T T) -8 NIL NIL) (-1078 2543727 2544422 2544543 "SEXOF" 2544548 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1077 2542861 2543608 2543676 "SEX" 2543681 T SEX (NIL) -8 NIL NIL) (-1076 2537637 2538326 2538421 "SEXCAT" 2542192 NIL SEXCAT (NIL T T T T T) -9 NIL 2542811) (-1075 2534817 2537571 2537619 "SET" 2537624 NIL SET (NIL T) -8 NIL NIL) (-1074 2533068 2533530 2533835 "SETMN" 2534558 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1073 2532674 2532800 2532830 "SETCAT" 2532947 T SETCAT (NIL) -9 NIL 2533032) (-1072 2532454 2532506 2532605 "SETCAT-" 2532610 NIL SETCAT- (NIL T) -8 NIL NIL) (-1071 2528841 2530915 2530958 "SETAGG" 2531828 NIL SETAGG (NIL T) -9 NIL 2532168) (-1070 2528299 2528415 2528652 "SETAGG-" 2528657 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1069 2527769 2527995 2528096 "SEQAST" 2528220 T SEQAST (NIL) -8 NIL NIL) (-1068 2526973 2527266 2527327 "SEGXCAT" 2527613 NIL SEGXCAT (NIL T T) -9 NIL 2527733) (-1067 2526029 2526639 2526821 "SEG" 2526826 NIL SEG (NIL T) -8 NIL NIL) (-1066 2524936 2525149 2525192 "SEGCAT" 2525774 NIL SEGCAT (NIL T) -9 NIL 2526012) (-1065 2523985 2524315 2524515 "SEGBIND" 2524771 NIL SEGBIND (NIL T) -8 NIL NIL) (-1064 2523606 2523665 2523778 "SEGBIND2" 2523920 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1063 2523207 2523407 2523484 "SEGAST" 2523551 T SEGAST (NIL) -8 NIL NIL) (-1062 2522426 2522552 2522756 "SEG2" 2523051 NIL SEG2 (NIL T T) -7 NIL NIL) (-1061 2521863 2522361 2522408 "SDVAR" 2522413 NIL SDVAR (NIL T) -8 NIL NIL) (-1060 2514153 2521633 2521763 "SDPOL" 2521768 NIL SDPOL (NIL T) -8 NIL NIL) (-1059 2512746 2513012 2513331 "SCPKG" 2513868 NIL SCPKG (NIL T) -7 NIL NIL) (-1058 2511882 2512062 2512262 "SCOPE" 2512568 T SCOPE (NIL) -8 NIL NIL) (-1057 2511103 2511236 2511415 "SCACHE" 2511737 NIL SCACHE (NIL T) -7 NIL NIL) (-1056 2510812 2510972 2511002 "SASTCAT" 2511007 T SASTCAT (NIL) -9 NIL 2511020) (-1055 2510251 2510572 2510657 "SAOS" 2510749 T SAOS (NIL) -8 NIL NIL) (-1054 2509816 2509851 2510024 "SAERFFC" 2510210 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1053 2503790 2509713 2509793 "SAE" 2509798 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1052 2503383 2503418 2503577 "SAEFACT" 2503749 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1051 2501704 2502018 2502419 "RURPK" 2503049 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1050 2500340 2500619 2500931 "RULESET" 2501538 NIL RULESET (NIL T T T) -8 NIL NIL) (-1049 2497527 2498030 2498495 "RULE" 2500021 NIL RULE (NIL T T T) -8 NIL NIL) (-1048 2497166 2497321 2497404 "RULECOLD" 2497479 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1047 2496664 2496883 2496977 "RSTRCAST" 2497094 T RSTRCAST (NIL) -8 NIL NIL) (-1046 2491513 2492307 2493227 "RSETGCD" 2495863 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1045 2480770 2485822 2485919 "RSETCAT" 2490038 NIL RSETCAT (NIL T T T T) -9 NIL 2491135) (-1044 2478697 2479236 2480060 "RSETCAT-" 2480065 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1043 2471084 2472459 2473979 "RSDCMPK" 2477296 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1042 2469089 2469530 2469604 "RRCC" 2470690 NIL RRCC (NIL T T) -9 NIL 2471034) (-1041 2468440 2468614 2468893 "RRCC-" 2468898 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1040 2467910 2468136 2468237 "RPTAST" 2468361 T RPTAST (NIL) -8 NIL NIL) (-1039 2442138 2451723 2451790 "RPOLCAT" 2462454 NIL RPOLCAT (NIL T T T) -9 NIL 2465613) (-1038 2433638 2435976 2439098 "RPOLCAT-" 2439103 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1037 2424685 2431849 2432331 "ROUTINE" 2433178 T ROUTINE (NIL) -8 NIL NIL) (-1036 2421443 2424236 2424385 "ROMAN" 2424558 T ROMAN (NIL) -8 NIL NIL) (-1035 2419718 2420303 2420563 "ROIRC" 2421248 NIL ROIRC (NIL T T) -8 NIL NIL) (-1034 2416169 2418408 2418438 "RNS" 2418742 T RNS (NIL) -9 NIL 2419014) (-1033 2414678 2415061 2415595 "RNS-" 2415670 NIL RNS- (NIL T) -8 NIL NIL) (-1032 2414127 2414509 2414539 "RNG" 2414544 T RNG (NIL) -9 NIL 2414565) (-1031 2413519 2413881 2413924 "RMODULE" 2413986 NIL RMODULE (NIL T) -9 NIL 2414028) (-1030 2412355 2412449 2412785 "RMCAT2" 2413420 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1029 2409060 2411529 2411854 "RMATRIX" 2412089 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1028 2402002 2404236 2404351 "RMATCAT" 2407710 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2408692) (-1027 2401377 2401524 2401831 "RMATCAT-" 2401836 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1026 2400944 2401019 2401147 "RINTERP" 2401296 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1025 2400032 2400552 2400582 "RING" 2400694 T RING (NIL) -9 NIL 2400789) (-1024 2399824 2399868 2399965 "RING-" 2399970 NIL RING- (NIL T) -8 NIL NIL) (-1023 2398665 2398902 2399160 "RIDIST" 2399588 T RIDIST (NIL) -7 NIL NIL) (-1022 2389981 2398133 2398339 "RGCHAIN" 2398513 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1021 2389357 2389737 2389778 "RGBCSPC" 2389836 NIL RGBCSPC (NIL T) -9 NIL 2389888) (-1020 2388541 2388896 2388937 "RGBCMDL" 2389169 NIL RGBCMDL (NIL T) -9 NIL 2389283) (-1019 2385535 2386149 2386819 "RF" 2387905 NIL RF (NIL T) -7 NIL NIL) (-1018 2385181 2385244 2385347 "RFFACTOR" 2385466 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1017 2384906 2384941 2385038 "RFFACT" 2385140 NIL RFFACT (NIL T) -7 NIL NIL) (-1016 2383023 2383387 2383769 "RFDIST" 2384546 T RFDIST (NIL) -7 NIL NIL) (-1015 2382476 2382568 2382731 "RETSOL" 2382925 NIL RETSOL (NIL T T) -7 NIL NIL) (-1014 2382064 2382144 2382187 "RETRACT" 2382380 NIL RETRACT (NIL T) -9 NIL NIL) (-1013 2381913 2381938 2382025 "RETRACT-" 2382030 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1012 2381542 2381735 2381805 "RETAST" 2381865 T RETAST (NIL) -8 NIL NIL) (-1011 2374396 2381195 2381322 "RESULT" 2381437 T RESULT (NIL) -8 NIL NIL) (-1010 2373022 2373665 2373864 "RESRING" 2374299 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1009 2372658 2372707 2372805 "RESLATC" 2372959 NIL RESLATC (NIL T) -7 NIL NIL) (-1008 2372364 2372398 2372505 "REPSQ" 2372617 NIL REPSQ (NIL T) -7 NIL NIL) (-1007 2369786 2370366 2370968 "REP" 2371784 T REP (NIL) -7 NIL NIL) (-1006 2369484 2369518 2369629 "REPDB" 2369745 NIL REPDB (NIL T) -7 NIL NIL) (-1005 2363394 2364773 2365996 "REP2" 2368296 NIL REP2 (NIL T) -7 NIL NIL) (-1004 2359771 2360452 2361260 "REP1" 2362621 NIL REP1 (NIL T) -7 NIL NIL) (-1003 2352497 2357912 2358368 "REGSET" 2359401 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1002 2351310 2351645 2351895 "REF" 2352282 NIL REF (NIL T) -8 NIL NIL) (-1001 2350687 2350790 2350957 "REDORDER" 2351194 NIL REDORDER (NIL T T) -7 NIL NIL) (-1000 2346698 2349906 2350131 "RECLOS" 2350516 NIL RECLOS (NIL T) -8 NIL NIL) (-999 2345755 2345936 2346149 "REALSOLV" 2346505 T REALSOLV (NIL) -7 NIL NIL) (-998 2345603 2345644 2345672 "REAL" 2345677 T REAL (NIL) -9 NIL 2345712) (-997 2342094 2342896 2343778 "REAL0Q" 2344768 NIL REAL0Q (NIL T) -7 NIL NIL) (-996 2337705 2338693 2339752 "REAL0" 2341075 NIL REAL0 (NIL T) -7 NIL NIL) (-995 2337207 2337426 2337518 "RDUCEAST" 2337633 T RDUCEAST (NIL) -8 NIL NIL) (-994 2336615 2336687 2336892 "RDIV" 2337129 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-993 2335688 2335862 2336073 "RDIST" 2336437 NIL RDIST (NIL T) -7 NIL NIL) (-992 2334289 2334576 2334946 "RDETRS" 2335396 NIL RDETRS (NIL T T) -7 NIL NIL) (-991 2332106 2332560 2333096 "RDETR" 2333831 NIL RDETR (NIL T T) -7 NIL NIL) (-990 2330720 2330998 2331400 "RDEEFS" 2331822 NIL RDEEFS (NIL T T) -7 NIL NIL) (-989 2329218 2329524 2329954 "RDEEF" 2330408 NIL RDEEF (NIL T T) -7 NIL NIL) (-988 2323555 2326426 2326454 "RCFIELD" 2327731 T RCFIELD (NIL) -9 NIL 2328461) (-987 2321624 2322128 2322821 "RCFIELD-" 2322894 NIL RCFIELD- (NIL T) -8 NIL NIL) (-986 2317955 2319740 2319781 "RCAGG" 2320852 NIL RCAGG (NIL T) -9 NIL 2321317) (-985 2317586 2317680 2317840 "RCAGG-" 2317845 NIL RCAGG- (NIL T T) -8 NIL NIL) (-984 2316926 2317038 2317201 "RATRET" 2317470 NIL RATRET (NIL T) -7 NIL NIL) (-983 2316483 2316550 2316669 "RATFACT" 2316854 NIL RATFACT (NIL T) -7 NIL NIL) (-982 2315798 2315918 2316068 "RANDSRC" 2316353 T RANDSRC (NIL) -7 NIL NIL) (-981 2315535 2315579 2315650 "RADUTIL" 2315747 T RADUTIL (NIL) -7 NIL NIL) (-980 2308600 2314278 2314595 "RADIX" 2315250 NIL RADIX (NIL NIL) -8 NIL NIL) (-979 2300256 2308444 2308572 "RADFF" 2308577 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-978 2299908 2299983 2300011 "RADCAT" 2300168 T RADCAT (NIL) -9 NIL NIL) (-977 2299693 2299741 2299838 "RADCAT-" 2299843 NIL RADCAT- (NIL T) -8 NIL NIL) (-976 2297844 2299468 2299557 "QUEUE" 2299637 NIL QUEUE (NIL T) -8 NIL NIL) (-975 2294420 2297781 2297826 "QUAT" 2297831 NIL QUAT (NIL T) -8 NIL NIL) (-974 2294058 2294101 2294228 "QUATCT2" 2294371 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-973 2287918 2291219 2291259 "QUATCAT" 2292039 NIL QUATCAT (NIL T) -9 NIL 2292805) (-972 2284062 2285099 2286486 "QUATCAT-" 2286580 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-971 2281582 2283146 2283187 "QUAGG" 2283562 NIL QUAGG (NIL T) -9 NIL 2283737) (-970 2281214 2281407 2281475 "QQUTAST" 2281534 T QQUTAST (NIL) -8 NIL NIL) (-969 2280139 2280612 2280784 "QFORM" 2281086 NIL QFORM (NIL NIL T) -8 NIL NIL) (-968 2271472 2276675 2276715 "QFCAT" 2277373 NIL QFCAT (NIL T) -9 NIL 2278372) (-967 2267044 2268245 2269836 "QFCAT-" 2269930 NIL QFCAT- (NIL T T) -8 NIL NIL) (-966 2266682 2266725 2266852 "QFCAT2" 2266995 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-965 2266142 2266252 2266382 "QEQUAT" 2266572 T QEQUAT (NIL) -8 NIL NIL) (-964 2259290 2260361 2261545 "QCMPACK" 2265075 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-963 2256866 2257287 2257715 "QALGSET" 2258945 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-962 2256111 2256285 2256517 "QALGSET2" 2256686 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-961 2254802 2255025 2255342 "PWFFINTB" 2255884 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-960 2252984 2253152 2253506 "PUSHVAR" 2254616 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-959 2248902 2249956 2249997 "PTRANFN" 2251881 NIL PTRANFN (NIL T) -9 NIL NIL) (-958 2247304 2247595 2247917 "PTPACK" 2248613 NIL PTPACK (NIL T) -7 NIL NIL) (-957 2246936 2246993 2247102 "PTFUNC2" 2247241 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-956 2241402 2245747 2245788 "PTCAT" 2246161 NIL PTCAT (NIL T) -9 NIL 2246323) (-955 2241060 2241095 2241219 "PSQFR" 2241361 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-954 2239655 2239953 2240287 "PSEUDLIN" 2240758 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-953 2226424 2228789 2231113 "PSETPK" 2237415 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-952 2219468 2222182 2222278 "PSETCAT" 2225299 NIL PSETCAT (NIL T T T T) -9 NIL 2226113) (-951 2217304 2217938 2218759 "PSETCAT-" 2218764 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-950 2216653 2216818 2216846 "PSCURVE" 2217114 T PSCURVE (NIL) -9 NIL 2217281) (-949 2213134 2214616 2214681 "PSCAT" 2215525 NIL PSCAT (NIL T T T) -9 NIL 2215765) (-948 2212197 2212413 2212813 "PSCAT-" 2212818 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-947 2210849 2211482 2211696 "PRTITION" 2212003 T PRTITION (NIL) -8 NIL NIL) (-946 2210351 2210570 2210662 "PRTDAST" 2210777 T PRTDAST (NIL) -8 NIL NIL) (-945 2199449 2201655 2203843 "PRS" 2208213 NIL PRS (NIL T T) -7 NIL NIL) (-944 2197307 2198799 2198839 "PRQAGG" 2199022 NIL PRQAGG (NIL T) -9 NIL 2199124) (-943 2196693 2196922 2196950 "PROPLOG" 2197135 T PROPLOG (NIL) -9 NIL 2197257) (-942 2193863 2194507 2194971 "PROPFRML" 2196261 NIL PROPFRML (NIL T) -8 NIL NIL) (-941 2193323 2193433 2193563 "PROPERTY" 2193753 T PROPERTY (NIL) -8 NIL NIL) (-940 2187408 2191489 2192309 "PRODUCT" 2192549 NIL PRODUCT (NIL T T) -8 NIL NIL) (-939 2184721 2186866 2187100 "PR" 2187219 NIL PR (NIL T T) -8 NIL NIL) (-938 2184517 2184549 2184608 "PRINT" 2184682 T PRINT (NIL) -7 NIL NIL) (-937 2183857 2183974 2184126 "PRIMES" 2184397 NIL PRIMES (NIL T) -7 NIL NIL) (-936 2181922 2182323 2182789 "PRIMELT" 2183436 NIL PRIMELT (NIL T) -7 NIL NIL) (-935 2181651 2181700 2181728 "PRIMCAT" 2181852 T PRIMCAT (NIL) -9 NIL NIL) (-934 2177812 2181589 2181634 "PRIMARR" 2181639 NIL PRIMARR (NIL T) -8 NIL NIL) (-933 2176819 2176997 2177225 "PRIMARR2" 2177630 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-932 2176462 2176518 2176629 "PREASSOC" 2176757 NIL PREASSOC (NIL T T) -7 NIL NIL) (-931 2175937 2176070 2176098 "PPCURVE" 2176303 T PPCURVE (NIL) -9 NIL 2176439) (-930 2175559 2175732 2175815 "PORTNUM" 2175874 T PORTNUM (NIL) -8 NIL NIL) (-929 2172918 2173317 2173909 "POLYROOT" 2175140 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-928 2166863 2172522 2172682 "POLY" 2172791 NIL POLY (NIL T) -8 NIL NIL) (-927 2166246 2166304 2166538 "POLYLIFT" 2166799 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-926 2162521 2162970 2163599 "POLYCATQ" 2165791 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-925 2149560 2154916 2154981 "POLYCAT" 2158495 NIL POLYCAT (NIL T T T) -9 NIL 2160423) (-924 2143010 2144871 2147255 "POLYCAT-" 2147260 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-923 2142597 2142665 2142785 "POLY2UP" 2142936 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-922 2142229 2142286 2142395 "POLY2" 2142534 NIL POLY2 (NIL T T) -7 NIL NIL) (-921 2140914 2141153 2141429 "POLUTIL" 2142003 NIL POLUTIL (NIL T T) -7 NIL NIL) (-920 2139269 2139546 2139877 "POLTOPOL" 2140636 NIL POLTOPOL 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PARSU2 (NIL T T) -7 NIL NIL) (-856 2010518 2010558 2010625 "PARSER" 2010707 T PARSER (NIL) -7 NIL NIL) (-855 2010139 2010202 2010304 "PARSCURV" 2010449 NIL PARSCURV (NIL T) -8 NIL NIL) (-854 2009771 2009828 2009937 "PARSC2" 2010076 NIL PARSC2 (NIL T T) -7 NIL NIL) (-853 2009410 2009468 2009565 "PARPCURV" 2009707 NIL PARPCURV (NIL T) -8 NIL NIL) (-852 2009042 2009099 2009208 "PARPC2" 2009347 NIL PARPC2 (NIL T T) -7 NIL NIL) (-851 2008562 2008648 2008767 "PAN2EXPR" 2008943 T PAN2EXPR (NIL) -7 NIL NIL) (-850 2007368 2007683 2007911 "PALETTE" 2008354 T PALETTE (NIL) -8 NIL NIL) (-849 2005836 2006373 2006733 "PAIR" 2007054 NIL PAIR (NIL T T) -8 NIL NIL) (-848 1999744 2005095 2005289 "PADICRC" 2005691 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-847 1993010 1999090 1999274 "PADICRAT" 1999592 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-846 1991360 1992947 1992992 "PADIC" 1992997 NIL PADIC (NIL NIL) -8 NIL NIL) (-845 1988605 1990135 1990175 "PADICCT" 1990756 NIL PADICCT (NIL NIL) -9 NIL 1991038) (-844 1987562 1987762 1988030 "PADEPAC" 1988392 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-843 1986774 1986907 1987113 "PADE" 1987424 NIL PADE (NIL T T T) -7 NIL NIL) (-842 1984824 1985610 1985927 "OWP" 1986541 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-841 1983933 1984429 1984601 "OVAR" 1984692 NIL OVAR (NIL NIL) -8 NIL NIL) (-840 1983197 1983318 1983479 "OUT" 1983792 T OUT (NIL) -7 NIL NIL) (-839 1972104 1974306 1976506 "OUTFORM" 1981017 T OUTFORM (NIL) -8 NIL NIL) (-838 1971525 1971701 1971828 "OUTBFILE" 1971997 T OUTBFILE (NIL) -8 NIL NIL) (-837 1971162 1971245 1971273 "OUTBCON" 1971424 T OUTBCON (NIL) -9 NIL 1971509) (-836 1971002 1971037 1971113 "OUTBCON-" 1971118 NIL OUTBCON- (NIL T) -8 NIL NIL) (-835 1970410 1970731 1970820 "OSI" 1970933 T OSI (NIL) -8 NIL NIL) (-834 1969966 1970278 1970306 "OSGROUP" 1970311 T OSGROUP (NIL) -9 NIL 1970333) (-833 1968711 1968938 1969223 "ORTHPOL" 1969713 NIL ORTHPOL (NIL T) -7 NIL NIL) (-832 1966121 1968370 1968509 "OREUP" 1968654 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-831 1963559 1965812 1965939 "ORESUP" 1966063 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-830 1961087 1961587 1962148 "OREPCTO" 1963048 NIL OREPCTO (NIL T T) -7 NIL NIL) (-829 1954998 1957165 1957206 "OREPCAT" 1959554 NIL OREPCAT (NIL T) -9 NIL 1960658) (-828 1952145 1952927 1953985 "OREPCAT-" 1953990 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-827 1951322 1951594 1951622 "ORDSET" 1951931 T ORDSET (NIL) -9 NIL 1952095) (-826 1950841 1950963 1951156 "ORDSET-" 1951161 NIL ORDSET- (NIL T) -8 NIL NIL) (-825 1949495 1950252 1950280 "ORDRING" 1950482 T ORDRING (NIL) -9 NIL 1950607) (-824 1949140 1949234 1949378 "ORDRING-" 1949383 NIL ORDRING- (NIL T) -8 NIL NIL) (-823 1948546 1948983 1949011 "ORDMON" 1949016 T ORDMON (NIL) -9 NIL 1949037) (-822 1947708 1947855 1948050 "ORDFUNS" 1948395 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-821 1947219 1947578 1947606 "ORDFIN" 1947611 T ORDFIN (NIL) -9 NIL 1947632) (-820 1943811 1945805 1946214 "ORDCOMP" 1946843 NIL ORDCOMP (NIL T) -8 NIL NIL) (-819 1943077 1943204 1943390 "ORDCOMP2" 1943671 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-818 1939584 1940467 1941304 "OPTPROB" 1942260 T OPTPROB (NIL) -8 NIL NIL) (-817 1936386 1937025 1937729 "OPTPACK" 1938900 T OPTPACK (NIL) -7 NIL NIL) (-816 1934099 1934839 1934867 "OPTCAT" 1935686 T OPTCAT (NIL) -9 NIL 1936336) (-815 1933867 1933906 1933972 "OPQUERY" 1934053 T OPQUERY (NIL) -7 NIL NIL) (-814 1931033 1932178 1932682 "OP" 1933396 NIL OP (NIL T) -8 NIL NIL) (-813 1927878 1929830 1930199 "ONECOMP" 1930697 NIL ONECOMP (NIL T) -8 NIL NIL) (-812 1927183 1927298 1927472 "ONECOMP2" 1927750 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-811 1926602 1926708 1926838 "OMSERVER" 1927073 T OMSERVER (NIL) -7 NIL NIL) (-810 1923490 1926042 1926082 "OMSAGG" 1926143 NIL OMSAGG (NIL T) -9 NIL 1926207) (-809 1922113 1922376 1922658 "OMPKG" 1923228 T OMPKG (NIL) -7 NIL NIL) (-808 1921543 1921646 1921674 "OM" 1921973 T OM (NIL) -9 NIL NIL) (-807 1920125 1921092 1921261 "OMLO" 1921424 NIL OMLO (NIL T T) -8 NIL NIL) (-806 1919050 1919197 1919424 "OMEXPR" 1919951 NIL OMEXPR (NIL T) -7 NIL NIL) (-805 1918368 1918596 1918732 "OMERR" 1918934 T OMERR (NIL) -8 NIL NIL) (-804 1917546 1917789 1917949 "OMERRK" 1918228 T OMERRK (NIL) -8 NIL NIL) (-803 1917024 1917223 1917331 "OMENC" 1917458 T OMENC (NIL) -8 NIL NIL) (-802 1910919 1912104 1913275 "OMDEV" 1915873 T OMDEV (NIL) -8 NIL NIL) (-801 1909988 1910159 1910353 "OMCONN" 1910745 T OMCONN (NIL) -8 NIL NIL) (-800 1908644 1909586 1909614 "OINTDOM" 1909619 T OINTDOM (NIL) -9 NIL 1909640) (-799 1904450 1905634 1906350 "OFMONOID" 1907960 NIL OFMONOID (NIL T) -8 NIL NIL) (-798 1903888 1904387 1904432 "ODVAR" 1904437 NIL ODVAR (NIL T) -8 NIL NIL) (-797 1901098 1903385 1903570 "ODR" 1903763 NIL ODR (NIL T T NIL) -8 NIL NIL) (-796 1893442 1900874 1901000 "ODPOL" 1901005 NIL ODPOL (NIL T) -8 NIL NIL) (-795 1887318 1893314 1893419 "ODP" 1893424 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-794 1886084 1886299 1886574 "ODETOOLS" 1887092 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-793 1883053 1883709 1884425 "ODESYS" 1885417 NIL ODESYS (NIL T T) -7 NIL NIL) (-792 1877935 1878843 1879868 "ODERTRIC" 1882128 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-791 1877361 1877443 1877637 "ODERED" 1877847 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-790 1874249 1874797 1875474 "ODERAT" 1876784 NIL ODERAT (NIL T T) -7 NIL NIL) (-789 1871209 1871673 1872270 "ODEPRRIC" 1873778 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-788 1869078 1869647 1870156 "ODEPROB" 1870720 T ODEPROB (NIL) -8 NIL NIL) (-787 1865600 1866083 1866730 "ODEPRIM" 1868557 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-786 1864849 1864951 1865211 "ODEPAL" 1865492 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-785 1861011 1861802 1862666 "ODEPACK" 1864005 T ODEPACK (NIL) -7 NIL NIL) (-784 1860044 1860151 1860380 "ODEINT" 1860900 NIL ODEINT (NIL T T) -7 NIL NIL) (-783 1854145 1855570 1857017 "ODEIFTBL" 1858617 T ODEIFTBL (NIL) -8 NIL NIL) (-782 1849480 1850266 1851225 "ODEEF" 1853304 NIL ODEEF (NIL T T) -7 NIL NIL) (-781 1848815 1848904 1849134 "ODECONST" 1849385 NIL ODECONST (NIL T T T) -7 NIL NIL) (-780 1846966 1847601 1847629 "ODECAT" 1848234 T ODECAT (NIL) -9 NIL 1848765) (-779 1843873 1846678 1846797 "OCT" 1846879 NIL OCT (NIL T) -8 NIL NIL) (-778 1843511 1843554 1843681 "OCTCT2" 1843824 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-777 1838372 1840772 1840812 "OC" 1841909 NIL OC (NIL T) -9 NIL 1842767) (-776 1835599 1836347 1837337 "OC-" 1837431 NIL OC- (NIL T T) -8 NIL NIL) (-775 1834977 1835419 1835447 "OCAMON" 1835452 T OCAMON (NIL) -9 NIL 1835473) (-774 1834534 1834849 1834877 "OASGP" 1834882 T OASGP (NIL) -9 NIL 1834902) (-773 1833821 1834284 1834312 "OAMONS" 1834352 T OAMONS (NIL) -9 NIL 1834395) (-772 1833261 1833668 1833696 "OAMON" 1833701 T OAMON (NIL) -9 NIL 1833721) (-771 1832565 1833057 1833085 "OAGROUP" 1833090 T OAGROUP (NIL) -9 NIL 1833110) (-770 1832255 1832305 1832393 "NUMTUBE" 1832509 NIL NUMTUBE (NIL T) -7 NIL NIL) (-769 1825828 1827346 1828882 "NUMQUAD" 1830739 T NUMQUAD (NIL) -7 NIL NIL) (-768 1821584 1822572 1823597 "NUMODE" 1824823 T NUMODE (NIL) -7 NIL NIL) (-767 1818965 1819819 1819847 "NUMINT" 1820770 T NUMINT (NIL) -9 NIL 1821534) (-766 1817913 1818110 1818328 "NUMFMT" 1818767 T NUMFMT (NIL) -7 NIL NIL) (-765 1804272 1807217 1809749 "NUMERIC" 1815420 NIL NUMERIC (NIL T) -7 NIL NIL) (-764 1798669 1803721 1803816 "NTSCAT" 1803821 NIL NTSCAT (NIL T T T T) -9 NIL 1803860) (-763 1797863 1798028 1798221 "NTPOLFN" 1798508 NIL NTPOLFN (NIL T) -7 NIL NIL) (-762 1785703 1794688 1795500 "NSUP" 1797084 NIL NSUP (NIL T) -8 NIL NIL) (-761 1785335 1785392 1785501 "NSUP2" 1785640 NIL NSUP2 (NIL T T) -7 NIL NIL) (-760 1775332 1785109 1785242 "NSMP" 1785247 NIL NSMP (NIL T T) -8 NIL NIL) (-759 1773764 1774065 1774422 "NREP" 1775020 NIL NREP (NIL T) -7 NIL NIL) (-758 1772355 1772607 1772965 "NPCOEF" 1773507 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-757 1771421 1771536 1771752 "NORMRETR" 1772236 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-756 1769462 1769752 1770161 "NORMPK" 1771129 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-755 1769147 1769175 1769299 "NORMMA" 1769428 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-754 1768974 1769104 1769133 "NONE" 1769138 T NONE (NIL) -8 NIL NIL) (-753 1768763 1768792 1768861 "NONE1" 1768938 NIL NONE1 (NIL T) -7 NIL NIL) (-752 1768246 1768308 1768494 "NODE1" 1768695 NIL NODE1 (NIL T T) -7 NIL NIL) (-751 1766586 1767409 1767664 "NNI" 1768011 T NNI (NIL) -8 NIL NIL) (-750 1765006 1765319 1765683 "NLINSOL" 1766254 NIL NLINSOL (NIL T) -7 NIL NIL) (-749 1761173 1762141 1763063 "NIPROB" 1764104 T NIPROB (NIL) -8 NIL NIL) (-748 1759930 1760164 1760466 "NFINTBAS" 1760935 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-747 1758638 1758869 1759150 "NCODIV" 1759698 NIL NCODIV (NIL T T) -7 NIL NIL) (-746 1758400 1758437 1758512 "NCNTFRAC" 1758595 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-745 1756580 1756944 1757364 "NCEP" 1758025 NIL NCEP (NIL T) -7 NIL NIL) (-744 1755491 1756230 1756258 "NASRING" 1756368 T NASRING (NIL) -9 NIL 1756442) (-743 1755286 1755330 1755424 "NASRING-" 1755429 NIL NASRING- (NIL T) -8 NIL NIL) (-742 1754439 1754938 1754966 "NARNG" 1755083 T NARNG (NIL) -9 NIL 1755174) (-741 1754131 1754198 1754332 "NARNG-" 1754337 NIL NARNG- (NIL T) -8 NIL NIL) (-740 1753010 1753217 1753452 "NAGSP" 1753916 T NAGSP (NIL) -7 NIL NIL) (-739 1744282 1745966 1747639 "NAGS" 1751357 T NAGS (NIL) -7 NIL NIL) (-738 1742830 1743138 1743469 "NAGF07" 1743971 T NAGF07 (NIL) -7 NIL NIL) (-737 1737368 1738659 1739966 "NAGF04" 1741543 T NAGF04 (NIL) -7 NIL NIL) (-736 1730336 1731950 1733583 "NAGF02" 1735755 T NAGF02 (NIL) -7 NIL NIL) (-735 1725560 1726660 1727777 "NAGF01" 1729239 T NAGF01 (NIL) -7 NIL NIL) (-734 1719188 1720754 1722339 "NAGE04" 1723995 T NAGE04 (NIL) -7 NIL NIL) (-733 1710357 1712478 1714608 "NAGE02" 1717078 T NAGE02 (NIL) -7 NIL NIL) (-732 1706310 1707257 1708221 "NAGE01" 1709413 T NAGE01 (NIL) -7 NIL NIL) (-731 1704105 1704639 1705197 "NAGD03" 1705772 T NAGD03 (NIL) -7 NIL NIL) (-730 1695855 1697783 1699737 "NAGD02" 1702171 T NAGD02 (NIL) -7 NIL NIL) (-729 1689666 1691091 1692531 "NAGD01" 1694435 T NAGD01 (NIL) -7 NIL NIL) (-728 1685875 1686697 1687534 "NAGC06" 1688849 T NAGC06 (NIL) -7 NIL NIL) (-727 1684340 1684672 1685028 "NAGC05" 1685539 T NAGC05 (NIL) -7 NIL NIL) (-726 1683716 1683835 1683979 "NAGC02" 1684216 T NAGC02 (NIL) -7 NIL NIL) (-725 1682776 1683333 1683373 "NAALG" 1683452 NIL NAALG (NIL T) -9 NIL 1683513) (-724 1682611 1682640 1682730 "NAALG-" 1682735 NIL NAALG- (NIL T T) -8 NIL NIL) (-723 1676561 1677669 1678856 "MULTSQFR" 1681507 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-722 1675880 1675955 1676139 "MULTFACT" 1676473 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-721 1669103 1672968 1673021 "MTSCAT" 1674091 NIL MTSCAT (NIL T T) -9 NIL 1674605) (-720 1668815 1668869 1668961 "MTHING" 1669043 NIL MTHING (NIL T) -7 NIL NIL) (-719 1668607 1668640 1668700 "MSYSCMD" 1668775 T MSYSCMD (NIL) -7 NIL NIL) (-718 1664719 1667362 1667682 "MSET" 1668320 NIL MSET (NIL T) -8 NIL NIL) (-717 1661814 1664280 1664321 "MSETAGG" 1664326 NIL MSETAGG (NIL T) -9 NIL 1664360) (-716 1657697 1659193 1659938 "MRING" 1661114 NIL MRING (NIL T T) -8 NIL NIL) (-715 1657263 1657330 1657461 "MRF2" 1657624 NIL MRF2 (NIL T T T) -7 NIL NIL) (-714 1656881 1656916 1657060 "MRATFAC" 1657222 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-713 1654493 1654788 1655219 "MPRFF" 1656586 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-712 1648553 1654347 1654444 "MPOLY" 1654449 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-711 1648043 1648078 1648286 "MPCPF" 1648512 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-710 1647557 1647600 1647784 "MPC3" 1647994 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-709 1646752 1646833 1647054 "MPC2" 1647472 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-708 1645053 1645390 1645780 "MONOTOOL" 1646412 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-707 1644304 1644595 1644623 "MONOID" 1644842 T MONOID (NIL) -9 NIL 1644989) (-706 1643850 1643969 1644150 "MONOID-" 1644155 NIL MONOID- (NIL T) -8 NIL NIL) (-705 1634900 1640806 1640865 "MONOGEN" 1641539 NIL MONOGEN (NIL T T) -9 NIL 1641995) (-704 1632118 1632853 1633853 "MONOGEN-" 1633972 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-703 1630977 1631397 1631425 "MONADWU" 1631817 T MONADWU (NIL) -9 NIL 1632055) (-702 1630349 1630508 1630756 "MONADWU-" 1630761 NIL MONADWU- (NIL T) -8 NIL NIL) (-701 1629734 1629952 1629980 "MONAD" 1630187 T MONAD (NIL) -9 NIL 1630299) (-700 1629419 1629497 1629629 "MONAD-" 1629634 NIL MONAD- (NIL T) -8 NIL NIL) (-699 1627735 1628332 1628611 "MOEBIUS" 1629172 NIL MOEBIUS (NIL T) -8 NIL NIL) (-698 1627127 1627505 1627545 "MODULE" 1627550 NIL MODULE (NIL T) -9 NIL 1627576) (-697 1626695 1626791 1626981 "MODULE-" 1626986 NIL MODULE- (NIL T T) -8 NIL NIL) (-696 1624410 1625059 1625386 "MODRING" 1626519 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-695 1621396 1622515 1623036 "MODOP" 1623939 NIL MODOP (NIL T T) -8 NIL NIL) (-694 1619583 1620035 1620376 "MODMONOM" 1621195 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-693 1609291 1617775 1618198 "MODMON" 1619211 NIL MODMON (NIL T T) -8 NIL NIL) (-692 1606482 1608135 1608411 "MODFIELD" 1609166 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-691 1605486 1605763 1605953 "MMLFORM" 1606312 T MMLFORM (NIL) -8 NIL NIL) (-690 1605012 1605055 1605234 "MMAP" 1605437 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-689 1603281 1604014 1604055 "MLO" 1604478 NIL MLO (NIL T) -9 NIL 1604720) (-688 1600648 1601163 1601765 "MLIFT" 1602762 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-687 1600039 1600123 1600277 "MKUCFUNC" 1600559 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-686 1599638 1599708 1599831 "MKRECORD" 1599962 NIL MKRECORD (NIL T T) -7 NIL NIL) (-685 1598686 1598847 1599075 "MKFUNC" 1599449 NIL MKFUNC (NIL T) -7 NIL NIL) (-684 1598074 1598178 1598334 "MKFLCFN" 1598569 NIL MKFLCFN (NIL T) -7 NIL NIL) (-683 1597500 1597867 1597956 "MKCHSET" 1598018 NIL MKCHSET (NIL T) -8 NIL NIL) (-682 1596777 1596879 1597064 "MKBCFUNC" 1597393 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-681 1593519 1596331 1596467 "MINT" 1596661 T MINT (NIL) -8 NIL NIL) (-680 1592331 1592574 1592851 "MHROWRED" 1593274 NIL MHROWRED (NIL T) -7 NIL NIL) (-679 1587757 1590866 1591271 "MFLOAT" 1591946 T MFLOAT (NIL) -8 NIL NIL) (-678 1587114 1587190 1587361 "MFINFACT" 1587669 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-677 1583429 1584277 1585161 "MESH" 1586250 T MESH (NIL) -7 NIL NIL) (-676 1581819 1582131 1582484 "MDDFACT" 1583116 NIL MDDFACT (NIL T) -7 NIL NIL) (-675 1578661 1580978 1581019 "MDAGG" 1581274 NIL MDAGG (NIL T) -9 NIL 1581417) (-674 1568441 1577954 1578161 "MCMPLX" 1578474 T MCMPLX (NIL) -8 NIL NIL) (-673 1567582 1567728 1567928 "MCDEN" 1568290 NIL MCDEN (NIL T T) -7 NIL NIL) (-672 1565472 1565742 1566122 "MCALCFN" 1567312 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-671 1564383 1564556 1564797 "MAYBE" 1565270 NIL MAYBE (NIL T) -8 NIL NIL) (-670 1561995 1562518 1563080 "MATSTOR" 1563854 NIL MATSTOR (NIL T) -7 NIL NIL) (-669 1558001 1561367 1561615 "MATRIX" 1561780 NIL MATRIX (NIL T) -8 NIL NIL) (-668 1553770 1554474 1555210 "MATLIN" 1557358 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-667 1543924 1547062 1547139 "MATCAT" 1552019 NIL MATCAT (NIL T T T) -9 NIL 1553436) (-666 1540288 1541301 1542657 "MATCAT-" 1542662 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-665 1538882 1539035 1539368 "MATCAT2" 1540123 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-664 1536994 1537318 1537702 "MAPPKG3" 1538557 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-663 1535975 1536148 1536370 "MAPPKG2" 1536818 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-662 1534474 1534758 1535085 "MAPPKG1" 1535681 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-661 1533580 1533880 1534057 "MAPPAST" 1534317 T MAPPAST (NIL) -8 NIL NIL) (-660 1533191 1533249 1533372 "MAPHACK3" 1533516 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-659 1532783 1532844 1532958 "MAPHACK2" 1533123 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-658 1532221 1532324 1532466 "MAPHACK1" 1532674 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-657 1530327 1530921 1531225 "MAGMA" 1531949 NIL MAGMA (NIL T) -8 NIL NIL) (-656 1529833 1530051 1530142 "MACROAST" 1530256 T MACROAST (NIL) -8 NIL NIL) (-655 1526300 1528072 1528533 "M3D" 1529405 NIL M3D (NIL T) -8 NIL NIL) (-654 1520455 1524670 1524711 "LZSTAGG" 1525493 NIL LZSTAGG (NIL T) -9 NIL 1525788) (-653 1516428 1517586 1519043 "LZSTAGG-" 1519048 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-652 1513542 1514319 1514806 "LWORD" 1515973 NIL LWORD (NIL T) -8 NIL NIL) (-651 1513145 1513346 1513421 "LSTAST" 1513487 T LSTAST (NIL) -8 NIL NIL) (-650 1506346 1512916 1513050 "LSQM" 1513055 NIL LSQM (NIL NIL T) -8 NIL NIL) (-649 1505570 1505709 1505937 "LSPP" 1506201 NIL LSPP (NIL T T T T) -7 NIL NIL) (-648 1503382 1503683 1504139 "LSMP" 1505259 NIL LSMP (NIL T T T T) -7 NIL NIL) (-647 1500161 1500835 1501565 "LSMP1" 1502684 NIL LSMP1 (NIL T) -7 NIL NIL) (-646 1494087 1499329 1499370 "LSAGG" 1499432 NIL LSAGG (NIL T) -9 NIL 1499510) (-645 1490782 1491706 1492919 "LSAGG-" 1492924 NIL LSAGG- (NIL T T) -8 NIL NIL) (-644 1488408 1489926 1490175 "LPOLY" 1490577 NIL LPOLY (NIL T T) -8 NIL NIL) (-643 1487990 1488075 1488198 "LPEFRAC" 1488317 NIL LPEFRAC (NIL T) -7 NIL NIL) (-642 1486337 1487084 1487337 "LO" 1487822 NIL LO (NIL T T T) -8 NIL NIL) (-641 1485989 1486101 1486129 "LOGIC" 1486240 T LOGIC (NIL) -9 NIL 1486321) (-640 1485851 1485874 1485945 "LOGIC-" 1485950 NIL LOGIC- (NIL T) -8 NIL NIL) (-639 1485044 1485184 1485377 "LODOOPS" 1485707 NIL LODOOPS (NIL T T) -7 NIL NIL) (-638 1482502 1484960 1485026 "LODO" 1485031 NIL LODO (NIL T NIL) -8 NIL NIL) (-637 1481040 1481275 1481628 "LODOF" 1482249 NIL LODOF (NIL T T) -7 NIL NIL) (-636 1477483 1479880 1479921 "LODOCAT" 1480359 NIL LODOCAT (NIL T) -9 NIL 1480570) (-635 1477216 1477274 1477401 "LODOCAT-" 1477406 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-634 1474571 1477057 1477175 "LODO2" 1477180 NIL LODO2 (NIL T T) -8 NIL NIL) (-633 1472041 1474508 1474553 "LODO1" 1474558 NIL LODO1 (NIL T) -8 NIL NIL) (-632 1470901 1471066 1471378 "LODEEF" 1471864 NIL LODEEF (NIL T T T) -7 NIL NIL) (-631 1466187 1469031 1469072 "LNAGG" 1470019 NIL LNAGG (NIL T) -9 NIL 1470463) (-630 1465334 1465548 1465890 "LNAGG-" 1465895 NIL LNAGG- (NIL T T) -8 NIL NIL) (-629 1461497 1462259 1462898 "LMOPS" 1464749 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-628 1460892 1461254 1461295 "LMODULE" 1461356 NIL LMODULE (NIL T) -9 NIL 1461398) (-627 1458138 1460537 1460660 "LMDICT" 1460802 NIL LMDICT (NIL T) -8 NIL NIL) (-626 1457864 1458046 1458106 "LITERAL" 1458111 NIL LITERAL (NIL T) -8 NIL NIL) (-625 1451091 1456810 1457108 "LIST" 1457599 NIL LIST (NIL T) -8 NIL NIL) (-624 1450616 1450690 1450829 "LIST3" 1451011 NIL LIST3 (NIL T T T) -7 NIL NIL) (-623 1449623 1449801 1450029 "LIST2" 1450434 NIL LIST2 (NIL T T) -7 NIL NIL) (-622 1447757 1448069 1448468 "LIST2MAP" 1449270 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-621 1446507 1447143 1447184 "LINEXP" 1447439 NIL LINEXP (NIL T) -9 NIL 1447588) (-620 1445154 1445414 1445711 "LINDEP" 1446259 NIL LINDEP (NIL T T) -7 NIL NIL) (-619 1441921 1442640 1443417 "LIMITRF" 1444409 NIL LIMITRF (NIL T) -7 NIL NIL) (-618 1440197 1440492 1440908 "LIMITPS" 1441616 NIL LIMITPS (NIL T T) -7 NIL NIL) (-617 1434652 1439708 1439936 "LIE" 1440018 NIL LIE (NIL T T) -8 NIL NIL) (-616 1433701 1434144 1434184 "LIECAT" 1434324 NIL LIECAT (NIL T) -9 NIL 1434475) (-615 1433542 1433569 1433657 "LIECAT-" 1433662 NIL LIECAT- (NIL T T) -8 NIL NIL) (-614 1426154 1432991 1433156 "LIB" 1433397 T LIB (NIL) -8 NIL NIL) (-613 1421791 1422672 1423607 "LGROBP" 1425271 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-612 1419657 1419931 1420293 "LF" 1421512 NIL LF (NIL T T) -7 NIL NIL) (-611 1418497 1419189 1419217 "LFCAT" 1419424 T LFCAT (NIL) -9 NIL 1419563) (-610 1415401 1416029 1416717 "LEXTRIPK" 1417861 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-609 1412172 1412971 1413474 "LEXP" 1414981 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-608 1411675 1411893 1411985 "LETAST" 1412100 T LETAST (NIL) -8 NIL NIL) (-607 1410073 1410386 1410787 "LEADCDET" 1411357 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-606 1409263 1409337 1409566 "LAZM3PK" 1409994 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-605 1404219 1407340 1407878 "LAUPOL" 1408775 NIL LAUPOL (NIL T T) -8 NIL NIL) (-604 1403784 1403828 1403996 "LAPLACE" 1404169 NIL LAPLACE (NIL T T) -7 NIL NIL) (-603 1401758 1402885 1403136 "LA" 1403617 NIL LA (NIL T T T) -8 NIL NIL) (-602 1400859 1401409 1401450 "LALG" 1401512 NIL LALG (NIL T) -9 NIL 1401571) (-601 1400573 1400632 1400768 "LALG-" 1400773 NIL LALG- (NIL T T) -8 NIL NIL) (-600 1399373 1399790 1400019 "KTVLOGIC" 1400364 T KTVLOGIC (NIL) -8 NIL NIL) (-599 1398277 1398464 1398763 "KOVACIC" 1399173 NIL KOVACIC (NIL T T) -7 NIL NIL) (-598 1398112 1398136 1398177 "KONVERT" 1398239 NIL KONVERT (NIL T) -9 NIL NIL) (-597 1397947 1397971 1398012 "KOERCE" 1398074 NIL KOERCE (NIL T) -9 NIL NIL) (-596 1395681 1396441 1396834 "KERNEL" 1397586 NIL KERNEL (NIL T) -8 NIL NIL) (-595 1395183 1395264 1395394 "KERNEL2" 1395595 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-594 1389034 1393722 1393776 "KDAGG" 1394153 NIL KDAGG (NIL T T) -9 NIL 1394359) (-593 1388563 1388687 1388892 "KDAGG-" 1388897 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-592 1381738 1388224 1388379 "KAFILE" 1388441 NIL KAFILE (NIL T) -8 NIL NIL) (-591 1376193 1381249 1381477 "JORDAN" 1381559 NIL JORDAN (NIL T T) -8 NIL NIL) (-590 1375599 1375842 1375963 "JOINAST" 1376092 T JOINAST (NIL) -8 NIL NIL) (-589 1375328 1375387 1375474 "JAVACODE" 1375532 T JAVACODE (NIL) -8 NIL NIL) (-588 1371627 1373533 1373587 "IXAGG" 1374516 NIL IXAGG (NIL T T) -9 NIL 1374975) (-587 1370546 1370852 1371271 "IXAGG-" 1371276 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-586 1366126 1370468 1370527 "IVECTOR" 1370532 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-585 1364892 1365129 1365395 "ITUPLE" 1365893 NIL ITUPLE (NIL T) -8 NIL NIL) (-584 1363328 1363505 1363811 "ITRIGMNP" 1364714 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-583 1362073 1362277 1362560 "ITFUN3" 1363104 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-582 1361705 1361762 1361871 "ITFUN2" 1362010 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-581 1359542 1360567 1360866 "ITAYLOR" 1361439 NIL ITAYLOR (NIL T) -8 NIL NIL) (-580 1348524 1353679 1354842 "ISUPS" 1358412 NIL ISUPS (NIL T) -8 NIL NIL) (-579 1347628 1347768 1348004 "ISUMP" 1348371 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-578 1342892 1347429 1347508 "ISTRING" 1347581 NIL ISTRING (NIL NIL) -8 NIL NIL) (-577 1342395 1342613 1342705 "ISAST" 1342820 T ISAST (NIL) -8 NIL NIL) (-576 1341605 1341686 1341902 "IRURPK" 1342309 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-575 1340541 1340742 1340982 "IRSN" 1341385 T IRSN (NIL) -7 NIL NIL) (-574 1338570 1338925 1339361 "IRRF2F" 1340179 NIL IRRF2F (NIL T) -7 NIL NIL) (-573 1338317 1338355 1338431 "IRREDFFX" 1338526 NIL IRREDFFX (NIL T) -7 NIL NIL) (-572 1336932 1337191 1337490 "IROOT" 1338050 NIL IROOT (NIL T) -7 NIL NIL) (-571 1333564 1334616 1335308 "IR" 1336272 NIL IR (NIL T) -8 NIL NIL) (-570 1331177 1331672 1332238 "IR2" 1333042 NIL IR2 (NIL T T) -7 NIL NIL) (-569 1330249 1330362 1330583 "IR2F" 1331060 NIL IR2F (NIL T T) -7 NIL NIL) (-568 1330040 1330074 1330134 "IPRNTPK" 1330209 T IPRNTPK (NIL) -7 NIL NIL) (-567 1326659 1329929 1329998 "IPF" 1330003 NIL IPF (NIL NIL) -8 NIL NIL) (-566 1325022 1326584 1326641 "IPADIC" 1326646 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-565 1324522 1324726 1324836 "IOMODE" 1324932 T IOMODE (NIL) -8 NIL NIL) (-564 1324286 1324426 1324454 "IOBCON" 1324459 T IOBCON (NIL) -9 NIL 1324480) (-563 1323783 1323841 1324031 "INVLAPLA" 1324222 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-562 1313432 1315785 1318171 "INTTR" 1321447 NIL INTTR (NIL T T) -7 NIL NIL) (-561 1309776 1310518 1311382 "INTTOOLS" 1312617 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-560 1309362 1309453 1309570 "INTSLPE" 1309679 T INTSLPE (NIL) -7 NIL NIL) (-559 1307357 1309285 1309344 "INTRVL" 1309349 NIL INTRVL (NIL T) -8 NIL NIL) (-558 1304959 1305471 1306046 "INTRF" 1306842 NIL INTRF (NIL T) -7 NIL NIL) (-557 1304370 1304467 1304609 "INTRET" 1304857 NIL INTRET (NIL T) -7 NIL NIL) (-556 1302367 1302756 1303226 "INTRAT" 1303978 NIL INTRAT (NIL T T) -7 NIL NIL) (-555 1299595 1300178 1300804 "INTPM" 1301852 NIL INTPM (NIL T T) -7 NIL NIL) (-554 1296298 1296897 1297642 "INTPAF" 1298981 NIL INTPAF (NIL T T T) -7 NIL NIL) (-553 1291477 1292439 1293490 "INTPACK" 1295267 T INTPACK (NIL) -7 NIL NIL) (-552 1288389 1291206 1291333 "INT" 1291370 T INT (NIL) -8 NIL NIL) (-551 1287641 1287793 1288001 "INTHERTR" 1288231 NIL INTHERTR (NIL T T) -7 NIL NIL) (-550 1287080 1287160 1287348 "INTHERAL" 1287555 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-549 1284926 1285369 1285826 "INTHEORY" 1286643 T INTHEORY (NIL) -7 NIL NIL) (-548 1276234 1277855 1279634 "INTG0" 1283278 NIL INTG0 (NIL T T T) -7 NIL NIL) (-547 1256807 1261597 1266407 "INTFTBL" 1271444 T INTFTBL (NIL) -8 NIL NIL) (-546 1256056 1256194 1256367 "INTFACT" 1256666 NIL INTFACT (NIL T) -7 NIL NIL) (-545 1253441 1253887 1254451 "INTEF" 1255610 NIL INTEF (NIL T T) -7 NIL NIL) (-544 1251943 1252648 1252676 "INTDOM" 1252977 T INTDOM (NIL) -9 NIL 1253184) (-543 1251312 1251486 1251728 "INTDOM-" 1251733 NIL INTDOM- (NIL T) -8 NIL NIL) (-542 1247845 1249731 1249785 "INTCAT" 1250584 NIL INTCAT (NIL T) -9 NIL 1250904) (-541 1247318 1247420 1247548 "INTBIT" 1247737 T INTBIT (NIL) -7 NIL NIL) (-540 1245989 1246143 1246457 "INTALG" 1247163 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-539 1245446 1245536 1245706 "INTAF" 1245893 NIL INTAF (NIL T T) -7 NIL NIL) (-538 1238900 1245256 1245396 "INTABL" 1245401 NIL INTABL (NIL T T T) -8 NIL NIL) (-537 1233955 1236626 1236654 "INS" 1237588 T INS (NIL) -9 NIL 1238252) (-536 1231195 1231966 1232940 "INS-" 1233013 NIL INS- (NIL T) -8 NIL NIL) (-535 1229970 1230197 1230495 "INPSIGN" 1230948 NIL INPSIGN (NIL T T) -7 NIL NIL) (-534 1229088 1229205 1229402 "INPRODPF" 1229850 NIL INPRODPF (NIL T T) -7 NIL NIL) (-533 1227982 1228099 1228336 "INPRODFF" 1228968 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-532 1226982 1227134 1227394 "INNMFACT" 1227818 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-531 1226179 1226276 1226464 "INMODGCD" 1226881 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-530 1224688 1224932 1225256 "INFSP" 1225924 NIL INFSP (NIL T T T) -7 NIL NIL) (-529 1223872 1223989 1224172 "INFPROD0" 1224568 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-528 1220754 1221937 1222452 "INFORM" 1223365 T INFORM (NIL) -8 NIL NIL) (-527 1220364 1220424 1220522 "INFORM1" 1220689 NIL INFORM1 (NIL T) -7 NIL NIL) (-526 1219887 1219976 1220090 "INFINITY" 1220270 T INFINITY (NIL) -7 NIL NIL) (-525 1218504 1218753 1219074 "INEP" 1219635 NIL INEP (NIL T T T) -7 NIL NIL) (-524 1217780 1218401 1218466 "INDE" 1218471 NIL INDE (NIL T) -8 NIL NIL) (-523 1217344 1217412 1217529 "INCRMAPS" 1217707 NIL INCRMAPS (NIL T) -7 NIL NIL) (-522 1216647 1216840 1216990 "INBFILE" 1217214 T INBFILE (NIL) -8 NIL NIL) (-521 1211958 1212883 1213827 "INBFF" 1215735 NIL INBFF (NIL T) -7 NIL NIL) (-520 1211627 1211703 1211731 "INBCON" 1211864 T INBCON (NIL) -9 NIL 1211942) (-519 1211467 1211502 1211578 "INBCON-" 1211583 NIL INBCON- (NIL T) -8 NIL NIL) (-518 1210969 1211188 1211280 "INAST" 1211395 T INAST (NIL) -8 NIL NIL) (-517 1210423 1210648 1210754 "IMPTAST" 1210883 T IMPTAST (NIL) -8 NIL NIL) (-516 1206917 1210267 1210371 "IMATRIX" 1210376 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-515 1205629 1205752 1206067 "IMATQF" 1206773 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-514 1203849 1204076 1204413 "IMATLIN" 1205385 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-513 1198475 1203773 1203831 "ILIST" 1203836 NIL ILIST (NIL T NIL) -8 NIL NIL) (-512 1196428 1198335 1198448 "IIARRAY2" 1198453 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-511 1191861 1196339 1196403 "IFF" 1196408 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-510 1191235 1191478 1191594 "IFAST" 1191765 T IFAST (NIL) -8 NIL NIL) (-509 1186278 1190527 1190715 "IFARRAY" 1191092 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-508 1185485 1186182 1186255 "IFAMON" 1186260 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-507 1185069 1185134 1185188 "IEVALAB" 1185395 NIL IEVALAB (NIL T T) -9 NIL NIL) (-506 1184744 1184812 1184972 "IEVALAB-" 1184977 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-505 1184402 1184658 1184721 "IDPO" 1184726 NIL IDPO (NIL T T) -8 NIL NIL) (-504 1183679 1184291 1184366 "IDPOAMS" 1184371 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-503 1183013 1183568 1183643 "IDPOAM" 1183648 NIL IDPOAM (NIL T T) -8 NIL NIL) (-502 1182098 1182348 1182401 "IDPC" 1182814 NIL IDPC (NIL T T) -9 NIL 1182963) (-501 1181594 1181990 1182063 "IDPAM" 1182068 NIL IDPAM (NIL T T) -8 NIL NIL) (-500 1180997 1181486 1181559 "IDPAG" 1181564 NIL IDPAG (NIL T T) -8 NIL NIL) (-499 1180727 1180912 1180962 "IDENT" 1180967 T IDENT (NIL) -8 NIL NIL) (-498 1176982 1177830 1178725 "IDECOMP" 1179884 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-497 1169855 1170905 1171952 "IDEAL" 1176018 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-496 1169019 1169131 1169330 "ICDEN" 1169739 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-495 1168118 1168499 1168646 "ICARD" 1168892 T ICARD (NIL) -8 NIL NIL) (-494 1166178 1166491 1166896 "IBPTOOLS" 1167795 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-493 1161812 1165798 1165911 "IBITS" 1166097 NIL IBITS (NIL NIL) -8 NIL NIL) (-492 1158535 1159111 1159806 "IBATOOL" 1161229 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-491 1156315 1156776 1157309 "IBACHIN" 1158070 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-490 1154192 1156161 1156264 "IARRAY2" 1156269 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-489 1150345 1154118 1154175 "IARRAY1" 1154180 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-488 1144340 1148759 1149239 "IAN" 1149885 T IAN (NIL) -8 NIL NIL) (-487 1143851 1143908 1144081 "IALGFACT" 1144277 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-486 1143379 1143492 1143520 "HYPCAT" 1143727 T HYPCAT (NIL) -9 NIL NIL) (-485 1142917 1143034 1143220 "HYPCAT-" 1143225 NIL HYPCAT- (NIL T) -8 NIL NIL) (-484 1142539 1142712 1142795 "HOSTNAME" 1142854 T HOSTNAME (NIL) -8 NIL NIL) (-483 1139218 1140549 1140590 "HOAGG" 1141571 NIL HOAGG (NIL T) -9 NIL 1142250) (-482 1137812 1138211 1138737 "HOAGG-" 1138742 NIL HOAGG- (NIL T T) -8 NIL NIL) (-481 1131700 1137253 1137419 "HEXADEC" 1137666 T HEXADEC (NIL) -8 NIL NIL) (-480 1130448 1130670 1130933 "HEUGCD" 1131477 NIL HEUGCD (NIL T) -7 NIL NIL) (-479 1129551 1130285 1130415 "HELLFDIV" 1130420 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-478 1127779 1129328 1129416 "HEAP" 1129495 NIL HEAP (NIL T) -8 NIL NIL) (-477 1127070 1127331 1127465 "HEADAST" 1127665 T HEADAST (NIL) -8 NIL NIL) (-476 1120990 1126985 1127047 "HDP" 1127052 NIL HDP (NIL NIL T) -8 NIL NIL) (-475 1114741 1120625 1120777 "HDMP" 1120891 NIL HDMP (NIL NIL T) -8 NIL NIL) (-474 1114066 1114205 1114369 "HB" 1114597 T HB (NIL) -7 NIL NIL) (-473 1107563 1113912 1114016 "HASHTBL" 1114021 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-472 1107066 1107284 1107376 "HASAST" 1107491 T HASAST (NIL) -8 NIL NIL) (-471 1104880 1106690 1106871 "HACKPI" 1106905 T HACKPI (NIL) -8 NIL NIL) (-470 1100575 1104733 1104846 "GTSET" 1104851 NIL GTSET (NIL T T T T) -8 NIL NIL) (-469 1094101 1100453 1100551 "GSTBL" 1100556 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-468 1086414 1093132 1093397 "GSERIES" 1093892 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-467 1085581 1085972 1086000 "GROUP" 1086203 T GROUP (NIL) -9 NIL 1086337) (-466 1084947 1085106 1085357 "GROUP-" 1085362 NIL GROUP- (NIL T) -8 NIL NIL) (-465 1083316 1083635 1084022 "GROEBSOL" 1084624 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-464 1082256 1082518 1082569 "GRMOD" 1083098 NIL GRMOD (NIL T T) -9 NIL 1083266) (-463 1082024 1082060 1082188 "GRMOD-" 1082193 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-462 1077349 1078378 1079378 "GRIMAGE" 1081044 T GRIMAGE (NIL) -8 NIL NIL) (-461 1075816 1076076 1076400 "GRDEF" 1077045 T GRDEF (NIL) -7 NIL NIL) (-460 1075260 1075376 1075517 "GRAY" 1075695 T GRAY (NIL) -7 NIL NIL) (-459 1074491 1074871 1074922 "GRALG" 1075075 NIL GRALG (NIL T T) -9 NIL 1075168) (-458 1074152 1074225 1074388 "GRALG-" 1074393 NIL GRALG- (NIL T T T) -8 NIL NIL) (-457 1070956 1073737 1073915 "GPOLSET" 1074059 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-456 1070310 1070367 1070625 "GOSPER" 1070893 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-455 1066069 1066748 1067274 "GMODPOL" 1070009 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-454 1065074 1065258 1065496 "GHENSEL" 1065881 NIL GHENSEL (NIL T T) -7 NIL NIL) (-453 1059125 1059968 1060995 "GENUPS" 1064158 NIL GENUPS (NIL T T) -7 NIL NIL) (-452 1058822 1058873 1058962 "GENUFACT" 1059068 NIL GENUFACT (NIL T) -7 NIL NIL) (-451 1058234 1058311 1058476 "GENPGCD" 1058740 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-450 1057708 1057743 1057956 "GENMFACT" 1058193 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-449 1056276 1056531 1056838 "GENEEZ" 1057451 NIL GENEEZ (NIL T T) -7 NIL NIL) (-448 1050189 1055887 1056049 "GDMP" 1056199 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-447 1039566 1043960 1045066 "GCNAALG" 1049172 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-446 1038028 1038856 1038884 "GCDDOM" 1039139 T GCDDOM (NIL) -9 NIL 1039296) (-445 1037498 1037625 1037840 "GCDDOM-" 1037845 NIL GCDDOM- (NIL T) -8 NIL NIL) (-444 1036170 1036355 1036659 "GB" 1037277 NIL GB (NIL T T T T) -7 NIL NIL) (-443 1024790 1027116 1029508 "GBINTERN" 1033861 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-442 1022627 1022919 1023340 "GBF" 1024465 NIL GBF (NIL T T T T) -7 NIL NIL) (-441 1021408 1021573 1021840 "GBEUCLID" 1022443 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-440 1020757 1020882 1021031 "GAUSSFAC" 1021279 T GAUSSFAC (NIL) -7 NIL NIL) (-439 1019124 1019426 1019740 "GALUTIL" 1020476 NIL GALUTIL (NIL T) -7 NIL NIL) (-438 1017432 1017706 1018030 "GALPOLYU" 1018851 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-437 1014797 1015087 1015494 "GALFACTU" 1017129 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-436 1006603 1008102 1009710 "GALFACT" 1013229 NIL GALFACT (NIL T) -7 NIL NIL) (-435 1003991 1004649 1004677 "FVFUN" 1005833 T FVFUN (NIL) -9 NIL 1006553) (-434 1003257 1003439 1003467 "FVC" 1003758 T FVC (NIL) -9 NIL 1003941) (-433 1002899 1003054 1003135 "FUNCTION" 1003209 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-432 1000569 1001120 1001609 "FT" 1002430 T FT (NIL) -8 NIL NIL) (-431 999387 999870 1000073 "FTEM" 1000386 T FTEM (NIL) -8 NIL NIL) (-430 997643 997932 998336 "FSUPFACT" 999078 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-429 996040 996329 996661 "FST" 997331 T FST (NIL) -8 NIL NIL) (-428 995211 995317 995512 "FSRED" 995922 NIL FSRED (NIL T T) -7 NIL NIL) (-427 993890 994145 994499 "FSPRMELT" 994926 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-426 990975 991413 991912 "FSPECF" 993453 NIL FSPECF (NIL T T) -7 NIL NIL) (-425 973417 981859 981899 "FS" 985747 NIL FS (NIL T) -9 NIL 988036) (-424 962067 965057 969113 "FS-" 969410 NIL FS- (NIL T T) -8 NIL NIL) (-423 961581 961635 961812 "FSINT" 962008 NIL FSINT (NIL T T) -7 NIL NIL) (-422 959908 960574 960877 "FSERIES" 961360 NIL FSERIES (NIL T T) -8 NIL NIL) (-421 958922 959038 959269 "FSCINT" 959788 NIL FSCINT (NIL T T) -7 NIL NIL) (-420 955156 957866 957907 "FSAGG" 958277 NIL FSAGG (NIL T) -9 NIL 958536) (-419 952918 953519 954315 "FSAGG-" 954410 NIL FSAGG- (NIL T T) -8 NIL NIL) (-418 951960 952103 952330 "FSAGG2" 952771 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-417 949615 949894 950448 "FS2UPS" 951678 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-416 949197 949240 949395 "FS2" 949566 NIL FS2 (NIL T T T T) -7 NIL NIL) (-415 948054 948225 948534 "FS2EXPXP" 949022 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-414 947480 947595 947747 "FRUTIL" 947934 NIL FRUTIL (NIL T) -7 NIL NIL) (-413 938941 942979 944335 "FR" 946156 NIL FR (NIL T) -8 NIL NIL) (-412 934016 936659 936699 "FRNAALG" 938095 NIL FRNAALG (NIL T) -9 NIL 938702) (-411 929694 930765 932040 "FRNAALG-" 932790 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-410 929332 929375 929502 "FRNAAF2" 929645 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-409 927739 928186 928481 "FRMOD" 929144 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-408 925518 926122 926439 "FRIDEAL" 927530 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-407 924713 924800 925089 "FRIDEAL2" 925425 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-406 923955 924369 924410 "FRETRCT" 924415 NIL FRETRCT (NIL T) -9 NIL 924591) (-405 923067 923298 923649 "FRETRCT-" 923654 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-404 920317 921493 921552 "FRAMALG" 922434 NIL FRAMALG (NIL T T) -9 NIL 922726) (-403 918451 918906 919536 "FRAMALG-" 919759 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-402 912411 917926 918202 "FRAC" 918207 NIL FRAC (NIL T) -8 NIL NIL) (-401 912047 912104 912211 "FRAC2" 912348 NIL FRAC2 (NIL T T) -7 NIL NIL) (-400 911683 911740 911847 "FR2" 911984 NIL FR2 (NIL T T) -7 NIL NIL) (-399 906413 909261 909289 "FPS" 910408 T FPS (NIL) -9 NIL 910965) (-398 905862 905971 906135 "FPS-" 906281 NIL FPS- (NIL T) -8 NIL NIL) (-397 903368 905003 905031 "FPC" 905256 T FPC (NIL) -9 NIL 905398) (-396 903161 903201 903298 "FPC-" 903303 NIL FPC- (NIL T) -8 NIL NIL) (-395 902039 902649 902690 "FPATMAB" 902695 NIL FPATMAB (NIL T) -9 NIL 902847) (-394 899739 900215 900641 "FPARFRAC" 901676 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-393 895132 895631 896313 "FORTRAN" 899171 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-392 892848 893348 893887 "FORT" 894613 T FORT (NIL) -7 NIL NIL) (-391 890524 891086 891114 "FORTFN" 892174 T FORTFN (NIL) -9 NIL 892798) (-390 890288 890338 890366 "FORTCAT" 890425 T FORTCAT (NIL) -9 NIL 890487) (-389 888348 888831 889230 "FORMULA" 889909 T FORMULA (NIL) -8 NIL NIL) (-388 888136 888166 888235 "FORMULA1" 888312 NIL FORMULA1 (NIL T) -7 NIL NIL) (-387 887659 887711 887884 "FORDER" 888078 NIL FORDER (NIL T T T T) -7 NIL NIL) (-386 886755 886919 887112 "FOP" 887486 T FOP (NIL) -7 NIL NIL) (-385 885363 886035 886209 "FNLA" 886637 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-384 884031 884420 884448 "FNCAT" 885020 T FNCAT (NIL) -9 NIL 885313) (-383 883597 883990 884018 "FNAME" 884023 T FNAME (NIL) -8 NIL NIL) (-382 882295 883224 883252 "FMTC" 883257 T FMTC (NIL) -9 NIL 883293) (-381 878657 879818 880447 "FMONOID" 881699 NIL FMONOID (NIL T) -8 NIL NIL) (-380 877876 878399 878548 "FM" 878553 NIL FM (NIL T T) -8 NIL NIL) (-379 875300 875946 875974 "FMFUN" 877118 T FMFUN (NIL) -9 NIL 877826) (-378 874569 874750 874778 "FMC" 875068 T FMC (NIL) -9 NIL 875250) (-377 871781 872615 872669 "FMCAT" 873864 NIL FMCAT (NIL T T) -9 NIL 874359) (-376 870674 871547 871647 "FM1" 871726 NIL FM1 (NIL T T) -8 NIL NIL) (-375 868448 868864 869358 "FLOATRP" 870225 NIL FLOATRP (NIL T) -7 NIL NIL) (-374 861999 866104 866734 "FLOAT" 867838 T FLOAT (NIL) -8 NIL NIL) (-373 859437 859937 860515 "FLOATCP" 861466 NIL FLOATCP (NIL T) -7 NIL NIL) (-372 858266 859070 859111 "FLINEXP" 859116 NIL FLINEXP (NIL T) -9 NIL 859209) (-371 857420 857655 857983 "FLINEXP-" 857988 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-370 856496 856640 856864 "FLASORT" 857272 NIL FLASORT (NIL T T) -7 NIL NIL) (-369 853713 854555 854607 "FLALG" 855834 NIL FLALG (NIL T T) -9 NIL 856301) (-368 847497 851199 851240 "FLAGG" 852502 NIL FLAGG (NIL T) -9 NIL 853154) (-367 846223 846562 847052 "FLAGG-" 847057 NIL FLAGG- (NIL T T) -8 NIL NIL) (-366 845265 845408 845635 "FLAGG2" 846076 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-365 842278 843252 843311 "FINRALG" 844439 NIL FINRALG (NIL T T) -9 NIL 844947) (-364 841438 841667 842006 "FINRALG-" 842011 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-363 840844 841057 841085 "FINITE" 841281 T FINITE (NIL) -9 NIL 841388) (-362 833302 835463 835503 "FINAALG" 839170 NIL FINAALG (NIL T) -9 NIL 840623) (-361 828643 829684 830828 "FINAALG-" 832207 NIL FINAALG- (NIL T T) -8 NIL NIL) (-360 828038 828398 828501 "FILE" 828573 NIL FILE (NIL T) -8 NIL NIL) (-359 826722 827034 827088 "FILECAT" 827772 NIL FILECAT (NIL T T) -9 NIL 827988) (-358 824642 826136 826164 "FIELD" 826204 T FIELD (NIL) -9 NIL 826284) (-357 823262 823647 824158 "FIELD-" 824163 NIL FIELD- (NIL T) -8 NIL NIL) (-356 821140 821897 822244 "FGROUP" 822948 NIL FGROUP (NIL T) -8 NIL NIL) (-355 820230 820394 820614 "FGLMICPK" 820972 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-354 816097 820155 820212 "FFX" 820217 NIL FFX (NIL T NIL) -8 NIL NIL) (-353 815698 815759 815894 "FFSLPE" 816030 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-352 811691 812470 813266 "FFPOLY" 814934 NIL FFPOLY (NIL T) -7 NIL NIL) (-351 811195 811231 811440 "FFPOLY2" 811649 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-350 807081 811114 811177 "FFP" 811182 NIL FFP (NIL T NIL) -8 NIL NIL) (-349 802514 806992 807056 "FF" 807061 NIL FF (NIL NIL NIL) -8 NIL NIL) (-348 797675 801857 802047 "FFNBX" 802368 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-347 792649 796810 797068 "FFNBP" 797529 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-346 787317 791933 792144 "FFNB" 792482 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-345 786149 786347 786662 "FFINTBAS" 787114 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-344 782433 784608 784636 "FFIELDC" 785256 T FFIELDC (NIL) -9 NIL 785632) (-343 781096 781466 781963 "FFIELDC-" 781968 NIL FFIELDC- (NIL T) -8 NIL NIL) (-342 780666 780711 780835 "FFHOM" 781038 NIL FFHOM (NIL T T T) -7 NIL NIL) (-341 778364 778848 779365 "FFF" 780181 NIL FFF (NIL T) -7 NIL NIL) (-340 774017 778106 778207 "FFCGX" 778307 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-339 769684 773749 773856 "FFCGP" 773960 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-338 764902 769411 769519 "FFCG" 769620 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-337 746960 755996 756082 "FFCAT" 761247 NIL FFCAT (NIL T T T) -9 NIL 762698) (-336 742158 743205 744519 "FFCAT-" 745749 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-335 741569 741612 741847 "FFCAT2" 742109 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-334 730781 734541 735761 "FEXPR" 740421 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-333 729781 730216 730257 "FEVALAB" 730341 NIL FEVALAB (NIL T) -9 NIL 730602) (-332 728940 729150 729488 "FEVALAB-" 729493 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-331 727533 728323 728526 "FDIV" 728839 NIL FDIV (NIL T T T T) -8 NIL NIL) (-330 724599 725314 725429 "FDIVCAT" 726997 NIL FDIVCAT (NIL T T T T) -9 NIL 727434) (-329 724361 724388 724558 "FDIVCAT-" 724563 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-328 723581 723668 723945 "FDIV2" 724268 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-327 722267 722526 722815 "FCPAK1" 723312 T FCPAK1 (NIL) -7 NIL NIL) (-326 721395 721767 721908 "FCOMP" 722158 NIL FCOMP (NIL T) -8 NIL NIL) (-325 705030 708444 712005 "FC" 717854 T FC (NIL) -8 NIL NIL) (-324 697683 701664 701704 "FAXF" 703506 NIL FAXF (NIL T) -9 NIL 704198) (-323 694962 695617 696442 "FAXF-" 696907 NIL FAXF- (NIL T T) -8 NIL NIL) (-322 690062 694338 694514 "FARRAY" 694819 NIL FARRAY (NIL T) -8 NIL NIL) (-321 685469 687501 687554 "FAMR" 688577 NIL FAMR (NIL T T) -9 NIL 689037) (-320 684359 684661 685096 "FAMR-" 685101 NIL FAMR- (NIL T T T) -8 NIL NIL) (-319 683555 684281 684334 "FAMONOID" 684339 NIL FAMONOID (NIL T) -8 NIL NIL) (-318 681385 682069 682122 "FAMONC" 683063 NIL FAMONC (NIL T T) -9 NIL 683449) (-317 680077 681139 681276 "FAGROUP" 681281 NIL FAGROUP (NIL T) -8 NIL NIL) (-316 677872 678191 678594 "FACUTIL" 679758 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-315 676971 677156 677378 "FACTFUNC" 677682 NIL FACTFUNC (NIL T) -7 NIL NIL) (-314 669376 676222 676434 "EXPUPXS" 676827 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-313 666859 667399 667985 "EXPRTUBE" 668810 T EXPRTUBE (NIL) -7 NIL NIL) (-312 663053 663645 664382 "EXPRODE" 666198 NIL EXPRODE (NIL T T) -7 NIL NIL) (-311 648427 661708 662136 "EXPR" 662657 NIL EXPR (NIL T) -8 NIL NIL) (-310 642834 643421 644234 "EXPR2UPS" 647725 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-309 642470 642527 642634 "EXPR2" 642771 NIL EXPR2 (NIL T T) -7 NIL NIL) (-308 633877 641602 641899 "EXPEXPAN" 642307 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-307 633704 633834 633863 "EXIT" 633868 T EXIT (NIL) -8 NIL NIL) (-306 633211 633428 633519 "EXITAST" 633633 T EXITAST (NIL) -8 NIL NIL) (-305 632838 632900 633013 "EVALCYC" 633143 NIL EVALCYC (NIL T) -7 NIL NIL) (-304 632379 632497 632538 "EVALAB" 632708 NIL EVALAB (NIL T) -9 NIL 632812) (-303 631860 631982 632203 "EVALAB-" 632208 NIL EVALAB- (NIL T T) -8 NIL NIL) (-302 629363 630631 630659 "EUCDOM" 631214 T EUCDOM (NIL) -9 NIL 631564) (-301 627768 628210 628800 "EUCDOM-" 628805 NIL EUCDOM- (NIL T) -8 NIL NIL) (-300 615308 618066 620816 "ESTOOLS" 625038 T ESTOOLS (NIL) -7 NIL NIL) (-299 614940 614997 615106 "ESTOOLS2" 615245 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-298 614691 614733 614813 "ESTOOLS1" 614892 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-297 608616 610344 610372 "ES" 613140 T ES (NIL) -9 NIL 614549) (-296 603563 604850 606667 "ES-" 606831 NIL ES- (NIL T) -8 NIL NIL) (-295 599938 600698 601478 "ESCONT" 602803 T ESCONT (NIL) -7 NIL NIL) (-294 599683 599715 599797 "ESCONT1" 599900 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-293 599358 599408 599508 "ES2" 599627 NIL ES2 (NIL T T) -7 NIL NIL) (-292 598988 599046 599155 "ES1" 599294 NIL ES1 (NIL T T) -7 NIL NIL) (-291 598204 598333 598509 "ERROR" 598832 T ERROR (NIL) -7 NIL NIL) (-290 591707 598063 598154 "EQTBL" 598159 NIL EQTBL (NIL T T) -8 NIL NIL) (-289 584264 587021 588470 "EQ" 590291 NIL -3839 (NIL T) -8 NIL NIL) (-288 583896 583953 584062 "EQ2" 584201 NIL EQ2 (NIL T T) -7 NIL NIL) (-287 579188 580234 581327 "EP" 582835 NIL EP (NIL T) -7 NIL NIL) (-286 577770 578071 578388 "ENV" 578891 T ENV (NIL) -8 NIL NIL) (-285 576969 577489 577517 "ENTIRER" 577522 T ENTIRER (NIL) -9 NIL 577568) (-284 573471 574924 575294 "EMR" 576768 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-283 572615 572800 572854 "ELTAGG" 573234 NIL ELTAGG (NIL T T) -9 NIL 573445) (-282 572334 572396 572537 "ELTAGG-" 572542 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-281 572123 572152 572206 "ELTAB" 572290 NIL ELTAB (NIL T T) -9 NIL NIL) (-280 571249 571395 571594 "ELFUTS" 571974 NIL ELFUTS (NIL T T) -7 NIL NIL) (-279 570991 571047 571075 "ELEMFUN" 571180 T ELEMFUN (NIL) -9 NIL NIL) (-278 570861 570882 570950 "ELEMFUN-" 570955 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-277 565752 568961 569002 "ELAGG" 569942 NIL ELAGG (NIL T) -9 NIL 570405) (-276 564037 564471 565134 "ELAGG-" 565139 NIL ELAGG- (NIL T T) -8 NIL NIL) (-275 562694 562974 563269 "ELABEXPR" 563762 T ELABEXPR (NIL) -8 NIL NIL) (-274 555560 557361 558188 "EFUPXS" 561970 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-273 549010 550811 551621 "EFULS" 554836 NIL EFULS (NIL T T T) -8 NIL NIL) (-272 546432 546790 547269 "EFSTRUC" 548642 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-271 535504 537069 538629 "EF" 544947 NIL EF (NIL T T) -7 NIL NIL) (-270 534605 534989 535138 "EAB" 535375 T EAB (NIL) -8 NIL NIL) (-269 533814 534564 534592 "E04UCFA" 534597 T E04UCFA (NIL) -8 NIL NIL) (-268 533023 533773 533801 "E04NAFA" 533806 T E04NAFA (NIL) -8 NIL NIL) (-267 532232 532982 533010 "E04MBFA" 533015 T E04MBFA (NIL) -8 NIL NIL) (-266 531441 532191 532219 "E04JAFA" 532224 T E04JAFA (NIL) -8 NIL NIL) (-265 530652 531400 531428 "E04GCFA" 531433 T E04GCFA (NIL) -8 NIL NIL) (-264 529863 530611 530639 "E04FDFA" 530644 T E04FDFA (NIL) -8 NIL NIL) (-263 529072 529822 529850 "E04DGFA" 529855 T E04DGFA (NIL) -8 NIL NIL) (-262 523250 524597 525961 "E04AGNT" 527728 T E04AGNT (NIL) -7 NIL NIL) (-261 521974 522454 522494 "DVARCAT" 522969 NIL DVARCAT (NIL T) -9 NIL 523168) (-260 521178 521390 521704 "DVARCAT-" 521709 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-259 514078 520977 521106 "DSMP" 521111 NIL DSMP (NIL T T T) -8 NIL NIL) (-258 508888 510023 511091 "DROPT" 513030 T DROPT (NIL) -8 NIL NIL) (-257 508553 508612 508710 "DROPT1" 508823 NIL DROPT1 (NIL T) -7 NIL NIL) (-256 503668 504794 505931 "DROPT0" 507436 T DROPT0 (NIL) -7 NIL NIL) (-255 502013 502338 502724 "DRAWPT" 503302 T DRAWPT (NIL) -7 NIL NIL) (-254 496600 497523 498602 "DRAW" 500987 NIL DRAW (NIL T) -7 NIL NIL) (-253 496233 496286 496404 "DRAWHACK" 496541 NIL DRAWHACK (NIL T) -7 NIL NIL) (-252 494964 495233 495524 "DRAWCX" 495962 T DRAWCX (NIL) -7 NIL NIL) (-251 494480 494548 494699 "DRAWCURV" 494890 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-250 484951 486910 489025 "DRAWCFUN" 492385 T DRAWCFUN (NIL) -7 NIL NIL) (-249 481764 483646 483687 "DQAGG" 484316 NIL DQAGG (NIL T) -9 NIL 484589) (-248 470283 476980 477063 "DPOLCAT" 478915 NIL DPOLCAT (NIL T T T T) -9 NIL 479460) (-247 465122 466468 468426 "DPOLCAT-" 468431 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-246 458277 464983 465081 "DPMO" 465086 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-245 451335 458057 458224 "DPMM" 458229 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-244 450755 450958 451072 "DOMAIN" 451241 T DOMAIN (NIL) -8 NIL NIL) (-243 444506 450390 450542 "DMP" 450656 NIL DMP (NIL NIL T) -8 NIL NIL) (-242 444106 444162 444306 "DLP" 444444 NIL DLP (NIL T) -7 NIL NIL) (-241 437750 443207 443434 "DLIST" 443911 NIL DLIST (NIL T) -8 NIL NIL) (-240 434596 436605 436646 "DLAGG" 437196 NIL DLAGG (NIL T) -9 NIL 437425) (-239 433446 434076 434104 "DIVRING" 434196 T DIVRING (NIL) -9 NIL 434279) (-238 432683 432873 433173 "DIVRING-" 433178 NIL DIVRING- (NIL T) -8 NIL NIL) (-237 430785 431142 431548 "DISPLAY" 432297 T DISPLAY (NIL) -7 NIL NIL) (-236 424727 430699 430762 "DIRPROD" 430767 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-235 423575 423778 424043 "DIRPROD2" 424520 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-234 413113 419065 419118 "DIRPCAT" 419528 NIL DIRPCAT (NIL NIL T) -9 NIL 420368) (-233 410439 411081 411962 "DIRPCAT-" 412299 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-232 409726 409886 410072 "DIOSP" 410273 T DIOSP (NIL) -7 NIL NIL) (-231 406428 408638 408679 "DIOPS" 409113 NIL DIOPS (NIL T) -9 NIL 409342) (-230 405977 406091 406282 "DIOPS-" 406287 NIL DIOPS- (NIL T T) -8 NIL NIL) (-229 404889 405483 405511 "DIFRING" 405698 T DIFRING (NIL) -9 NIL 405808) (-228 404535 404612 404764 "DIFRING-" 404769 NIL DIFRING- (NIL T) -8 NIL NIL) (-227 402360 403598 403639 "DIFEXT" 404002 NIL DIFEXT (NIL T) -9 NIL 404296) (-226 400645 401073 401739 "DIFEXT-" 401744 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-225 397967 400177 400218 "DIAGG" 400223 NIL DIAGG (NIL T) -9 NIL 400243) (-224 397351 397508 397760 "DIAGG-" 397765 NIL DIAGG- (NIL T T) -8 NIL NIL) (-223 392816 396310 396587 "DHMATRIX" 397120 NIL DHMATRIX (NIL T) -8 NIL NIL) (-222 388428 389337 390347 "DFSFUN" 391826 T DFSFUN (NIL) -7 NIL NIL) (-221 383544 387359 387671 "DFLOAT" 388136 T DFLOAT (NIL) -8 NIL NIL) (-220 381772 382053 382449 "DFINTTLS" 383252 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-219 378837 379793 380193 "DERHAM" 381438 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-218 376686 378612 378701 "DEQUEUE" 378781 NIL DEQUEUE (NIL T) -8 NIL NIL) (-217 375901 376034 376230 "DEGRED" 376548 NIL DEGRED (NIL T T) -7 NIL NIL) (-216 372296 373041 373894 "DEFINTRF" 375129 NIL DEFINTRF (NIL T) -7 NIL NIL) (-215 369823 370292 370891 "DEFINTEF" 371815 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-214 369200 369443 369558 "DEFAST" 369728 T DEFAST (NIL) -8 NIL NIL) (-213 363088 368641 368807 "DECIMAL" 369054 T DECIMAL (NIL) -8 NIL NIL) (-212 360600 361058 361564 "DDFACT" 362632 NIL DDFACT (NIL T T) -7 NIL NIL) (-211 360196 360239 360390 "DBLRESP" 360551 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-210 357906 358240 358609 "DBASE" 359954 NIL DBASE (NIL T) -8 NIL NIL) (-209 357175 357386 357532 "DATABUF" 357805 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-208 356308 357134 357162 "D03FAFA" 357167 T D03FAFA (NIL) -8 NIL NIL) (-207 355442 356267 356295 "D03EEFA" 356300 T D03EEFA (NIL) -8 NIL NIL) (-206 353392 353858 354347 "D03AGNT" 354973 T D03AGNT (NIL) -7 NIL NIL) (-205 352708 353351 353379 "D02EJFA" 353384 T D02EJFA (NIL) -8 NIL NIL) (-204 352024 352667 352695 "D02CJFA" 352700 T D02CJFA (NIL) -8 NIL NIL) (-203 351340 351983 352011 "D02BHFA" 352016 T D02BHFA (NIL) -8 NIL NIL) (-202 350656 351299 351327 "D02BBFA" 351332 T D02BBFA (NIL) -8 NIL NIL) (-201 343854 345442 347048 "D02AGNT" 349070 T D02AGNT (NIL) -7 NIL NIL) (-200 341623 342145 342691 "D01WGTS" 343328 T D01WGTS (NIL) -7 NIL NIL) (-199 340718 341582 341610 "D01TRNS" 341615 T D01TRNS (NIL) -8 NIL NIL) (-198 339813 340677 340705 "D01GBFA" 340710 T D01GBFA (NIL) -8 NIL NIL) (-197 338908 339772 339800 "D01FCFA" 339805 T D01FCFA (NIL) -8 NIL NIL) (-196 338003 338867 338895 "D01ASFA" 338900 T D01ASFA (NIL) -8 NIL NIL) (-195 337098 337962 337990 "D01AQFA" 337995 T D01AQFA (NIL) -8 NIL NIL) (-194 336193 337057 337085 "D01APFA" 337090 T D01APFA (NIL) -8 NIL NIL) (-193 335288 336152 336180 "D01ANFA" 336185 T D01ANFA (NIL) -8 NIL NIL) (-192 334383 335247 335275 "D01AMFA" 335280 T D01AMFA (NIL) -8 NIL NIL) (-191 333478 334342 334370 "D01ALFA" 334375 T D01ALFA (NIL) -8 NIL NIL) (-190 332573 333437 333465 "D01AKFA" 333470 T D01AKFA (NIL) -8 NIL NIL) (-189 331668 332532 332560 "D01AJFA" 332565 T D01AJFA (NIL) -8 NIL NIL) (-188 324965 326516 328077 "D01AGNT" 330127 T D01AGNT (NIL) -7 NIL NIL) (-187 324302 324430 324582 "CYCLOTOM" 324833 T CYCLOTOM (NIL) -7 NIL NIL) (-186 321037 321750 322477 "CYCLES" 323595 T CYCLES (NIL) -7 NIL NIL) (-185 320349 320483 320654 "CVMP" 320898 NIL CVMP (NIL T) -7 NIL NIL) (-184 318120 318378 318754 "CTRIGMNP" 320077 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-183 317537 317743 317857 "CTOR" 318026 T CTOR (NIL) -8 NIL NIL) (-182 317073 317268 317369 "CTORKIND" 317456 T CTORKIND (NIL) -8 NIL NIL) (-181 316584 316773 316872 "CTORCALL" 316994 T CTORCALL (NIL) -8 NIL NIL) (-180 315958 316057 316210 "CSTTOOLS" 316481 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 311757 312414 313172 "CRFP" 315270 NIL CRFP (NIL T T) -7 NIL NIL) (-178 311259 311478 311570 "CRCEAST" 311685 T CRCEAST (NIL) -8 NIL NIL) (-177 310306 310491 310719 "CRAPACK" 311063 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 309690 309791 309995 "CPMATCH" 310182 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 309415 309443 309549 "CPIMA" 309656 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 305779 306451 307169 "COORDSYS" 308750 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 305163 305292 305442 "CONTOUR" 305649 T CONTOUR (NIL) -8 NIL NIL) (-172 301089 303166 303658 "CONTFRAC" 304703 NIL CONTFRAC (NIL T) -8 NIL NIL) (-171 300969 300990 301018 "CONDUIT" 301055 T CONDUIT (NIL) -9 NIL NIL) (-170 300162 300682 300710 "COMRING" 300715 T COMRING (NIL) -9 NIL 300767) (-169 299243 299520 299704 "COMPPROP" 299998 T COMPPROP (NIL) -8 NIL NIL) (-168 298904 298939 299067 "COMPLPAT" 299202 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 288963 298713 298822 "COMPLEX" 298827 NIL COMPLEX (NIL T) -8 NIL NIL) (-166 288599 288656 288763 "COMPLEX2" 288900 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-165 288317 288352 288450 "COMPFACT" 288558 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 272715 282931 282971 "COMPCAT" 283975 NIL COMPCAT (NIL T) -9 NIL 285370) (-163 262230 265154 268781 "COMPCAT-" 269137 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 261959 261987 262090 "COMMUPC" 262196 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 261754 261787 261846 "COMMONOP" 261920 T COMMONOP (NIL) -7 NIL NIL) (-160 261337 261505 261592 "COMM" 261687 T COMM (NIL) -8 NIL NIL) (-159 260941 261141 261216 "COMMAAST" 261282 T COMMAAST (NIL) -8 NIL NIL) (-158 260190 260384 260412 "COMBOPC" 260750 T COMBOPC (NIL) -9 NIL 260925) (-157 259086 259296 259538 "COMBINAT" 259980 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 255284 255857 256497 "COMBF" 258508 NIL COMBF (NIL T T) -7 NIL NIL) (-155 254070 254400 254635 "COLOR" 255069 T COLOR (NIL) -8 NIL NIL) (-154 253573 253791 253883 "COLONAST" 253998 T COLONAST (NIL) -8 NIL NIL) (-153 253213 253260 253385 "CMPLXRT" 253520 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 252688 252913 253012 "CLLCTAST" 253134 T CLLCTAST (NIL) -8 NIL NIL) (-151 248190 249218 250298 "CLIP" 251628 T CLIP (NIL) -7 NIL NIL) (-150 246572 247296 247535 "CLIF" 248017 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242794 244718 244759 "CLAGG" 245688 NIL CLAGG (NIL T) -9 NIL 246224) (-148 241216 241673 242256 "CLAGG-" 242261 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240760 240845 240985 "CINTSLPE" 241125 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 238261 238732 239280 "CHVAR" 240288 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 237524 238044 238072 "CHARZ" 238077 T CHARZ (NIL) -9 NIL 238092) (-144 237278 237318 237396 "CHARPOL" 237478 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 236425 236978 237006 "CHARNZ" 237053 T CHARNZ (NIL) -9 NIL 237109) (-142 234450 235115 235450 "CHAR" 236110 T CHAR (NIL) -8 NIL NIL) (-141 234176 234237 234265 "CFCAT" 234376 T CFCAT (NIL) -9 NIL NIL) (-140 233421 233532 233714 "CDEN" 234060 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 229413 232574 232854 "CCLASS" 233161 T CCLASS (NIL) -8 NIL NIL) (-138 229332 229358 229393 "CATEGORY" 229398 T -10 (NIL) -8 NIL NIL) (-137 228806 229032 229131 "CATAST" 229253 T CATAST (NIL) -8 NIL NIL) (-136 228309 228527 228619 "CASEAST" 228734 T CASEAST (NIL) -8 NIL NIL) (-135 223361 224338 225091 "CARTEN" 227612 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-134 222469 222617 222838 "CARTEN2" 223208 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-133 220811 221619 221876 "CARD" 222232 T CARD (NIL) -8 NIL NIL) (-132 220414 220615 220690 "CAPSLAST" 220756 T CAPSLAST (NIL) -8 NIL NIL) (-131 219786 220114 220142 "CACHSET" 220274 T CACHSET (NIL) -9 NIL 220351) (-130 219282 219578 219606 "CABMON" 219656 T CABMON (NIL) -9 NIL 219712) (-129 218209 218637 218833 "BYTE" 219106 T BYTE (NIL) -8 NIL NIL) (-128 214157 218156 218190 "BYTEARY" 218195 T BYTEARY (NIL) -8 NIL NIL) (-127 211714 213849 213956 "BTREE" 214083 NIL BTREE (NIL T) -8 NIL NIL) (-126 209212 211362 211484 "BTOURN" 211624 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206630 208683 208724 "BTCAT" 208792 NIL BTCAT (NIL T) -9 NIL 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7972) (-4284 . 7825) + (-4285 . 7768) (-4286 . 7551) (-4287 . 7399) (-4288 . 7328) + (-4289 . 7231) (-4290 . 7176) (-4291 . 6957) (-4292 . 6834) + (-4293 . 6676) (-4294 . 6513) (-4295 . 6431) (-4296 . 6214) + (-4297 . 6026) (-4298 . 5883) (-4299 . 5782) (-4300 . 5727) + (-4301 . 5508) (-4302 . 5409) (-4303 . 5251) (-4304 . 5172) + (-4305 . 5100) (-4306 . 4841) (-4307 . 4534) (-4308 . 4437) + (-4309 . 4359) (-4310 . 4140) (-4311 . 3991) (-4312 . 3833) + (-4313 . 3751) (-4314 . 3674) (-4315 . 3240) (-4316 . 3067) + (-4317 . 2955) (-4318 . 2811) (-4319 . 2734) (-4320 . 2515) + (-4321 . 2416) (-4322 . 2258) (-4323 . 2099) (-4324 . 2022) + (-4325 . 1468) (-4326 . 1295) (-4327 . 1183) (-4328 . 912) + (-4329 . 835) (-4330 . 616) (-4331 . 461) (-4332 . 188) (-4333 . 30))
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