diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/ChangeLog | 7 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 714 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1124 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 4 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8214 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 5410 |
6 files changed, 7740 insertions, 7733 deletions
diff --git a/src/share/ChangeLog b/src/share/ChangeLog index 62b8f8fc..4b5d7c56 100644 --- a/src/share/ChangeLog +++ b/src/share/ChangeLog @@ -1,3 +1,10 @@ +2007-11-22 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/browse.daase: Update. + * algebra/category.daase: Likewise. + * algebra/compress.daase: Likewise. + * algebra/interp.daase: Likewise. + 2007-11-13 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/browse.daase: Update. diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 283ba313..b72c00da 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2205538 . 3404130410) +(2205538 . 3404712024) (-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."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -46,13 +46,13 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4180 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4176 . T) (-4181 . T) (-4175 . T) (-3252 . T)) +((-4180 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4176 . T) (-4181 . T) (-4175 . T) (-3371 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) NIL NIL -(-31 R -2184) +(-31 R -1709) ((|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 -952) (QUOTE (-517))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4183))) (-33) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-3252 . T)) +((-3371 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -84,11 +84,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-39 -2184 UP UPUP -3962) +(-39 -1709 UP UPUP -3668) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3763 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3763 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) -(-40 R -2184) +((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3782 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3782 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3782 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3782 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) +(-40 R -1709) ((|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 (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) @@ -107,7 +107,7 @@ NIL (-44 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (-3782 (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))))) (-45 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -2184) +(-53 |Base| R -1709) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-56 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -159,64 +159,64 @@ NIL (-57 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-58 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4183 . T) (-4184 . T)) ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) -(-59 -1211) +(-59 -1214) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -1211) +(-60 -1214) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -1211) +(-61 -1214) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -1211) +(-62 -1214) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -1211) +(-63 -1214) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -1211) +(-64 -1214) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -1211) +(-65 -1214) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -1211) +(-66 -1214) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -1211) +(-67 -1214) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -1211) +(-68 -1214) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-69 -1211) +(-69 -1214) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -1211) +(-70 -1214) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -1211) +(-71 -1214) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-72 -1211) +(-72 -1214) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -228,55 +228,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -1211) +(-75 -1214) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -1211) +(-76 -1214) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -1211) +(-77 -1214) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -1211) +(-78 -1214) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -1211) +(-79 -1214) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -1211) +(-80 -1214) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -1211) +(-81 -1214) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -1211) +(-82 -1214) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -1211) +(-83 -1214) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -1211) +(-84 -1214) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -1211) +(-85 -1214) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -1211) +(-86 -1214) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-87 -1211) +(-87 -1214) ((|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 @@ -338,12 +338,12 @@ NIL NIL (-102 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-103) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) +((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3782 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) (-104) ((|constructor| (NIL "This domain provides an implementation of binary files. Data is accessed one byte at a time as a small integer.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "\\spad{position!(f,{} i)} sets the current byte-position to \\spad{i}.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{f}.")) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL @@ -368,7 +368,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-110 -2184 UP) +(-110 -1709 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 @@ -379,14 +379,14 @@ NIL (-112 |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}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-111 |#1|) (QUOTE (-831))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-937))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1050))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3763 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) +((|HasCategory| (-111 |#1|) (QUOTE (-831))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-937))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1050))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3782 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) (-113 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4184))) (-114 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-3252 . T)) +((-3371 . T)) NIL (-115 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."))) @@ -402,7 +402,7 @@ NIL NIL (-118) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-119 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -410,7 +410,7 @@ NIL NIL (-120 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) @@ -432,18 +432,18 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4185 "*") . T)) NIL -(-126 |minix| -2630 S T$) +(-126 |minix| -2839 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-127 |minix| -2630 R) +(-127 |minix| -2839 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 (-128) ((|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}."))) ((-4183 . T) (-4173 . T) (-4184 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3782 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) (-129 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 @@ -468,7 +468,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4180 . T)) NIL -(-135 -2184 UP UPUP) +(-135 -1709 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 @@ -482,7 +482,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasAttribute| |#1| (QUOTE -4183))) (-138 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."))) -((-3252 . T)) +((-3371 . T)) NIL (-139 |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."))) @@ -500,7 +500,7 @@ 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 -(-143 R -2184) +(-143 R -1709) ((|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 @@ -530,7 +530,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-1095))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4179)) (|HasAttribute| |#2| (QUOTE -4182)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) (-150 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4176 -3763 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4179 |has| |#1| (-6 -4179)) (-4182 |has| |#1| (-6 -4182)) (-3295 . T) (-3252 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-4176 -3782 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4179 |has| |#1| (-6 -4179)) (-4182 |has| |#1| (-6 -4182)) (-3417 . T) (-3371 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-151 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."))) @@ -542,8 +542,8 @@ NIL NIL (-153 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4176 -3763 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4179 |has| |#1| (-6 -4179)) (-4182 |has| |#1| (-6 -4182)) (-3295 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . 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T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1095))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-1095)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE 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(|HasCategory| |#1| (QUOTE (-207))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-207))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1095)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4179)) (|HasAttribute| |#1| (QUOTE -4182)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-319))))) (-154 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 @@ -584,7 +584,7 @@ NIL ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) NIL NIL -(-164 R -2184) +(-164 R -1709) ((|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 @@ -688,19 +688,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-190 -2184 UP UPUP R) +(-190 -1709 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 -(-191 -2184 FP) +(-191 -1709 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 (-192) ((|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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) -(-193 R -2184) +((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3782 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) +(-193 R -1709) ((|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 @@ -720,13 +720,13 @@ NIL ((|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}."))) ((-4180 . T)) NIL -(-198 R -2184) +(-198 R -1709) ((|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 (-199) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3405 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-200) ((|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)}.}"))) @@ -742,7 +742,7 @@ NIL NIL (-203 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."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-204 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}."))) @@ -766,28 +766,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4183))) (-209 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}."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-210) ((|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 -(-211 S -2630 R) +(-211 S -2839 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 (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4180)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1003)))) -(-212 -2630 R) +(-212 -2839 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"))) -((-4177 |has| |#2| (-961)) (-4178 |has| |#2| (-961)) (-4180 |has| |#2| (-6 -4180)) ((-4185 "*") |has| |#2| (-156)) (-4183 . T) (-3252 . T)) +((-4177 |has| |#2| (-961)) (-4178 |has| |#2| (-961)) (-4180 |has| |#2| (-6 -4180)) ((-4185 "*") |has| |#2| (-156)) (-4183 . T) (-3371 . T)) NIL -(-213 -2630 A B) +(-213 -2839 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 -(-214 -2630 R) +(-214 -2839 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. 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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 @@ -802,12 +802,12 @@ NIL NIL (-218 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."))) -((-3252 . T)) +((-3371 . T)) NIL (-219 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) ((-4184 . T) (-4183 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -815,19 +815,19 @@ NIL (-221 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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|#3| (QUOTE -4180)) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3782 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074))))))) (-225 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 @@ -838,7 +838,7 @@ NIL NIL (-227 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}."))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-228) ((|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."))) @@ -879,7 +879,7 @@ NIL (-237 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"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-238 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 @@ -924,11 +924,11 @@ 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 -(-249 R -2184) +(-249 R -1709) ((|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 -(-250 R -2184) +(-250 R -1709) ((|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 @@ -946,7 +946,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003)))) (-254 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}."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-255 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}."))) @@ -972,7 +972,7 @@ 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 -(-261 S R |Mod| -1476 -2262 |exactQuo|) +(-261 S R |Mod| -2137 -1676 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL @@ -990,21 +990,21 @@ NIL NIL (-265 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) -((-4180 -3763 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4177 |has| |#1| (-961)) (-4178 |has| |#1| (-961))) -((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1015))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1003))))) +((-4180 -3782 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4177 |has| |#1| (-961)) (-4178 |has| |#1| (-961))) +((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3782 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3782 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1015))) (-3782 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-21))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3782 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1003))))) (-266 |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."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) (-267) ((|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 -(-268 -2184 S) +(-268 -1709 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 -(-269 E -2184) +(-269 E -1709) ((|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 @@ -1052,7 +1052,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-281 -2184) +(-281 -1709) ((|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 @@ -1063,7 +1063,7 @@ NIL (-283 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))}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-1050))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3763 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))) (-3763 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))))) +((|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-1050))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3782 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))) (-3782 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1141 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))))) (-284 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 @@ -1074,9 +1074,9 @@ NIL NIL (-286 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."))) -((-4180 -3763 (-1651 (|has| |#1| (-961)) (|has| |#1| (-579 (-517)))) (-12 (|has| |#1| (-509)) (-3763 (-1651 (|has| |#1| (-961)) (|has| |#1| (-579 (-517)))) (|has| |#1| (-961)) (|has| |#1| (-442)))) (|has| |#1| (-961)) (|has| |#1| (-442))) (-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4181 |has| 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-377) (QUOTE (-517))))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (LIST (QUOTE -952) (QUOTE (-517))))) +(-287 R -1709) ((|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 @@ -1087,7 +1087,7 @@ NIL (-289 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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-290 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 @@ -1119,12 +1119,12 @@ NIL (-297 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."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) -(-298 S -2184) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +(-298 S -1709) ((|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 (-338)))) -(-299 -2184) +(-299 -1709) ((|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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL @@ -1144,15 +1144,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-304 S -2184 UP UPUP R) +(-304 S -1709 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 -(-305 -2184 UP UPUP R) +(-305 -1709 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 -(-306 -2184 UP UPUP R) +(-306 -1709 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 @@ -1172,26 +1172,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-311 S -2184 UP UPUP) +(-311 S -1709 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-333)))) -(-312 -2184 UP UPUP) +(-312 -1709 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-313 |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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) +((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3782 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) (-314 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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-315 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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-316 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 @@ -1208,31 +1208,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL -(-320 R UP -2184) +(-320 R UP -1709) ((|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 (-321 |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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) +((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3782 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) (-322 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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-323 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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-324 |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}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) +((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3782 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) (-325 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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) -(-326 -2184 GF) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +(-326 -1709 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 @@ -1240,14 +1240,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-328 -2184 FP FPP) +(-328 -1709 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 (-329 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}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3782 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) (-330 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 @@ -1302,7 +1302,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003)))) (-343 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4183 . T) (-3252 . T)) +((-4183 . T) (-3371 . T)) NIL (-344 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1326,7 +1326,7 @@ NIL NIL (-349) ((|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}."))) -((-4166 . T) (-4174 . T) (-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-4166 . T) (-4174 . T) (-3405 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-350 |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}."))) @@ -1342,11 +1342,11 @@ NIL NIL (-353) ((|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}."))) -((-3252 . T)) +((-3371 . T)) NIL (-354) ((|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.}"))) -((-3252 . T)) +((-3371 . T)) NIL (-355 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."))) @@ -1376,7 +1376,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-362 -2184 UP UPUP R) +(-362 -1709 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 @@ -1390,27 +1390,27 @@ NIL NIL (-365) ((|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."))) -((-3252 . T)) +((-3371 . T)) NIL (-366) ((|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.}"))) -((-3252 . T)) +((-3371 . T)) NIL (-367) ((|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 -(-368 -1211 |returnType| |arguments| |symbols|) +(-368 -1214 |returnType| |arguments| |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 -(-369 -2184 UP) +(-369 -1709 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-370 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-3252 . T)) +((-3371 . T)) NIL (-371 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1426,7 +1426,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4166)) (|HasAttribute| |#1| (QUOTE -4174))) (-374) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3405 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-375 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."))) @@ -1439,7 +1439,7 @@ NIL (-377 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."))) ((-4170 -12 (|has| |#1| (-6 -4181)) (|has| |#1| (-421)) (|has| |#1| (-6 -4170))) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4181)) (|HasAttribute| |#1| (QUOTE -4170)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4181)) (|HasAttribute| |#1| (QUOTE -4170)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-378 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1460,11 +1460,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-383 R -2184 UP A) +(-383 R -1709 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4180 . T)) NIL -(-384 R -2184 UP A |ibasis|) +(-384 R -1709 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 -952) (|devaluate| |#2|)))) @@ -1483,7 +1483,7 @@ NIL (-388 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."))) ((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1113))))) +((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1113))))) (-389 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 @@ -1510,9 +1510,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) (-395 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4183 . T) (-4173 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4173 . T) (-4184 . T) (-3371 . T)) NIL -(-396 R -2184) +(-396 R -1709) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1520,7 +1520,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4170 -12 (|has| |#1| (-6 -4170)) (|has| |#2| (-6 -4170))) (-4177 . T) (-4178 . T) (-4180 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4170)) (|HasAttribute| |#2| (QUOTE -4170)))) -(-398 R -2184) +(-398 R -1709) ((|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 @@ -1530,17 +1530,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (-400 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}."))) -((-4180 -3763 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-509)) (-4175 |has| |#1| (-509)) (-3252 . T)) +((-4180 -3782 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-509)) (-4175 |has| |#1| (-509)) (-3371 . T)) NIL -(-401 R -2184) +(-401 R -1709) ((|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 -(-402 R -2184) +(-402 R -1709) ((|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)))) -(-403 R -2184) +(-403 R -1709) ((|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 @@ -1548,7 +1548,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-405 R -2184 UP) +(-405 R -1709 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 -952) (QUOTE (-47))))) @@ -1566,17 +1566,17 @@ NIL NIL (-409) ((|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}."))) -((-3252 . T)) +((-3371 . T)) NIL (-410) ((|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.}"))) -((-3252 . T)) +((-3371 . T)) NIL (-411 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 -(-412 R UP -2184) +(-412 R UP -1709) ((|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 @@ -1623,7 +1623,7 @@ NIL (-423 |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"))) (((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) +((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3782 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) (-424 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 @@ -1688,7 +1688,7 @@ 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 -(-440 |lv| -2184 R) +(-440 |lv| -1709 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 @@ -1703,11 +1703,11 @@ NIL (-443 |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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-444 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) (-445 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4184 . T) (-4183 . T)) @@ -1719,7 +1719,7 @@ NIL (-447 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) (-448) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1727,16 +1727,16 @@ NIL (-449 |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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . 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((-4183 . T) (-4184 . T)) ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) -(-452 -2184 UP UPUP R) +(-452 -1709 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 @@ -1747,14 +1747,14 @@ NIL (-454) ((|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.")) 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In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4183)) (|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) (-456 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-3252 . T)) +((-3371 . T)) NIL (-457 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1764,7 +1764,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-459 -2184 UP |AlExt| |AlPol|) +(-459 -1709 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 @@ -1775,7 +1775,7 @@ NIL (-461 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-462 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."))) ((-4183 . T) (-4184 . T)) @@ -1784,7 +1784,7 @@ NIL ((|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 -(-464 R UP -2184) +(-464 R UP -1709) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1804,7 +1804,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-469 -2184 |Expon| |VarSet| |DPoly|) +(-469 -1709 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-1074))))) @@ -1851,11 +1851,11 @@ NIL (-480 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-481 |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}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) +((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3782 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) (-482 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}."))) ((-4183 . T) (-4184 . T)) @@ -1863,7 +1863,7 @@ NIL (-483 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."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-484 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 @@ -1888,7 +1888,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-490 K -2184 |Par|) +(-490 K -1709 |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 @@ -1908,7 +1908,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-495 K -2184 |Par|) +(-495 K -1709 |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 @@ -1943,12 +1943,12 @@ NIL (-503 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) -(-504 R -2184) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) +(-504 R -1709) ((|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 -(-505 R0 -2184 UP UPUP R) +(-505 R0 -1709 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 @@ -1958,7 +1958,7 @@ NIL NIL (-507 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."))) -((-3284 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3405 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-508 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."))) @@ -1968,7 +1968,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL -(-510 R -2184) +(-510 R -1709) ((|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 @@ -1980,7 +1980,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-513 R -2184 L) +(-513 R -1709 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 -593) (|devaluate| |#2|)))) @@ -1988,11 +1988,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ^= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-515 -2184 UP UPUP R) +(-515 -1709 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 -(-516 -2184 UP) +(-516 -1709 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 @@ -2004,15 +2004,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-519 R -2184 L) +(-519 R -1709 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 -593) (|devaluate| |#2|)))) -(-520 R -2184) +(-520 R -1709) ((|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 -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1038)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) -(-521 -2184 UP) +(-521 -1709 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 @@ -2020,27 +2020,27 @@ 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 -(-523 -2184) +(-523 -1709) ((|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 (-524 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."))) -((-3284 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3405 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-525) ((|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 -(-526 R -2184) +(-526 R -1709) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) -(-527 -2184 UP) +(-527 -1709 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 -(-528 R -2184) +(-528 R -1709) ((|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 @@ -2056,15 +2056,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-532 R -2184) +(-532 R -1709) ((|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 -(-533 E -2184) +(-533 E -1709) ((|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 -(-534 -2184) +(-534 -1709) ((|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}."))) ((-4178 . T) (-4177 . T)) ((|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1074))))) @@ -2091,7 +2091,7 @@ NIL (-540 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4184 . T) (-4183 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-3763 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-3782 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3782 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3782 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) (-541 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 @@ -2099,7 +2099,7 @@ NIL (-542 |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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074))))))) (-543 |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.}"))) ((-4178 |has| |#1| (-509)) (-4177 |has| |#1| (-509)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4180 . T)) @@ -2112,7 +2112,7 @@ 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 -(-546 R -2184 FG) +(-546 R -1709 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 @@ -2123,30 +2123,30 @@ NIL (-548 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-549 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 -4184)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4183)) (|HasCategory| |#3| (QUOTE (-1003)))) (-550 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-3252 . T)) +((-3371 . T)) NIL (-551 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4180 -3763 (-1651 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) -((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) +((-4180 -3782 (-4032 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) +((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3782 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) (-552 |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."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#1|))))))) +((|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#1|))))))) (-553 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 (-554 |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}."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-555 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"))) @@ -2164,7 +2164,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-559 -2184 UP) +(-559 -1709 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2180,7 +2180,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4177 . T) (-4178 . T) (-4180 . T)) ((|HasCategory| |#1| (QUOTE (-777)))) -(-563 R -2184) +(-563 R -1709) ((|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 @@ -2208,18 +2208,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-570 R -2184) +(-570 R -1709) ((|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 -(-571 |lv| -2184) +(-571 |lv| -1709) ((|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 (-572) ((|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."))) ((-4184 . T)) -((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003))))) +((|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1338) (QUOTE (-51))))))) (-3782 (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003))))) (-573 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2230,8 +2230,8 @@ NIL NIL (-575 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4180 -3763 (-1651 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) -((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) +((-4180 -3782 (-4032 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) +((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3782 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) (-576 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2243,7 +2243,7 @@ NIL (-578 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 -((|HasCategory| |#1| (QUOTE (-333))) (-2455 (|HasCategory| |#1| (QUOTE (-333))))) +((|HasCategory| |#1| (QUOTE (-333))) (-2650 (|HasCategory| |#1| (QUOTE (-333))))) (-579 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4180 . T)) @@ -2263,7 +2263,7 @@ NIL (-583 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-584 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."))) ((-4183 . T) (-4184 . T)) @@ -2282,9 +2282,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4184))) (-588 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})}."))) -((-3252 . T)) +((-3371 . T)) NIL -(-589 R -2184 L) +(-589 R -1709 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 @@ -2304,11 +2304,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4177 . T) (-4178 . T) (-4180 . T)) NIL -(-594 -2184 UP) +(-594 -1709 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)))) -(-595 A -1328) +(-595 A -2994) ((|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}}"))) ((-4177 . T) (-4178 . T) (-4180 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) @@ -2342,13 +2342,13 @@ NIL NIL (-603 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}."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL -(-604 -2184) +(-604 -1709) ((|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 -(-605 -2184 |Row| |Col| M) +(-605 -1709 |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 @@ -2359,7 +2359,7 @@ NIL (-607 |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."))) ((-4180 . T) (-4183 . T) (-4177 . T) (-4178 . T)) -((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3763 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) +((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3782 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3782 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) (-608 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2370,12 +2370,12 @@ NIL NIL (-610 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-3252 . T)) +((-3371 . T)) NIL (-611 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 -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-612 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2414,7 +2414,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) (-621 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"))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-622 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."))) @@ -2423,12 +2423,12 @@ NIL (-623 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."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4185 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4185 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-624 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-625 S -2184 FLAF FLAS) +(-625 S -1709 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 @@ -2438,11 +2438,11 @@ NIL NIL (-627) ((|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"))) -((-4176 . T) (-4181 |has| (-632) (-333)) (-4175 |has| (-632) (-333)) (-3295 . T) (-4182 |has| (-632) (-6 -4182)) (-4179 |has| (-632) (-6 -4179)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3763 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-937))) (|HasCategory| (-632) (QUOTE (-1095))) (-12 (|HasCategory| (-632) (QUOTE (-918))) (|HasCategory| (-632) (QUOTE (-1095)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-970))) (-12 (|HasCategory| (-632) (QUOTE (-970))) (|HasCategory| (-632) (QUOTE (-1095)))) (-3763 (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3763 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-831))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4182)) (|HasAttribute| (-632) (QUOTE -4179)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-319))))) +((-4176 . T) (-4181 |has| (-632) (-333)) (-4175 |has| (-632) (-333)) (-3417 . T) (-4182 |has| (-632) (-6 -4182)) (-4179 |has| (-632) (-6 -4179)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3782 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-937))) (|HasCategory| (-632) (QUOTE (-1095))) (-12 (|HasCategory| (-632) (QUOTE (-918))) (|HasCategory| (-632) (QUOTE (-1095)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-970))) (-12 (|HasCategory| (-632) (QUOTE (-970))) (|HasCategory| (-632) (QUOTE (-1095)))) (-3782 (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3782 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-831))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4182)) (|HasAttribute| (-632) (QUOTE -4179)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3782 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3782 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3782 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-319))))) (-628 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}."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-629 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}."))) @@ -2452,13 +2452,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-631 OV E -2184 PG) +(-631 OV E -1709 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 (-632) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3405 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-633 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."))) @@ -2488,7 +2488,7 @@ 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 -(-640 S -2553 I) +(-640 S -2738 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 @@ -2504,14 +2504,14 @@ NIL ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-644 R |Mod| -1476 -2262 |exactQuo|) +(-644 R |Mod| -2137 -1676 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-645 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-646 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) -(-648 R |Mod| -1476 -2262 |exactQuo|) +(-648 R |Mod| -2137 -1676 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4180 . T)) NIL @@ -2532,7 +2532,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4178 . T) (-4177 . T)) NIL -(-651 -2184) +(-651 -1709) ((|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]]}."))) ((-4180 . T)) NIL @@ -2568,7 +2568,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-660 -2184 UP) +(-660 -1709 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 @@ -2587,7 +2587,7 @@ NIL (-664 |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."))) (((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) +((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3782 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) (-665 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2606,7 +2606,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-779)))) (-669 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4173 . T) (-4184 . T) (-3252 . T)) +((-4173 . T) (-4184 . T) (-3371 . T)) NIL (-670 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2720,15 +2720,15 @@ 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 -(-698 -2184) +(-698 -1709) ((|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 -(-699 P -2184) +(-699 P -1709) ((|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 -(-700 UP -2184) +(-700 UP -1709) ((|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 @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4185 "*") . T)) NIL -(-704 R -2184) +(-704 R -1709) ((|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 @@ -2764,7 +2764,7 @@ 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 -(-709 -2184 |ExtF| |SUEx| |ExtP| |n|) +(-709 -1709 |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 @@ -2779,7 +2779,7 @@ NIL (-712 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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) 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|#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-713 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -2787,14 +2787,14 @@ NIL (-714 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)}"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-715 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-716 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.}"))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-717 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}."))) @@ -2848,23 +2848,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4177 . T) (-4178 . T) (-4180 . T)) NIL -(-730 -3763 R OS S) +(-730 -3782 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-731 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (-3763 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (-3782 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3782 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (-732) ((|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 -(-733 R -2184 L) +(-733 R -1709 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 -(-734 R -2184) +(-734 R -1709) ((|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 @@ -2872,7 +2872,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-736 R -2184) +(-736 R -1709) ((|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 @@ -2880,11 +2880,11 @@ 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 -(-738 -2184 UP UPUP R) +(-738 -1709 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 -(-739 -2184 UP L LQ) +(-739 -1709 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 @@ -2892,38 +2892,38 @@ 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 -(-741 -2184 UP L LQ) +(-741 -1709 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 -(-742 -2184 UP) +(-742 -1709 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 -(-743 -2184 L UP A LO) +(-743 -1709 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 -(-744 -2184 UP) +(-744 -1709 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)))) -(-745 -2184 LO) +(-745 -1709 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 -(-746 -2184 LODO) +(-746 -1709 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)]}."))) NIL NIL -(-747 -2630 S |f|) +(-747 -2839 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4177 |has| |#2| (-961)) (-4178 |has| |#2| (-961)) (-4180 |has| |#2| (-6 -4180)) ((-4185 "*") |has| |#2| (-156)) (-4183 . 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . 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(|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."))) (((-4185 "*") |has| |#2| (-333)) (-4176 |has| |#2| (-333)) (-4181 |has| |#2| (-333)) (-4175 |has| |#2| (-333)) (-4180 . T) (-4178 . T) (-4177 . T)) @@ -2978,7 +2978,7 @@ NIL NIL (-762 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4183 . T) (-4173 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4173 . T) (-4184 . T) (-3371 . T)) NIL (-763) ((|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."))) @@ -2991,7 +2991,7 @@ NIL (-765 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."))) ((-4180 |has| |#1| (-777))) -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3782 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3782 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) (-766 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) @@ -3019,12 +3019,12 @@ NIL (-772 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."))) ((-4180 |has| |#1| (-777))) -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) +((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3782 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3782 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) (-773) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-774 -2630 S) +(-774 -2839 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 @@ -3060,11 +3060,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) -(-783 R |sigma| -2234) +(-783 R |sigma| -4125) ((|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."))) ((-4177 . T) (-4178 . T) (-4180 . T)) ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) -(-784 |x| R |sigma| -2234) +(-784 |x| R |sigma| -4125) ((|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."))) ((-4177 . T) (-4178 . T) (-4180 . T)) ((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) @@ -3111,11 +3111,11 @@ NIL (-795 |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)."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-794 |#1|) (QUOTE (-831))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-937))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1050))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3763 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) +((|HasCategory| (-794 |#1|) (QUOTE (-831))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-937))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1050))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3782 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) (-796 |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)}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3763 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) +((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3782 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) (-797) ((|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 @@ -3167,7 +3167,7 @@ NIL (-809 |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 -((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (-12 (-2455 (|HasCategory| |#2| (QUOTE (-961)))) (-2455 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2455 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074))))))) +((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (-12 (-2650 (|HasCategory| |#2| (QUOTE (-961)))) (-2650 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2650 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074))))))) (-810 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 @@ -3176,7 +3176,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-812 R -2553) +(-812 R -2738) ((|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 @@ -3200,7 +3200,7 @@ 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 -(-818 UP -2184) +(-818 UP -1709) ((|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 @@ -3239,7 +3239,7 @@ NIL (-827 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."))) ((-4180 . T)) -((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) +((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) (-828 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 @@ -3260,7 +3260,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) -(-833 R0 -2184 UP UPUP R) +(-833 R0 -1709 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 @@ -3288,7 +3288,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-840 -2184) +(-840 -1709) ((|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 @@ -3304,11 +3304,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4185 "*") . T)) NIL -(-844 -2184 P) +(-844 -1709 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-845 |xx| -2184) +(-845 |xx| -1709) ((|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 @@ -3332,7 +3332,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-851 R -2184) +(-851 R -1709) ((|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 @@ -3344,7 +3344,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-854 S R -2184) +(-854 S R -1709) ((|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 @@ -3364,11 +3364,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -808) (|devaluate| |#1|)))) -(-859 R -2184 -2553) +(-859 R -1709 -2738) ((|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 -(-860 -2553) +(-860 -2738) ((|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 @@ -3391,7 +3391,7 @@ NIL (-865 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-866 |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 @@ -3416,7 +3416,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) NIL -(-872 E V R P -2184) +(-872 E V R P -1709) ((|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 @@ -3427,8 +3427,8 @@ NIL (-874 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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-875 E V R P -2184) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +(-875 E V R P -1709) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-421)))) @@ -3447,12 +3447,12 @@ NIL (-879 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-880) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-881 -2184) +(-881 -1709) ((|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 @@ -3467,14 +3467,14 @@ NIL (-884 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}"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) (-885 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"))) ((-4180 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) -((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 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(QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) (-886 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}."))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-887 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}}"))) @@ -3502,7 +3502,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-509)))) (-893 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."))) -((-4183 . T) (-3252 . T)) +((-4183 . T) (-3371 . T)) NIL (-894 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."))) @@ -3518,7 +3518,7 @@ NIL NIL (-897 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}."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-898 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3536,7 +3536,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-902 K R UP -2184) +(-902 K R UP -1709) ((|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 @@ -3566,7 +3566,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1050)))) (-909 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}."))) -((-3252 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3371 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-910 |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}."))) @@ -3574,7 +3574,7 @@ NIL NIL (-911 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."))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-912 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}."))) @@ -3591,7 +3591,7 @@ NIL (-915 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.}"))) ((-4176 |has| |#1| (-262)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3763 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3782 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) (-916 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}."))) ((-4183 . T) (-4184 . T)) @@ -3604,14 +3604,14 @@ 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 -(-919 -2184 UP UPUP |radicnd| |n|) +(-919 -1709 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3763 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3763 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) +((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3782 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3782 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3782 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3782 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-920 |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."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) +((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3782 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) (-921) ((|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 @@ -3634,7 +3634,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (QUOTE (-1003)))) (-926 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}."))) -((-3252 . T)) +((-3371 . T)) NIL (-927 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3644,19 +3644,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4176 . T) (-4181 . T) (-4175 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4180 . T)) NIL -(-929 R -2184) +(-929 R -1709) ((|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 -(-930 R -2184) +(-930 R -1709) ((|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 -(-931 -2184 UP) +(-931 -1709 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 -(-932 -2184 UP) +(-932 -1709 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 @@ -3687,8 +3687,8 @@ NIL (-939 |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"))) ((-4176 . T) (-4181 . T) (-4175 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) -(-940 -2184 L) +((|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (-3782 (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) +(-940 -1709 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 @@ -3724,14 +3724,14 @@ 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 -(-949 -2184 |Expon| |VarSet| |FPol| |LFPol|) +(-949 -1709 |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"))) (((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-950) ((|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.}"))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) +((|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1338) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) (-951 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3776,7 +3776,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4180 . T)) NIL -(-962 |xx| -2184) +(-962 |xx| -1709) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3786,12 +3786,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-278))) (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-509))) (|HasCategory| |#4| (QUOTE (-156)))) (-964 |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"))) -((-4183 . T) (-3252 . T) (-4178 . T) (-4177 . T)) +((-4183 . T) (-3371 . T) (-4178 . T) (-4177 . T)) NIL (-965 |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}."))) ((-4183 . T) (-4178 . T) (-4177 . T)) -((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3763 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) +((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3782 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3782 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) (-966 |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 @@ -3823,7 +3823,7 @@ NIL (-973) ((|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}"))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) +((|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1338) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) (-974 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 @@ -3850,7 +3850,7 @@ NIL NIL (-980 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}."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-981 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."))) @@ -3860,11 +3860,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-983 |Base| R -2184) +(-983 |Base| R -1709) ((|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 -(-984 |Base| R -2184) +(-984 |Base| R -1709) ((|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 @@ -3879,7 +3879,7 @@ NIL (-987 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."))) ((-4176 |has| |#1| (-333)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) +((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) (-988 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 @@ -3899,7 +3899,7 @@ NIL (-992 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"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-993 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 @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1003)))) (-997 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."))) -((-3252 . T)) +((-3371 . T)) NIL (-998 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3926,7 +3926,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1003)))) (-999 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-3252 . T)) +((-3371 . T)) NIL (-1000 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3934,7 +3934,7 @@ NIL NIL (-1001 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4173 . T) (-3252 . T)) +((-4173 . T) (-3371 . T)) NIL (-1002 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}."))) @@ -3951,7 +3951,7 @@ NIL (-1005 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)}}"))) ((-4183 . T) (-4173 . T) (-4184 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) (-1006 |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 @@ -3978,7 +3978,7 @@ NIL NIL (-1012 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.}"))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-1013) ((|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."))) @@ -3995,12 +3995,12 @@ NIL (-1016 |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}."))) ((-4177 |has| |#3| (-961)) (-4178 |has| |#3| (-961)) (-4180 |has| |#3| (-6 -4180)) ((-4185 "*") |has| |#3| (-156)) (-4183 . 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(|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 (-421)))) -(-1018 R -2184) +(-1018 R -1709) ((|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 @@ -4018,7 +4018,7 @@ NIL NIL (-1022 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4183 . T) (-4184 . T) (-3252 . T)) +((-4183 . T) (-4184 . T) (-3371 . T)) NIL (-1023 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4026,7 +4026,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-333))) (|HasAttribute| |#3| (QUOTE (-4185 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) (-1024 |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."))) -((-3252 . T) (-4183 . T) (-4177 . T) (-4178 . T) (-4180 . T)) +((-3371 . T) (-4183 . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-1025 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}."))) @@ -4035,16 +4035,16 @@ NIL (-1026 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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) +((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) (-1027 |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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) (-1028 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}"))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL -(-1029 UP -2184) +(-1029 UP -1709) ((|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 @@ -4095,14 +4095,14 @@ NIL (-1041 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) ((-4180 . T) (-4172 |has| |#2| (-6 (-4185 "*"))) (-4183 . T) (-4177 . T) (-4178 . T)) -((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) +((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (-3782 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3782 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) (-1042 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1043) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-1044 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.}"))) @@ -4122,12 +4122,12 @@ NIL NIL (-1048 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})}."))) -((-3252 . T)) +((-3371 . T)) NIL (-1049 |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."))) ((-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) (-1050) ((|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 @@ -4154,16 +4154,16 @@ NIL ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779)))) (-1056) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-1057) NIL ((-4184 . T) (-4183 . T)) -((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) +((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3782 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) (-1058 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#1|)))))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) +((|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#1|)))))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (-1059 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 @@ -4190,9 +4190,9 @@ NIL NIL (-1065 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-1072 |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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-1073) ((|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 @@ -4235,7 +4235,7 @@ NIL (-1076 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-888) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-888) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) (-1077) ((|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 @@ -4263,7 +4263,7 @@ NIL (-1083 |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}"))) ((-4183 . T) (-4184 . T)) -((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) +((|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3458) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1338) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3782 (|HasCategory| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) (-1084 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 @@ -4274,7 +4274,7 @@ NIL NIL (-1086 |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})}."))) -((-4184 . T) (-3252 . T)) +((-4184 . T) (-3371 . T)) NIL (-1087 |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."))) @@ -4324,7 +4324,7 @@ 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 -(-1099 R -2184) +(-1099 R -1709) ((|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 @@ -4332,7 +4332,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1101 R -2184) +(-1101 R -1709) ((|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 -558) (LIST (QUOTE -814) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -808) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -808) (|devaluate| |#1|))))) @@ -4342,12 +4342,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-338)))) (-1103 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-1104 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) (-1105 |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 @@ -4360,13 +4360,13 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) -(-1108 -2184) +(-1108 -1709) ((|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 (-1109) ((|constructor| (NIL "The fundamental Type."))) -((-3252 . T)) +((-3371 . T)) NIL (-1110 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}.}"))) @@ -4398,16 +4398,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-333)))) (-1117 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-3252 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) +(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-3371 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) NIL (-1118 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . 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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 @@ -4443,7 +4443,7 @@ NIL (-1128 |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."))) (((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4179 |has| |#2| (-333)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) -((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) +((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3782 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3782 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3782 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) (-1129 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 @@ -4459,7 +4459,7 @@ NIL (-1132 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 -822) (QUOTE (-1074)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2182) (LIST (|devaluate| |#2|) (QUOTE (-1074)))))) +((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2254) (LIST (|devaluate| |#2|) (QUOTE (-1074)))))) (-1133 |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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) @@ -4487,22 +4487,22 @@ NIL (-1139 |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)}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-1140 |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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3782 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-1141 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))}."))) (((-4185 "*") |has| (-1140 |#2| |#3| |#4|) (-156)) (-4176 |has| (-1140 |#2| |#3| |#4|) (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-421))) (-3763 (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-509)))) +((|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-421))) (-3782 (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-509)))) (-1142 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4184))) (-1143 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-3252 . T)) +((-3371 . T)) NIL (-1144 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4511,7 +4511,7 @@ NIL (-1145 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-517)))) (|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-1095))) (|HasSignature| |#2| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2863) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1074))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-1095))) (|HasSignature| |#2| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3563) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1074))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) (-1146 |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."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) @@ -4519,12 +4519,12 @@ NIL (-1147 |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}."))) (((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3782 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2254) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3782 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -3563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1357) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) (-1148 |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 -(-1149 -2184 UP L UTS) +(-1149 -1709 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 (-509)))) @@ -4538,7 +4538,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1152 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4184 . T) (-4183 . T) (-3252 . T)) +((-4184 . T) (-4183 . T) (-3371 . T)) NIL (-1153 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4547,7 +4547,7 @@ NIL (-1154 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4184 . T) (-4183 . T)) -((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) +((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3782 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3782 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) (-1155) ((|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 @@ -4580,7 +4580,7 @@ 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 -(-1163 K R UP -2184) +(-1163 K R UP -1709) ((|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 @@ -4608,11 +4608,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) NIL -(-1170 S -2184) +(-1170 S -1709) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134)))) -(-1171 -2184) +(-1171 -1709) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index d73ba07d..638a28c8 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(143833 . 3404130415) -(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(143833 . 3404712031) +(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) (((|#2| |#2|) . T)) ((((-517)) . T)) -((($ $) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) ((|#2| |#2|) . T) (((-377 (-517)) (-377 (-517))) |has| |#2| (-37 (-377 (-517))))) +((($ $) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) ((|#2| |#2|) . T) (((-377 (-517)) (-377 (-517))) |has| |#2| (-37 (-377 (-517))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#2|) . T)) -((($) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) ((|#2|) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517))))) +((($) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) ((|#2|) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517))))) (|has| |#1| (-831)) ((((-787)) . T)) ((((-787)) . T)) @@ -23,28 +23,28 @@ ((((-199)) . T) (((-787)) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1|) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-777))) -((($ $) . T) (((-377 (-517)) (-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1| |#1|) . T)) -(-3763 (|has| |#1| (-752)) (|has| |#1| (-779))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-777))) +((($ $) . T) (((-377 (-517)) (-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1| |#1|) . T)) +(-3782 (|has| |#1| (-752)) (|has| |#1| (-779))) ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) ((((-787)) . T)) ((((-787)) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (|has| |#1| (-777)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +((($) . T) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) ((((-787)) . T)) ((((-787)) |has| |#1| (-1003))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) -(((|#2| (-450 (-2210 |#1|) (-703))) . T)) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(((|#2| (-450 (-2290 |#1|) (-703))) . T)) (((|#1| (-489 (-1074))) . T)) ((((-794 |#1|) (-794 |#1|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (|has| |#4| (-338)) (|has| |#3| (-338)) (((|#1|) . T)) @@ -54,10 +54,10 @@ (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-509)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) ((($) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) ((((-493)) |has| |#1| (-558 (-493)))) ((($) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-787)) . T)) ((((-787)) . T)) ((((-377 (-517))) . T) (($) . T)) -((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) (($) . T) ((|#1|) . T)) +((((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) (($) . T) ((|#1|) . T)) ((((-787)) . 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T)) ((((-493)) . T) (((-199)) . T) (((-349)) . T) (((-814 (-349))) . T)) ((((-787)) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) (((|#1|) |has| |#1| (-156))) (((|#1| $) |has| |#1| (-258 |#1| |#1|))) ((((-787)) . T)) @@ -255,13 +255,13 @@ (|has| |#1| (-779)) (|has| |#1| (-1003)) (((|#1|) . 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T)) (((|#1| (-888)) . T)) ((((-794 |#1|) $) |has| (-794 |#1|) (-258 (-794 |#1|) (-794 |#1|)))) @@ -270,7 +270,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1050)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) (|has| (-1141 |#1| |#2| |#3| |#4|) (-132)) (|has| (-1141 |#1| |#2| |#3| |#4|) (-134)) (|has| |#1| (-132)) @@ -287,20 +287,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-961))) ((((-787)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) (((|#1|) . 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T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($ $) -3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((((-787)) . T)) ((((-787)) . T)) (|has| (-1140 |#2| |#3| |#4|) (-134)) @@ -310,16 +310,16 @@ (|has| |#1| (-1003)) (((|#1|) . T)) (((|#1|) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) (((|#1|) . 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T)) ((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) |has| |#1| (-156)) (($) |has| |#1| (-509))) (|has| |#1| (-333)) -(-3763 (-12 (|has| (-1147 |#1| |#2| |#3|) (-207)) (|has| |#1| (-333))) (|has| |#1| (-15 * (|#1| (-517) |#1|)))) +(-3782 (-12 (|has| (-1147 |#1| |#2| |#3|) (-207)) (|has| |#1| (-333))) (|has| |#1| (-15 * (|#1| (-517) |#1|)))) (|has| |#1| (-15 * (|#1| (-377 (-517)) |#1|))) (|has| |#1| (-333)) (|has| |#1| (-15 * (|#1| (-703) |#1|))) @@ -342,31 +342,31 @@ (((|#1|) . T)) ((((-517) |#1|) . T)) (((|#2|) . T)) -(-3763 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) (((|#1|) . 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T)) (|has| (-377 |#2|) (-134)) (|has| (-377 |#2|) (-132)) @@ -677,21 +677,21 @@ (|has| |#1| (-509)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-787)) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) (|has| |#1| (-37 (-377 (-517)))) -((((-358) (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-358) (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#2| (-1050)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (((|#1|) . T)) ((((-358) (-1057)) . T)) (|has| |#1| (-509)) ((((-111 |#1|)) . T)) ((((-517) |#1|) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (((|#2|) . T)) ((((-787)) . T)) ((((-751 |#1|)) . T)) @@ -704,7 +704,7 @@ (((|#1|) |has| |#1| (-156))) ((((-787)) . T)) ((((-493)) |has| |#1| (-558 (-493)))) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) (((|#2|) |has| |#2| (-280 |#2|))) ((((-517) (-517)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) (((|#1|) . T)) @@ -714,7 +714,7 @@ ((((-517) (-517)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) ((($) . T) (((-517)) . T) (((-377 (-517))) . T)) (|has| |#2| (-338)) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) @@ -725,9 +725,9 @@ ((((-1072 |#1| |#2| |#3|) $) -12 (|has| (-1072 |#1| |#2| |#3|) (-258 (-1072 |#1| |#2| |#3|) (-1072 |#1| |#2| |#3|))) (|has| |#1| (-333))) (($ $) . T)) ((((-787)) . T)) ((((-787)) . T)) -((($) . T) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +((($) . T) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) ((((-493)) |has| |#1| (-558 (-493)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) ((($ $) . T)) ((($ $) . T)) ((((-787)) . T)) @@ -736,12 +736,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((((-377 (-517))) . T) (((-517)) . T)) ((((-517) (-131)) . T)) ((((-131)) . T)) (((|#1|) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((((-107)) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) ((((-107)) . T)) @@ -749,38 +749,38 @@ ((((-493)) |has| |#1| (-558 (-493))) (((-199)) |has| |#1| (-937)) (((-349)) |has| |#1| (-937))) ((((-787)) . T)) (|has| |#1| (-752)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (|has| |#1| (-779)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-509))) (|has| |#1| (-509)) (|has| |#1| (-831)) (((|#1|) . T)) (|has| |#1| (-1003)) ((((-787)) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-509))) ((((-787)) . T)) ((((-787)) . T)) ((((-787)) . T)) (((|#1| (-1154 |#1|) (-1154 |#1|)) . T)) ((((-517) (-131)) . T)) ((($) . T)) -(-3763 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) -(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) +(-3782 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) +(-3782 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((((-787)) . T)) (|has| |#1| (-1003)) (((|#1| (-888)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) -(-3763 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) (-12 (|has| |#1| (-659)) (|has| |#2| (-659)))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) (-12 (|has| |#1| (-659)) (|has| |#2| (-659)))) (((|#1|) . T)) (|has| |#2| (-725)) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (|has| |#2| (-777)) @@ -795,7 +795,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-377 (-517))) . T) (($) . T)) -((($) . T) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) +((($) . T) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) (|has| |#1| (-760)) ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) (|has| |#1| (-1003)) @@ -806,8 +806,8 @@ (((|#3|) |has| |#3| (-1003))) (|has| |#3| (-338)) (((|#1|) . T) (((-787)) . T)) -((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) -(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509)))) +((((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) +(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509)))) ((((-787)) . T)) ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#2|) . T)) @@ -817,30 +817,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-156))) ((((-377 (-517))) . T) (((-517)) . T)) -((($ $) -3763 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($ $) -3782 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) ((((-131)) . T)) (((|#1|) . T)) ((((-131)) . T)) -((($) -3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961)))) +((($) -3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961)))) ((((-131)) . T)) (((|#1| |#2| |#3|) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) (|has| $ (-134)) (|has| $ (-134)) (|has| |#1| (-1003)) ((((-787)) . T)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-442)) (|has| |#1| (-509)) (|has| |#1| (-961)) (|has| |#1| (-1015))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-442)) (|has| |#1| (-509)) (|has| |#1| (-961)) (|has| |#1| (-1015))) ((($ $) |has| |#1| (-258 $ $)) ((|#1| $) |has| |#1| (-258 |#1| |#1|))) (((|#1| (-377 (-517))) . T)) (((|#1|) . T)) ((((-1074)) . T)) (|has| |#1| (-509)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (|has| |#1| (-509)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) @@ -851,7 +851,7 @@ (|has| |#1| (-134)) (|has| |#1| (-132)) (|has| |#4| (-777)) -(((|#2| (-214 (-2210 |#1|) (-703)) (-789 |#1|)) . T)) +(((|#2| (-214 (-2290 |#1|) (-703)) (-789 |#1|)) . T)) (|has| |#3| (-777)) (((|#1| (-489 |#3|) |#3|) . T)) (|has| |#1| (-134)) @@ -865,21 +865,21 @@ (|has| |#1| (-132)) ((((-377 (-517))) |has| |#2| (-333)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-319)) (|has| |#1| (-338))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-319)) (|has| |#1| (-338))) ((((-1041 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-156)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-207)) (|has| |#2| (-961))) -(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) -(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) +(((|#2|) . T) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +(-3782 (|has| |#3| (-725)) (|has| |#3| (-777))) +(-3782 (|has| |#3| (-725)) (|has| |#3| (-777))) ((((-787)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-632)) . T)) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) (|has| |#1| (-509)) (((|#1|) . T)) (((|#1|) . T)) @@ -901,10 +901,10 @@ (((|#1| (-377 (-517))) . T)) (((|#3|) . T) (((-556 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) ((((-1072 |#1| |#2| |#3|) (-1072 |#1| |#2| |#3|)) -12 (|has| (-1072 |#1| |#2| |#3|) (-280 (-1072 |#1| |#2| |#3|))) (|has| |#1| (-333))) (((-1074) (-1072 |#1| |#2| |#3|)) -12 (|has| (-1072 |#1| |#2| |#3|) (-478 (-1074) (-1072 |#1| |#2| |#3|))) (|has| |#1| (-333)))) @@ -912,8 +912,8 @@ ((((-787)) . T)) ((((-787)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) -(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))))) +(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) +(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) |has| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (-280 (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))))) ((((-787)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -924,10 +924,10 @@ ((($ $) . T) (((-789 |#1|) $) . T) (((-789 |#1|) |#2|) . T)) (|has| |#1| (-760)) (|has| |#1| (-1003)) -(((|#2| |#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($ $) |has| |#2| (-156))) -(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)))) -((((-517) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($) |has| |#2| (-156))) +(((|#2| |#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($ $) |has| |#2| (-156))) +(((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)))) +((((-517) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($) |has| |#2| (-156))) ((((-703)) . T)) ((((-517)) . T)) (|has| |#1| (-509)) @@ -940,29 +940,29 @@ ((((-111 |#1|)) . T)) (((|#1|) . 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T)) -((($) -3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319)) (|has| |#1| (-509))) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +((($) -3782 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319)) (|has| |#1| (-509))) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) ((((-517) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -970,37 +970,37 @@ (-12 (|has| |#1| (-338)) (|has| |#2| (-338))) ((((-787)) . T)) ((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-280 |#1|))) (|has| |#1| (-338)) @@ -1008,31 +1008,31 @@ (|has| |#1| (-338)) ((((-1074) $) |has| |#1| (-478 (-1074) $)) (($ $) |has| |#1| (-280 $)) ((|#1| |#1|) |has| |#1| (-280 |#1|)) (((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|))) ((((-1074)) |has| |#1| (-822 (-1074)))) -(-3763 (-12 (|has| |#1| (-207)) (|has| |#1| (-333))) (|has| |#1| (-319))) +(-3782 (-12 (|has| |#1| (-207)) (|has| |#1| (-333))) (|has| |#1| (-319))) ((((-358) (-1021)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-358) |#1|) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-1003)) ((((-787)) . T)) ((((-787)) . T)) ((((-832 |#1|)) . 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T) (($) . T) (((-377 (-517))) . T)) ((((-787)) . T)) ((((-787)) . T)) @@ -1059,14 +1059,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-777)) (|has| |#1| (-777)) -((($) . T) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))))) +((($) . T) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-509))) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) |has| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (-280 (-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))))) ((($) . T)) (|has| |#2| (-779)) ((($) . 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T)) ((((-517)) |has| |#1| (-808 (-517))) (((-349)) |has| |#1| (-808 (-349)))) -((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) ((|#1|) . T)) +((((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) ((|#1|) . T)) (((|#1|) . T)) ((((-583 |#4|)) . T) (((-787)) . T)) ((((-493)) |has| |#4| (-558 (-493)))) @@ -1139,17 +1139,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1074)) |has| (-377 |#2|) (-822 (-1074)))) -(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-787)) -3763 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-557 (-787))) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) (((-1154 |#3|)) . T)) +((((-787)) -3782 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-557 (-787))) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) (((-1154 |#3|)) . T)) ((((-517) |#2|) . T)) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) -(((|#2| |#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($ $) |has| |#2| (-156))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(((|#2| |#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($ $) |has| |#2| (-156))) ((((-787)) . T)) ((((-787)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T) ((|#2|) . T)) ((((-787)) . T)) ((((-787)) . T)) ((((-1057) (-1074) (-517) (-199) (-787)) . T)) @@ -1184,8 +1184,8 @@ (|has| |#1| (-37 (-377 (-517)))) ((((-787)) . T)) ((((-493)) |has| |#1| (-558 (-493)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) -(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($) |has| |#2| (-156))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +(((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($) |has| |#2| (-156))) (|has| $ (-134)) ((((-377 |#2|)) . T)) ((((-377 (-517))) |has| (-377 |#2|) (-952 (-377 (-517)))) (((-517)) |has| (-377 |#2|) (-952 (-517))) (((-377 |#2|)) . T)) @@ -1196,11 +1196,11 @@ (((|#3|) |has| |#3| (-156))) (|has| |#1| (-134)) (|has| |#1| (-132)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) (((|#1|) . T)) (((|#2|) . T)) @@ -1231,7 +1231,7 @@ ((((-915 |#1|)) . T) ((|#1|) . T)) ((((-787)) . T)) ((((-787)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-377 (-517))) . T) (((-377 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1070 |#1|)) . T)) ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) @@ -1239,9 +1239,9 @@ (|has| |#1| (-779)) (((|#2|) . T)) ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) ((((-517) |#2|) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (((|#2|) . T)) ((((-517) |#3|) . T)) (((|#2|) . T)) @@ -1256,7 +1256,7 @@ (((|#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-333)) (((|#2|) . T) (((-517)) |has| |#2| (-952 (-517))) (((-377 (-517))) |has| |#2| (-952 (-377 (-517))))) @@ -1286,19 +1286,19 @@ (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1| |#2|) . T)) ((((-517) (-131)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) -((($) -3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) +((($) -3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (|has| |#1| (-779)) (((|#2| (-703) (-989)) . T)) (((|#1| |#2|) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-509))) (|has| |#1| (-723)) (((|#1|) |has| |#1| (-156))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3763 (|has| |#1| (-134)) (-12 (|has| |#1| (-333)) (|has| |#2| (-134)))) -(-3763 (|has| |#1| (-132)) (-12 (|has| |#1| (-333)) (|has| |#2| (-132)))) +(-3782 (|has| |#1| (-134)) (-12 (|has| |#1| (-333)) (|has| |#2| (-134)))) +(-3782 (|has| |#1| (-132)) (-12 (|has| |#1| (-333)) (|has| |#2| (-132)))) (((|#4|) . T)) (|has| |#1| (-132)) ((((-1057) |#1|) . T)) @@ -1311,10 +1311,10 @@ (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#3|) . T)) ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) (((|#1|) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003))) (((-879 |#1|)) . T)) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003))) (((-879 |#1|)) . T)) (|has| |#1| (-777)) (|has| |#1| (-777)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) @@ -1327,8 +1327,8 @@ ((($) . T)) ((((-358) (-1057)) . T)) ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((((-787)) -3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-557 (-787))) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((-1154 |#2|)) . T)) -((((-51)) . T) (((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) +((((-787)) -3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-557 (-787))) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((-1154 |#2|)) . T)) +((((-51)) . T) (((-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) . T)) (((|#1|) . T)) ((((-787)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) @@ -1336,7 +1336,7 @@ (|has| |#2| (-132)) (|has| |#2| (-134)) (|has| |#1| (-442)) -(-3763 (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) (|has| |#1| (-333)) ((((-787)) . T)) (|has| |#1| (-37 (-377 (-517)))) @@ -1345,8 +1345,8 @@ (|has| |#1| (-777)) (|has| |#1| (-777)) ((((-787)) . T)) -((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) -(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509)))) +((((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) +(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509)))) ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#1| |#2|) . T)) ((((-1074)) |has| |#1| (-822 (-1074)))) @@ -1354,7 +1354,7 @@ ((((-787)) . T)) ((((-787)) . T)) (|has| |#1| (-1003)) -(((|#2| (-450 (-2210 |#1|) (-703)) (-789 |#1|)) . T)) +(((|#2| (-450 (-2290 |#1|) (-703)) (-789 |#1|)) . T)) ((((-377 (-517))) |has| |#2| (-333)) (($) |has| |#2| (-333))) (((|#1| (-489 (-1074)) (-1074)) . T)) (((|#1|) . T)) @@ -1374,16 +1374,16 @@ (|has| |#1| (-134)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) ((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-1074) (-51)) . T)) ((($ $) . T)) (((|#1| (-517)) . T)) ((((-832 |#1|)) . T)) -(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961))) (($) -3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)))) +(((|#1|) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961))) (($) -3782 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)))) (((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) (|has| |#1| (-779)) (|has| |#1| (-779)) @@ -1398,13 +1398,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) (((|#1|) |has| |#1| (-156))) (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) -(((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)))) +(((|#3|) -3782 (|has| |#3| (-156)) (|has| |#3| (-333)))) (|has| |#2| (-779)) (|has| |#1| (-779)) -(-3763 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-831))) ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) ((((-517) |#2|) . T)) -(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)))) +(((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)))) (|has| |#1| (-319)) (((|#3| |#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) ((($) . T) (((-377 (-517))) . T)) @@ -1412,7 +1412,7 @@ (|has| |#1| (-752)) (|has| |#1| (-752)) (((|#1|) . T)) -(-3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-777)) (|has| |#1| (-777)) (|has| |#1| (-777)) @@ -1421,13 +1421,13 @@ ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-37 (-377 (-517)))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-1074)) |has| |#1| (-822 (-1074))) (((-989)) . T)) (((|#1|) . T)) (|has| |#1| (-777)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))))) +((((-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) |has| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (-280 (-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (|has| |#1| (-1003)) (((|#1|) . T)) @@ -1445,7 +1445,7 @@ (((|#1|) . T)) ((((-131)) . T)) (((|#2|) |has| |#2| (-156))) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((|#1|) . T)) (|has| |#1| (-132)) (|has| |#1| (-134)) @@ -1466,32 +1466,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))))) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) +(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) |has| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (-280 (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-831))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)))) +(((|#3|) -3782 (|has| |#3| (-156)) (|has| |#3| (-333)))) (|has| |#1| (-779)) (|has| |#1| (-509)) ((((-530 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-752))) (-12 (|has| |#1| (-333)) (|has| |#2| (-779)))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (-12 (|has| |#1| (-333)) (|has| |#2| (-752))) (-12 (|has| |#1| (-333)) (|has| |#2| (-779)))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) ((((-832 |#1|)) . T)) (((|#1| (-461 |#1| |#3|) (-461 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-703)) . 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T)) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) ((((-608 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1499,17 +1499,17 @@ ((((-787)) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) ((((-787)) . T)) -((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) +((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) ((((-787)) . T)) ((((-787)) . T)) ((((-787)) . T)) (((|#2|) . T)) -(-3763 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) (|has| |#1| (-1095)) (|has| |#1| (-1095)) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (|has| |#1| (-1095)) (|has| |#1| (-1095)) (((|#3| |#3|) . T)) @@ -1522,43 +1522,43 @@ (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) ((((-1057) (-51)) . T)) (|has| |#1| (-1003)) -(-3763 (|has| |#2| (-752)) (|has| |#2| (-779))) +(-3782 (|has| |#2| (-752)) (|has| |#2| (-779))) (((|#1|) . T)) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) (((|#1|) |has| |#1| (-156)) (($) . T)) ((($) . T)) ((((-1072 |#1| |#2| |#3|)) -12 (|has| (-1072 |#1| |#2| |#3|) (-280 (-1072 |#1| |#2| |#3|))) (|has| |#1| (-333)))) ((((-787)) . T)) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) ((($) . T)) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) ((((-787)) . T)) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-831))) (|has| |#2| (-831)) (|has| |#1| (-333)) (((|#2|) |has| |#2| (-1003))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((($) . T) ((|#2|) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-831))) (|has| |#1| (-831)) (|has| |#1| (-831)) ((((-493)) . T) (((-377 (-1070 (-517)))) . T) (((-199)) . T) (((-349)) . T)) ((((-349)) . T) (((-199)) . T) (((-787)) . T)) (|has| |#1| (-831)) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) ((($ $) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((($ $) . T)) ((((-517) (-107)) . T)) ((($) . T)) (((|#1|) . T)) ((((-517)) . T)) ((((-107)) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) (|has| |#1| (-37 (-377 (-517)))) (((|#1| (-517)) . T)) ((($) . T)) @@ -1580,7 +1580,7 @@ (((|#1| (-1119 |#1| |#2| |#3|)) . T)) (((|#1| (-703)) . T)) (((|#1|) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-787)) . T)) (|has| |#1| (-1003)) ((((-1057) |#1|) . T)) @@ -1599,18 +1599,18 @@ (((|#1|) . T)) ((((-517)) . T)) ((((-787)) . T)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-319))) ((((-787)) . T)) (|has| |#1| (-134)) (((|#3|) . T)) -(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) +(-3782 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((((-787)) . T)) ((((-1140 |#2| |#3| |#4|)) . T) (((-1141 |#1| |#2| |#3| |#4|)) . T)) ((((-787)) . T)) -((((-47)) -12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (((-556 $)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) -3763 (-12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (|has| |#1| (-952 (-377 (-517))))) (((-377 (-874 |#1|))) |has| |#1| (-509)) (((-874 |#1|)) |has| |#1| (-961)) (((-1074)) . T)) +((((-47)) -12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (((-556 $)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) -3782 (-12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (|has| |#1| (-952 (-377 (-517))))) (((-377 (-874 |#1|))) |has| |#1| (-509)) (((-874 |#1|)) |has| |#1| (-961)) (((-1074)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-703)) . T)) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) (((|#1|) |has| |#1| (-280 |#1|))) ((((-1141 |#1| |#2| |#3| |#4|)) . T)) ((((-517)) |has| |#1| (-808 (-517))) (((-349)) |has| |#1| (-808 (-349)))) @@ -1618,14 +1618,14 @@ (|has| |#1| (-509)) (((|#1|) . T)) ((((-787)) . T)) -(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) (((|#1|) |has| |#1| (-156))) ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1003))) -(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)))) +(((|#2|) -3782 (|has| |#2| (-156)) (|has| |#2| (-333)))) ((((-1140 |#2| |#3| |#4|)) . T)) ((((-107)) . T)) (|has| |#1| (-752)) @@ -1635,8 +1635,8 @@ (|has| |#1| (-777)) (|has| |#1| (-777)) (((|#1| (-517) (-989)) . T)) -(-3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +(-3782 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1| (-377 (-517)) (-989)) . T)) (((|#1| (-703) (-989)) . T)) (|has| |#1| (-779)) @@ -1652,28 +1652,28 @@ (((|#1|) . T)) (|has| |#1| (-1003)) ((((-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-579 (-517)))) ((|#2|) |has| |#1| (-333))) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((|#2|) |has| |#2| (-156))) (((|#1|) |has| |#1| (-156))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) ((((-787)) . T)) (|has| |#3| (-777)) ((((-787)) . T)) ((((-1140 |#2| |#3| |#4|) (-289 |#2| |#3| |#4|)) . T)) ((((-787)) . T)) -(((|#1| |#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) +(((|#1| |#1|) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) (((|#1|) . T)) ((((-517)) . T)) ((((-517)) . T)) -(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) +(((|#1|) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) (((|#2|) |has| |#2| (-333))) ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-333))) (|has| |#1| (-779)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) |has| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (-280 (-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-831))) (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) ((((-787)) . T)) ((((-787)) . T)) @@ -1707,18 +1707,18 @@ (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) (((|#1|) . T)) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) (((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) ((((-787)) . T)) (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (|has| |#1| (-333)) (|has| |#1| (-333)) (|has| (-377 |#2|) (-207)) (|has| |#1| (-831)) (((|#2|) |has| |#2| (-961))) -(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) (|has| |#1| (-333)) (((|#1|) |has| |#1| (-156))) (((|#1| |#1|) . T)) @@ -1743,7 +1743,7 @@ (((|#1| (-377 (-517)) (-989)) . T)) (((|#1| (-703) (-989)) . T)) ((((-377 |#2|) (-377 |#2|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) -(((|#1|) . T) (((-517)) -3763 (|has| (-377 (-517)) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) . T)) +(((|#1|) . T) (((-517)) -3782 (|has| (-377 (-517)) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) . T)) (((|#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-156))) (((|#1|) . T)) @@ -1762,24 +1762,24 @@ ((((-632)) . T)) (((|#2|) |has| |#2| (-156))) (|has| |#2| (-777)) -((((-107)) |has| |#1| (-1003)) (((-787)) -3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003)))) +((((-107)) |has| |#1| (-1003)) (((-787)) -3782 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) . T)) ((((-787)) . T)) ((((-517) |#1|) . T)) ((((-632)) . T) (((-377 (-517))) . T) (((-517)) . T)) (((|#1| |#1|) |has| |#1| (-156))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) ((((-349)) . T)) ((((-632)) . T)) ((((-377 (-517))) |has| |#2| (-333)) (($) |has| |#2| (-333))) (((|#1|) |has| |#1| (-156))) ((((-377 (-874 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (((|#2|) . T)) (|has| |#2| (-779)) (((|#3|) |has| |#3| (-961))) @@ -1789,14 +1789,14 @@ (|has| |#1| (-779)) ((((-1074)) |has| |#2| (-822 (-1074)))) ((((-787)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-377 (-517))) . T) (($) . T)) (|has| |#1| (-442)) (|has| |#1| (-338)) (|has| |#1| (-338)) (|has| |#1| (-338)) (|has| |#1| (-333)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-442)) (|has| |#1| (-509)) (|has| |#1| (-961)) (|has| |#1| (-1015))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-442)) (|has| |#1| (-509)) (|has| |#1| (-961)) (|has| |#1| (-1015))) (|has| |#1| (-37 (-377 (-517)))) ((((-111 |#1|)) . T)) ((((-111 |#1|)) . T)) @@ -1817,11 +1817,11 @@ (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-779)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-134)) (|has| |#1| (-132)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) (((|#2|) . T)) (((|#3|) . T)) ((((-111 |#1|)) . T)) @@ -1839,11 +1839,11 @@ ((((-493)) |has| |#1| (-558 (-493))) (((-814 (-517))) |has| |#1| (-558 (-814 (-517)))) (((-814 (-349))) |has| |#1| (-558 (-814 (-349)))) (((-349)) |has| |#1| (-937)) (((-199)) |has| |#1| (-937))) (((|#1|) |has| |#1| (-333))) ((((-787)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((($ $) . T) (((-556 $) $) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) ((($) . T) (((-1141 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . T)) -((($) -3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-509))) +((($) -3782 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-509))) (|has| |#1| (-333)) (|has| |#1| (-333)) (|has| |#1| (-333)) @@ -1854,11 +1854,11 @@ ((((-349)) . T)) (((|#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) ((((-787)) . T)) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-831))) (((|#1|) . T)) (|has| |#1| (-779)) (|has| |#1| (-779)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) ((((-493)) |has| |#1| (-558 (-493)))) (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) (|has| |#1| (-1003)) @@ -1867,13 +1867,13 @@ (|has| |#1| (-132)) (|has| |#1| (-134)) ((((-517)) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) ((((-1140 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517)))) (($) . T)) ((((-517)) . T)) (|has| |#1| (-333)) -(-3763 (-12 (|has| (-1147 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) -(-3763 (-12 (|has| (-1147 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) +(-3782 (-12 (|has| (-1147 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) +(-3782 (-12 (|has| (-1147 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) (|has| |#1| (-333)) (|has| |#1| (-132)) (|has| |#1| (-134)) @@ -1890,18 +1890,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-517)) |has| |#1| (-579 (-517)))) (((|#3|) |has| |#3| (-156))) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) ((((-517)) . T)) (((|#1| $) |has| |#1| (-258 |#1| |#1|))) ((((-377 (-517))) . T) (($) . T) (((-377 |#1|)) . T) ((|#1|) . T)) ((((-787)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3763 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517)) (-377 (-517))) |has| |#1| (-333))) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3782 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517)) (-377 (-517))) |has| |#1| (-333))) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) ((($) . T)) ((((-517) |#1|) . T)) ((((-1074)) |has| (-377 |#2|) (-822 (-1074)))) -(((|#1|) . T) (($) -3763 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517))) |has| |#1| (-333))) +(((|#1|) . T) (($) -3782 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517))) |has| |#1| (-333))) ((((-493)) |has| |#2| (-558 (-493)))) ((((-623 |#2|)) . T) (((-787)) . T)) (((|#1|) . T)) @@ -1909,8 +1909,8 @@ (((|#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) ((((-794 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) -(-3763 (|has| |#4| (-725)) (|has| |#4| (-777))) -(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) +(-3782 (|has| |#4| (-725)) (|has| |#4| (-777))) +(-3782 (|has| |#3| (-725)) (|has| |#3| (-777))) ((((-787)) . T)) ((((-787)) . T)) (((|#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) @@ -1926,17 +1926,17 @@ ((((-377 (-517))) . T) (($) . T)) ((((-377 (-517))) . T) (($) . T)) ((((-377 (-517))) . T) (($) . T)) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-1113))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-1113))) ((($) . T)) ((((-377 (-517))) |has| (-377 |#2|) (-952 (-377 (-517)))) (((-517)) |has| (-377 |#2|) (-952 (-517))) (((-377 |#2|)) . T)) (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) (((|#1| (-703)) . T)) (|has| |#1| (-779)) (((|#1|) . T) (((-517)) |has| |#1| (-579 (-517)))) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) ((((-517)) . T)) (|has| |#1| (-37 (-377 (-517)))) -((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))))) +((((-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) |has| (-2 (|:| -3458 (-1057)) (|:| -1338 (-51))) (-280 (-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))))) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (|has| |#1| (-777)) (|has| |#1| (-37 (-377 (-517)))) @@ -1961,24 +1961,24 @@ (((|#1| |#2|) . T)) ((((-131)) . T)) ((((-712 |#1| (-789 |#2|))) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (|has| |#1| (-1095)) (((|#1|) . T)) -(-3763 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) +(-3782 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) ((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|))) (((|#2|) . T)) -((($ $) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($ $) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((((-832 |#1|)) . T)) ((($) . T)) ((((-377 (-874 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) ((((-493)) |has| |#4| (-558 (-493)))) ((((-787)) . T) (((-583 |#4|)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-777)) -(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))))) +(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) |has| (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|)) (-280 (-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))))) (|has| |#1| (-1003)) (|has| |#1| (-333)) (|has| |#1| (-779)) @@ -1986,16 +1986,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-377 (-517))) . T)) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) (|has| |#1| (-132)) (|has| |#1| (-134)) -(-3763 (-12 (|has| (-1072 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) -(-3763 (-12 (|has| (-1072 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) +(-3782 (-12 (|has| (-1072 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) +(-3782 (-12 (|has| (-1072 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-134)) (|has| |#1| (-132)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) (|has| |#1| (-777)) (((|#1| |#2|) . T)) @@ -2018,9 +2018,9 @@ ((((-787)) . T)) ((((-787)) . T)) ((((-493)) |has| |#1| (-558 (-493)))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) -(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)))) +(((|#1|) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)))) ((((-286 |#1|)) . T)) (((|#2|) |has| |#2| (-333))) (((|#2|) . T)) @@ -2041,14 +2041,14 @@ (|has| |#1| (-132)) (|has| |#1| (-134)) ((($ $) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003))) (|has| |#1| (-509)) (((|#2|) . T)) ((((-517)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((((-530 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2073,12 +2073,12 @@ (((|#1| |#2|) . T)) ((((-1074) |#1|) . T)) (((|#4|) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((((-1074) (-51)) . T)) ((((-1140 |#2| |#3| |#4|) (-289 |#2| |#3| |#4|)) . T)) ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) ((((-787)) . T)) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) ((((-1141 |#1| |#2| |#3| |#4|) (-1141 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-156)) (((-377 (-517)) (-377 (-517))) |has| |#1| (-509)) (($ $) |has| |#1| (-509))) (((|#1|) . T) (($) . T) (((-377 (-517))) . T)) @@ -2097,14 +2097,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) (((|#2| |#3|) . T)) -(-3763 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) (((|#1| (-489 |#2|)) . T)) (((|#1| (-703)) . T)) (((|#1| (-489 (-993 (-1074)))) . T)) (((|#1|) |has| |#1| (-156))) (((|#1|) . T)) (|has| |#2| (-831)) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) ((((-787)) . T)) ((($ $) . T) (((-1140 |#2| |#3| |#4|) (-1140 |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517))))) ((((-832 |#1|)) . T)) @@ -2113,13 +2113,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-333)) -(-3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319)) (|has| |#1| (-509))) (|has| |#1| (-333)) ((($) . T) (((-1140 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517))))) (((|#1| |#2|) . T)) ((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) -(-3763 (-12 (|has| |#1| (-278)) (|has| |#1| (-831))) (|has| |#1| (-333)) (|has| |#1| (-319))) -(-3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) +(-3782 (-12 (|has| |#1| (-278)) (|has| |#1| (-831))) (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) ((((-517)) |has| |#1| (-579 (-517))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-787)) . T)) @@ -2151,27 +2151,27 @@ (((|#1|) |has| |#1| (-156))) ((((-787)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) -(((|#2|) -3763 (|has| |#2| (-6 (-4185 "*"))) (|has| |#2| (-156)))) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(((|#2|) -3782 (|has| |#2| (-6 (-4185 "*"))) (|has| |#2| (-156)))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#1| (-831)) (((|#2|) |has| |#2| (-156))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) ((((-787)) . T)) ((((-787)) . T)) ((((-493)) . T) (((-517)) . T) (((-814 (-517))) . T) (((-349)) . T) (((-199)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) . T)) (((|#1|) . T)) ((((-787)) . T)) (((|#1| |#2|) . T)) (((|#1| (-377 (-517))) . T)) (((|#1|) . T)) -(-3763 (|has| |#1| (-262)) (|has| |#1| (-333))) +(-3782 (|has| |#1| (-262)) (|has| |#1| (-333))) ((((-131)) . T)) ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) (|has| |#1| (-777)) @@ -2186,7 +2186,7 @@ ((((-377 (-517))) . T) (($) . T)) ((((-787)) . T)) ((((-787)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-787)) . T)) ((((-787)) . T)) @@ -2197,7 +2197,7 @@ (((|#1|) . T)) ((((-583 (-131))) . T) (((-1057)) . T)) ((((-787)) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) ((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) (|has| |#1| (-779)) ((((-787)) . T)) @@ -2209,16 +2209,16 @@ ((((-787)) . T) (((-583 |#4|)) . T)) (((|#2|) . T)) ((((-832 |#1|)) . T) (((-377 (-517))) . T) (($) . T)) -(-3763 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) -(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) +(-3782 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) +(-3782 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((((-1074) (-51)) . T)) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) (|has| |#1| (-831)) (|has| |#1| (-831)) (((|#2|) . T)) @@ -2233,12 +2233,12 @@ (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (|has| |#1| (-752)) ((((-832 |#1|) (-832 |#1|)) . T) (($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) ((((-377 |#2|)) . T)) (|has| |#1| (-777)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) . T) (((-517) (-517)) . T) (($ $) . T)) ((((-832 |#1|)) . T) (($) . T) (((-377 (-517))) . T)) (((|#2|) |has| |#2| (-961)) (((-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-961)))) @@ -2247,25 +2247,25 @@ (|has| |#1| (-134)) (|has| |#1| (-132)) (((|#2|) . T)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) -((((-51)) . T) (((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) +((((-51)) . T) (((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) (|has| |#1| (-319)) ((((-517)) . T)) ((((-787)) . T)) ((((-1141 |#1| |#2| |#3| |#4|) $) |has| (-1141 |#1| |#2| |#3| |#4|) (-258 (-1141 |#1| |#2| |#3| |#4|) (-1141 |#1| |#2| |#3| |#4|)))) (|has| |#1| (-333)) ((((-989) |#1|) . T) (((-989) $) . T) (($ $) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) ((((-377 (-517)) (-377 (-517))) . T) (((-632) (-632)) . T) (($ $) . T)) ((((-286 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-377 (-517))) |has| |#1| (-333))) (|has| |#1| (-1003)) (((|#1|) . T)) -(((|#1|) -3763 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) -(((|#1|) -3763 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) +(((|#1|) -3782 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) +(((|#1|) -3782 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) (((|#2|) . T)) ((((-377 (-517))) . T) (((-632)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2284,7 +2284,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-517)) . T)) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2321,7 +2321,7 @@ (|has| |#2| (-937)) ((($) . T)) (|has| |#1| (-831)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2329,24 +2329,24 @@ ((($) . T)) (|has| |#1| (-333)) ((((-832 |#1|)) . T)) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) -(-3763 (|has| |#1| (-338)) (|has| |#1| (-779))) +(-3782 (|has| |#1| (-338)) (|has| |#1| (-779))) (((|#1|) . T)) ((((-787)) . T)) ((((-1074)) -12 (|has| |#1| (-15 * (|#1| (-377 (-517)) |#1|))) (|has| |#1| (-822 (-1074))))) ((((-377 |#2|) |#3|) . T)) ((($) . T) (((-377 (-517))) . T)) ((((-703) |#1|) . T)) -(((|#2| (-214 (-2210 |#1|) (-703))) . T)) +(((|#2| (-214 (-2290 |#1|) (-703))) . T)) (((|#1| (-489 |#3|)) . T)) ((((-377 (-517))) . T)) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((((-787)) . T)) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))))) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) |has| (-2 (|:| -3458 (-1074)) (|:| -1338 (-51))) (-280 (-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))))) (|has| |#1| (-831)) (|has| |#2| (-333)) -(-3763 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((((-153 (-349))) . T) (((-199)) . T) (((-349)) . T)) ((((-787)) . T)) (((|#1|) . T)) @@ -2363,11 +2363,11 @@ (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-37 (-377 (-517)))) (-12 (|has| |#1| (-502)) (|has| |#1| (-760))) ((((-787)) . T)) -((((-1074)) -3763 (-12 (|has| |#1| (-15 * (|#1| (-517) |#1|))) (|has| |#1| (-822 (-1074)))) (-12 (|has| |#1| (-333)) (|has| |#2| (-822 (-1074)))))) +((((-1074)) -3782 (-12 (|has| |#1| (-15 * (|#1| (-517) |#1|))) (|has| |#1| (-822 (-1074)))) (-12 (|has| |#1| (-333)) (|has| |#2| (-822 (-1074)))))) (|has| |#1| (-333)) ((((-1074)) -12 (|has| |#1| (-15 * (|#1| (-377 (-517)) |#1|))) (|has| |#1| (-822 (-1074))))) (|has| |#1| (-333)) @@ -2377,7 +2377,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-333))) (((|#2|) |has| |#1| (-333))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-156))) (((|#1|) . T)) @@ -2400,31 +2400,31 @@ (((|#2|) |has| |#1| (-333))) ((((-349)) -12 (|has| |#1| (-333)) (|has| |#2| (-808 (-349)))) (((-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-808 (-517))))) (|has| |#1| (-333)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (|has| |#1| (-333)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) (|has| |#1| (-333)) (|has| |#1| (-509)) (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) (((|#3|) . T)) (((|#1|) . T)) -(-3763 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) (((|#2|) . T)) (((|#2|) . T)) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (|has| |#1| (-37 (-377 (-517)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) ((((-1057) |#1|) . T)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-338))) (|has| |#1| (-134)) ((((-530 |#1|)) . T)) ((($) . T)) @@ -2432,7 +2432,7 @@ (|has| |#1| (-509)) (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-37 (-377 (-517)))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-319))) (|has| |#1| (-134)) ((((-787)) . T)) ((($) . T)) @@ -2457,7 +2457,7 @@ (|has| |#1| (-723)) (|has| |#1| (-723)) ((((-493)) |has| |#1| (-558 (-493)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) ((((-109)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2476,7 +2476,7 @@ (((|#2|) . T)) ((((-517)) . T)) ((((-517)) . T)) -(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) +(-3782 (|has| |#2| (-725)) (|has| |#2| (-777))) ((((-153 (-349))) . T) (((-199)) . T) (((-349)) . T)) ((((-787)) . T)) ((((-787)) . T)) @@ -2488,9 +2488,9 @@ (((|#1|) . T) (($) . T) (((-377 (-517))) . T)) (|has| |#1| (-333)) (|has| |#1| (-333)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003))) (|has| |#1| (-1050)) ((((-517) |#1|) . T)) (((|#1|) . T)) @@ -2508,8 +2508,8 @@ (((|#1|) . T)) (|has| |#1| (-509)) ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) ((((-349)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2518,7 +2518,7 @@ (|has| |#1| (-509)) (|has| |#1| (-1003)) ((((-712 |#1| (-789 |#2|))) |has| (-712 |#1| (-789 |#2|)) (-280 (-712 |#1| (-789 |#2|))))) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-831)) @@ -2528,12 +2528,12 @@ (|has| |#1| (-207)) (((|#1| (-489 (-993 (-1074)))) . T)) (|has| |#2| (-333)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) ((((-787)) . T)) ((((-787)) . T)) -(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) +(-3782 (|has| |#3| (-725)) (|has| |#3| (-777))) ((((-787)) . T)) ((((-787)) . T)) (((|#1|) . T)) @@ -2542,8 +2542,8 @@ ((((-517)) . T)) (((|#3|) . T)) ((((-787)) . T)) -(-3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) -(-3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) +(-3782 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((((-530 |#1|) (-530 |#1|)) . T) (($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) (((|#1|) |has| |#1| (-156))) @@ -2556,27 +2556,27 @@ (((|#1|) . T)) ((((-265 |#3|)) . T)) (((|#1|) . T)) -((((-377 (-517)) (-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2| |#2|) . 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T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($ $) -3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((((-787)) . T)) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (|has| |#2| (-831)) (|has| |#1| (-831)) -((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#1|) . T)) -((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) +((((-2 (|:| -3458 (-1057)) (|:| -1338 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2590,10 +2590,10 @@ (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) ((((-377 (-517)) (-377 (-517))) . T)) ((((-377 (-517))) . T)) -(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) (((|#1|) . T)) (((|#1|) . T)) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((((-493)) . T)) ((((-787)) . T)) ((((-1074)) |has| |#2| (-822 (-1074))) (((-989)) . T)) @@ -2607,12 +2607,12 @@ ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) ((((-1074)) |has| |#1| (-822 (-1074)))) ((((-832 |#1|)) . T) (((-377 (-517))) . T) (($) . T)) -((($) . T) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) -((((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3763 (|has| |#1| (-156)) (|has| |#1| (-509)))) +((($) . T) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) +((((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3782 (|has| |#1| (-156)) (|has| |#1| (-509)))) ((($) . T) (((-377 (-517))) . T)) (((|#1|) . T) (((-377 (-517))) . T) (((-517)) . T) (($) . T)) (((|#2|) |has| |#2| (-961)) (((-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-961)))) -((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T) (($) -3763 (|has| |#1| (-156)) (|has| |#1| (-509)))) +((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T) (($) -3782 (|has| |#1| (-156)) (|has| |#1| (-509)))) (|has| |#1| (-509)) (((|#1|) |has| |#1| (-333))) ((((-517)) . T)) @@ -2631,8 +2631,8 @@ ((((-787)) . T)) (|has| |#2| (-752)) (|has| |#2| (-752)) -((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#2|) |has| |#1| (-333)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) . T)) +((((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#2|) |has| |#1| (-333)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-377 (-517))) -3782 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) ((((-517)) |has| |#1| (-808 (-517))) (((-349)) |has| |#1| (-808 (-349)))) @@ -2658,12 +2658,12 @@ (((|#2| (-703)) . T)) ((((-1074)) . T)) ((((-794 |#1|)) . 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T)) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) ((((-493)) |has| |#2| (-558 (-493))) (((-814 (-349))) |has| |#2| (-558 (-814 (-349)))) (((-814 (-517))) |has| |#2| (-558 (-814 (-517))))) ((((-787)) . T)) ((((-787)) . T)) @@ -2722,11 +2722,11 @@ ((((-377 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1003)) -(((|#2| (-450 (-2210 |#1|) (-703))) . T)) +(((|#2| (-450 (-2290 |#1|) (-703))) . T)) ((((-517) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-489 (-1074))) . T)) -(-3763 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((((-517)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2736,9 +2736,9 @@ ((($) . T) (((-377 (-517))) . T)) ((($) . T)) ((($) . T)) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) (((|#1|) . 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T)) -(-3763 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) -(-3763 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-123)) (|has| |#2| (-123))) (-12 (|has| |#1| (-725)) (|has| |#2| (-725)))) +(-3782 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-123)) (|has| |#2| (-123))) (-12 (|has| |#1| (-725)) (|has| |#2| (-725)))) ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) ((($) . T) (((-794 |#1|)) . T) (((-377 (-517))) . T)) ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) @@ -2929,15 +2929,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-377 |#2|)) . 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T)) (((|#2| |#2|) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) ((((-517)) . T)) @@ -2966,32 +2966,32 @@ ((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) ((((-1074)) . T) (((-787)) . T)) (|has| |#1| (-333)) -((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) +((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) . T)) -((($) -3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) -((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) ((((-1007)) . T)) ((((-787)) . T)) ((($) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T)) ((($) . T)) -((($) -3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) +((($) -3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (|has| |#2| (-831)) (|has| |#1| (-831)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-156))) ((((-632)) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (((|#1|) |has| |#1| (-156))) (((|#1|) |has| |#1| (-156))) ((((-377 (-517))) . T) (($) . T)) (((|#1| (-517)) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-333)) (|has| |#1| (-333)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) -(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-156)) (|has| |#1| (-509))) (((|#1| (-517)) . T)) (((|#1| (-377 (-517))) . T)) (((|#1| (-703)) . T)) @@ -3006,16 +3006,16 @@ ((((-814 (-349))) . T) (((-814 (-517))) . T) (((-1074)) . T) (((-493)) . T)) (((|#1|) . T)) ((((-787)) . T)) -(-3763 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) -(-3763 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-123)) (|has| |#2| (-123))) (-12 (|has| |#1| (-725)) (|has| |#2| (-725)))) +(-3782 (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-123)) (|has| |#2| (-123))) (-12 (|has| |#1| (-725)) (|has| |#2| (-725)))) ((((-517)) . T)) ((((-517)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) +(-3782 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) ((((-1074)) -12 (|has| |#2| (-822 (-1074))) (|has| |#2| (-961)))) -(-3763 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) (-12 (|has| |#1| (-659)) (|has| |#2| (-659)))) +(-3782 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) (-12 (|has| |#1| (-659)) (|has| |#2| (-659)))) (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-333)) @@ -3039,7 +3039,7 @@ ((((-1057) (-1074) (-517) (-199) (-787)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3763 (|has| |#1| (-319)) (|has| |#1| (-338))) +(-3782 (|has| |#1| (-319)) (|has| |#1| (-338))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-787)) . T)) @@ -3047,7 +3047,7 @@ ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) (((|#2|) |has| |#2| (-1003)) (((-517)) -12 (|has| |#2| (-952 (-517))) (|has| |#2| (-1003))) (((-377 (-517))) -12 (|has| |#2| (-952 (-377 (-517)))) (|has| |#2| (-1003)))) ((((-493)) |has| |#1| (-558 (-493)))) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) ((($) . T) (((-377 (-517))) . T)) (|has| |#1| (-831)) (|has| |#1| (-831)) @@ -3056,10 +3056,10 @@ ((((-787)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-156))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-777))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-509))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-777))) (((|#2|) . T)) -(-3763 (|has| |#1| (-21)) (|has| |#1| (-777))) +(-3782 (|has| |#1| (-21)) (|has| |#1| (-777))) (((|#1|) |has| |#1| (-156))) (((|#1|) . T)) (((|#1|) . T)) @@ -3074,17 +3074,17 @@ (((|#1|) . T) (((-377 (-517))) . T) (((-517)) . T) (($) . T)) ((((-517) (-517)) . T)) ((($) . T) (((-377 (-517))) . T)) -(-3763 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) -(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) +(-3782 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) +(-3782 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) (|has| |#4| (-725)) -(-3763 (|has| |#4| (-725)) (|has| |#4| (-777))) +(-3782 (|has| |#4| (-725)) (|has| |#4| (-777))) (|has| |#4| (-777)) (|has| |#3| (-725)) -(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) +(-3782 (|has| |#3| (-725)) (|has| |#3| (-777))) (|has| |#3| (-777)) ((((-517)) . T)) (((|#2|) . T)) -((((-1074)) -3763 (-12 (|has| (-1072 |#1| |#2| |#3|) (-822 (-1074))) (|has| |#1| (-333))) (-12 (|has| |#1| (-15 * (|#1| (-517) |#1|))) (|has| |#1| (-822 (-1074)))))) +((((-1074)) -3782 (-12 (|has| (-1072 |#1| |#2| |#3|) (-822 (-1074))) (|has| |#1| (-333))) (-12 (|has| |#1| (-15 * (|#1| (-517) |#1|))) (|has| |#1| (-822 (-1074)))))) ((((-1074)) -12 (|has| |#1| (-15 * (|#1| (-377 (-517)) |#1|))) (|has| |#1| (-822 (-1074))))) ((((-1074)) -12 (|has| |#1| (-15 * (|#1| (-703) |#1|))) (|has| |#1| (-822 (-1074))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3099,11 +3099,11 @@ ((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) ((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) ((((-1039 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) ((($) . T)) (|has| |#1| (-937)) -(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) ((((-787)) . T)) ((((-493)) |has| |#2| (-558 (-493))) (((-814 (-517))) |has| |#2| (-558 (-814 (-517)))) (((-814 (-349))) |has| |#2| (-558 (-814 (-349)))) (((-349)) |has| |#2| (-937)) (((-199)) |has| |#2| (-937))) ((((-1074) (-51)) . T)) @@ -3115,15 +3115,15 @@ ((((-1072 |#1| |#2| |#3|)) . T)) ((((-1072 |#1| |#2| |#3|)) . T) (((-1065 |#1| |#2| |#3|)) . T)) ((((-787)) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) ((((-517) |#1|) . T)) ((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-333)) -(((|#3|) . T) ((|#2|) . T) (($) -3763 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) ((|#4|) -3763 (|has| |#4| (-156)) (|has| |#4| (-333)) (|has| |#4| (-961)))) -(((|#2|) . T) (($) -3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-961)))) +(((|#3|) . T) ((|#2|) . T) (($) -3782 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) ((|#4|) -3782 (|has| |#4| (-156)) (|has| |#4| (-333)) (|has| |#4| (-961)))) +(((|#2|) . T) (($) -3782 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((|#3|) -3782 (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-961)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-333)) @@ -3135,37 +3135,37 @@ ((((-787)) . T)) ((((-787)) . T)) (((|#1|) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) ((((-517) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-333)) (|has| |#2| (-258 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-831))) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-831))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) ((((-787)) . T)) ((((-787)) . T)) ((((-787)) . T)) (((|#1| (-489 |#2|)) . T)) -((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) +((((-2 (|:| -3458 (-1074)) (|:| -1338 (-51)))) . T)) (((|#1| (-517)) . T)) (((|#1| (-377 (-517))) . T)) (((|#1| (-703)) . T)) ((((-111 |#1|)) . T) (($) . T) (((-377 (-517))) . T)) -(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) -(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) +(-3782 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) +(-3782 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((($) . T)) (((|#2| (-489 (-789 |#1|))) . T)) ((((-517) |#1|) . T)) (((|#2|) . T)) (((|#2| (-703)) . T)) -((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) +((((-787)) -3782 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1057) |#1|) . T)) ((((-377 |#2|)) . T)) -((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) +((((-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) . T)) (|has| |#1| (-509)) (|has| |#1| (-509)) ((($) . T) ((|#2|) . T)) @@ -3173,12 +3173,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-258 |#2| |#2|))) (((|#1| (-583 |#1|)) |has| |#1| (-777))) -(-3763 (|has| |#1| (-207)) (|has| |#1| (-319))) -(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-207)) (|has| |#1| (-319))) +(-3782 (|has| |#1| (-333)) (|has| |#1| (-319))) (|has| |#1| (-1003)) (((|#1|) . T)) ((((-377 (-517))) . T) (($) . T)) -((((-915 |#1|)) . T) ((|#1|) . T) (((-517)) -3763 (|has| (-915 |#1|) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) -3763 (|has| (-915 |#1|) (-952 (-377 (-517)))) (|has| |#1| (-952 (-377 (-517)))))) +((((-915 |#1|)) . T) ((|#1|) . T) (((-517)) -3782 (|has| (-915 |#1|) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) -3782 (|has| (-915 |#1|) (-952 (-377 (-517)))) (|has| |#1| (-952 (-377 (-517)))))) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) @@ -3189,9 +3189,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) ((((-1039 |#1| |#2|) (-1039 |#1| |#2|)) |has| (-1039 |#1| |#2|) (-280 (-1039 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))) |has| (-2 (|:| -3458 |#1|) (|:| -1338 |#2|)) (-280 (-2 (|:| -3458 |#1|) (|:| -1338 |#2|))))) ((((-111 |#1|)) |has| (-111 |#1|) (-280 (-111 |#1|)))) -(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) +(-3782 (|has| |#1| (-779)) (|has| |#1| (-1003))) ((($ $) . T)) ((($ $) . T) (((-789 |#1|) $) . T) (((-789 |#1|) |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-207)) ((|#2| |#1|) |has| |#1| (-207)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 7224bcf6..110eba09 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,3 +1,3 @@ -(30 . 3404130409) -(4186 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| |AlgebraicallyClosedField&| |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AlgebraicFunction| |Aggregate&| |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate| |Algebra&| |Algebra| |AlgFactor| |AlgebraicFunctionField| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraPackage| |AlgebraGivenByStructuralConstants| |AssociationList| |AbelianMonoidRing&| |AbelianMonoidRing| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |AnyFunctions1| |Any| |ApplyUnivariateSkewPolynomial| |ApplyRules| |TwoDimensionalArrayCategory&| |TwoDimensionalArrayCategory| |OneDimensionalArrayFunctions2| |OneDimensionalArray| |TwoDimensionalArray| |Asp10| |Asp12| |Asp19| |Asp1| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp41| |Asp42| |Asp49| |Asp4| |Asp50| |Asp55| |Asp6| |Asp73| |Asp74| |Asp77| |Asp78| |Asp7| |Asp80| |Asp8| |Asp9| |AssociatedEquations| |ArrayStack| |ArcTrigonometricFunctionCategory&| |ArcTrigonometricFunctionCategory| |AttributeButtons| |AttributeRegistry| |Automorphism| |BalancedFactorisation| |BasicType&| |BasicType| |BalancedBinaryTree| |BezoutMatrix| |BasicFunctions| |BagAggregate&| |BagAggregate| |BinaryExpansion| |BinaryFile| |Bits| |BiModule| |Boolean| |BasicOperatorFunctions1| |BasicOperator| |BoundIntegerRoots| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| |BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate| |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| |BinaryTree| |CancellationAbelianMonoid| |CachableSet| |CardinalNumber| |CartesianTensorFunctions2| |CartesianTensor| |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory| |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage| |CharacteristicZero| |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| |ComplexRootPackage| |Color| |CombinatorialFunction| |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| |CommonOperators| |CommuteUnivariatePolynomialCategory| |ComplexCategory&| |ComplexCategory| |ComplexFactorization| |ComplexFunctions2| |Complex| |ComplexPattern| |SubSpaceComponentProperty| |CommutativeRing| |ContinuedFraction| |CoordinateSystems| 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|DifferentialRing&| |DifferentialRing| |DictionaryOperations&| |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| |DirectProductCategory| |DirectProductFunctions2| |DirectProduct| |DisplayPackage| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |Domain| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| |DrawOptionFunctions1| |DrawOption| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| |EntireRing| |EigenPackage| |EquationFunctions2| |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |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| |FiniteField| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| |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| |Factored| |FactoredFunctionUtilities| |FunctionSpaceToExponentialExpansion| |FunctionSpaceFunctions2| |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregateFunctions2| |FiniteSetAggregate&| |FiniteSetAggregate| |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| |FunctionSpace&| |FunctionSpace| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| |FunctionSpaceUnivariatePolynomialFactor| |FortranTemplate| |FortranType| |FunctionCalled| |FortranVectorCategory| |FortranVectorFunctionCategory| |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| |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| |HashTable| |HallBasis| |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousAggregate| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |InnerNormalBasisFieldFunctions| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |Infinity| |InputFormFunctions1| |InputForm| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |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| |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| |IntegrationResultToFunction| |IntegrationResultFunctions2| |IntegrationResult| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| |InternalRationalUnivariateRepresentationPackage| |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| |CoercibleTo| |ConvertibleTo| |Kovacic| |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| |ListFunctions3| |List| |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| |LinearAggregate| |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| |ListAggregate| |LinearSystemMatrixPackage1| |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| |LieSquareMatrix| |LyndonWord| |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| |Magma| |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategoryFunctions2| |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| |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| |NoneFunctions1| |None| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| |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| |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrdSetInts| |OutputForm| |OutputPackage| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResultFunctions2| |PatternMatchResult| |PatternFunctions1| |PatternFunctions2| |Pattern| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |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| |FunctionSpaceAttachPredicates| |AttachPredicates| |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| 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|TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RandomFloatDistributions| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunction| |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| |RegularTriangularSetGcdPackage| |RuleCalled| |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtensionAlgFactor| |SimpleAlgebraicExtension| |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| |SortedCache| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |SegmentFunctions2| |SegmentBindingFunctions2| |SegmentBinding| |SegmentCategory| |Segment| |SegmentExpansionCategory| |SetAggregate&| |SetAggregate| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |Set| |SExpressionCategory| |SExpression| |SExpressionOf| |SimpleFortranProgram| |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| 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|SubSpace| |SuchThat| |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemSolvePackage| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| |TriangularMatrixOperations| |TranscendentalManipulations| |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| |UnivariateTaylorSeriesODESolver| |UTSodetools| |Variable| |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| |TwoDimensionalViewport| |ThreeDimensionalViewport| |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| |Union| |Category| |ranges| |paren| |shade| |alphabetic?| |yRange| |rename!| 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|SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |Syntax| |SystemSolvePackage| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| |TriangularMatrixOperations| |TranscendentalManipulations| |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UnivariateLaurentSeriesFunctions2| 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|failed?| |LiePolyIfCan| |wreath| |factorSFBRlcUnit| |removeRoughlyRedundantFactorsInPols| |insertionSort!| |var1StepsDefault| |fixedPoint| |entries| |associator| |comment| |toseSquareFreePart| |decreasePrecision| |knownInfBasis| |rootRadius| |besselJ| |setLabelValue| |besselK| |zeroMatrix| |OMgetAttr| |omError| |FormatRoman| |tanQ| |createPrimitiveNormalPoly| |repSq| |charpol| |setvalue!| |makeCrit| |mesh?| |diagonalMatrix| |subresultantVector| |bitTruth| |monic?| |super| |patternMatch| |preprocess| |orbits| |permutationGroup| |rootNormalize| |getMeasure| |rightRegularRepresentation| |critMTonD1| |shiftRight| |B1solve| |trunc| |asechIfCan| |monicModulo| |printTypes| |lifting| |att2Result| |legendreP| |hasHi| |cfirst| |subset?| |nextLatticePermutation| |ode2| |addPoint| |nonLinearPart| |divideIfCan!| |romberg| |llprop| |float| |aQuartic| |subscript| |computeInt| |factor1| |reduceLODE| |rightGcd| |subResultantChain| |cyclicEqual?| |double| |indiceSubResultantEuclidean| |setfirst!| 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(-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-33) . 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T) ((-37 |#2|) |has| |#2| (-156)) ((-97) -3782 (|has| |#2| (-1003)) (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-106 |#2| |#2|) -3782 (|has| |#2| (-961)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-106 $ $) |has| |#2| (-156)) ((-123) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123))) ((-557 (-787)) -3782 (|has| |#2| (-1003)) (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-557 (-787))) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-557 (-1154 |#2|)) . T) ((-156) |has| |#2| (-156)) ((-205 |#2|) |has| |#2| (-961)) ((-207) -12 (|has| |#2| (-207)) (|has| |#2| (-961))) ((-258 (-517) |#2|) . T) ((-260 (-517) |#2|) . T) ((-280 |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) ((-338) |has| |#2| (-338)) ((-347 |#2|) |has| |#2| (-961)) ((-381 |#2|) |has| |#2| (-1003)) ((-456 |#2|) . T) ((-550 (-517) |#2|) . T) ((-478 |#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) ((-585 |#2|) -3782 (|has| |#2| (-961)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-585 $) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-579 (-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-961))) ((-579 |#2|) |has| |#2| (-961)) ((-650 |#2|) -3782 (|has| |#2| (-333)) (|has| |#2| (-156))) ((-659) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-723) |has| |#2| (-777)) ((-724) -3782 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-725) |has| |#2| (-725)) ((-726) -3782 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-727) -3782 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-777) |has| |#2| (-777)) ((-779) -3782 (|has| |#2| (-777)) (|has| |#2| (-725))) ((-822 (-1074)) -12 (|has| |#2| (-822 (-1074))) (|has| |#2| (-961))) ((-952 (-377 (-517))) -12 (|has| |#2| (-952 (-377 (-517)))) (|has| |#2| (-1003))) ((-952 (-517)) -12 (|has| |#2| (-952 (-517))) (|has| |#2| (-1003))) ((-952 |#2|) |has| |#2| (-1003)) ((-967 |#2|) -3782 (|has| |#2| (-961)) (|has| |#2| (-333)) (|has| |#2| (-156))) ((-967 $) |has| |#2| (-156)) ((-961) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-968) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1015) -3782 (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-156))) ((-1003) -3782 (|has| |#2| (-1003)) (|has| |#2| (-961)) (|has| |#2| (-777)) (|has| |#2| (-725)) (|has| |#2| (-338)) (|has| |#2| (-333)) (|has| |#2| (-156)) (|has| |#2| (-123)) (|has| |#2| (-25))) ((-1109) . T) ((-1161 |#2|) |has| |#2| (-333))) +((-3014 (((-214 |#1| |#3|) (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 21)) (-1292 ((|#3| (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|) 23)) (-1939 (((-214 |#1| |#3|) (-1 |#3| |#2|) (-214 |#1| |#2|)) 18))) +(((-213 |#1| |#2| |#3|) (-10 -7 (-15 -3014 ((-214 |#1| |#3|) (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|)) (-15 -1292 (|#3| (-1 |#3| |#2| |#3|) (-214 |#1| |#2|) |#3|)) (-15 -1939 ((-214 |#1| |#3|) (-1 |#3| |#2|) (-214 |#1| |#2|)))) (-703) (-1109) (-1109)) (T -213)) +((-1939 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1109)) (-4 *7 (-1109)) (-5 *2 (-214 *5 *7)) (-5 *1 (-213 *5 *6 *7)))) (-1292 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-214 *5 *6)) (-14 *5 (-703)) (-4 *6 (-1109)) (-4 *2 (-1109)) (-5 *1 (-213 *5 *6 *2)))) (-3014 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-214 *6 *7)) (-14 *6 (-703)) (-4 *7 (-1109)) (-4 *5 (-1109)) (-5 *2 (-214 *6 *5)) (-5 *1 (-213 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-296 |#1| |#4|) . T) ((-347 |#1|) . T) ((-381 |#1|) . T) ((-421) -3763 (|has| |#1| (-831)) (|has| |#1| (-421))) ((-478 |#2| |#1|) |has| |#1| (-207)) ((-478 |#2| $) |has| |#1| (-207)) ((-478 |#3| |#1|) . T) ((-478 |#3| $) . T) ((-478 $ $) . T) ((-509) -3763 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-585 (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-585 |#1|) . T) ((-585 $) . T) ((-579 (-517)) |has| |#1| (-579 (-517))) ((-579 |#1|) . T) ((-650 (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-650 |#1|) |has| |#1| (-156)) ((-650 $) -3763 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-659) . T) ((-779) |has| |#1| (-779)) ((-822 (-1074)) |has| |#1| (-822 (-1074))) ((-822 |#3|) . T) ((-808 (-349)) -12 (|has| |#1| (-808 (-349))) (|has| |#3| (-808 (-349)))) ((-808 (-517)) -12 (|has| |#1| (-808 (-517))) (|has| |#3| (-808 (-517)))) ((-871 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| |#4|) . T) ((-25) . T) ((-37 (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-37 |#1|) |has| |#1| (-156)) ((-37 $) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-97) . T) ((-106 (-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-106 |#1| |#1|) . T) ((-106 $ $) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421)) (|has| |#1| (-156))) ((-123) . T) ((-132) |has| |#1| (-132)) ((-134) |has| |#1| (-134)) ((-557 (-787)) . T) ((-156) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421)) (|has| |#1| (-156))) ((-558 (-493)) -12 (|has| |#1| (-558 (-493))) (|has| |#3| (-558 (-493)))) ((-558 (-814 (-349))) -12 (|has| |#1| (-558 (-814 (-349)))) (|has| |#3| (-558 (-814 (-349))))) ((-558 (-814 (-517))) -12 (|has| |#1| (-558 (-814 (-517)))) (|has| |#3| (-558 (-814 (-517))))) ((-205 |#1|) . T) ((-207) |has| |#1| (-207)) ((-262) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-280 $) . T) ((-296 |#1| |#4|) . T) ((-347 |#1|) . T) ((-381 |#1|) . T) ((-421) -3782 (|has| |#1| (-831)) (|has| |#1| (-421))) ((-478 |#2| |#1|) |has| |#1| (-207)) ((-478 |#2| $) |has| |#1| (-207)) ((-478 |#3| |#1|) . T) ((-478 |#3| $) . T) ((-478 $ $) . T) ((-509) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-585 (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-585 |#1|) . T) ((-585 $) . T) ((-579 (-517)) |has| |#1| (-579 (-517))) ((-579 |#1|) . T) ((-650 (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((-650 |#1|) |has| |#1| (-156)) ((-650 $) -3782 (|has| |#1| (-831)) (|has| |#1| (-509)) (|has| |#1| (-421))) ((-659) . T) ((-779) |has| |#1| (-779)) ((-822 (-1074)) |has| |#1| (-822 (-1074))) ((-822 |#3|) . T) ((-808 (-349)) -12 (|has| |#1| (-808 (-349))) (|has| |#3| (-808 (-349)))) ((-808 (-517)) -12 (|has| |#1| (-808 (-517))) (|has| |#3| (-808 (-517)))) ((-871 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-46 |#1| (-517)) . T) ((-25) . T) ((-37 (-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-37 |#1|) |has| |#1| (-156)) ((-37 |#2|) |has| |#1| (-333)) ((-37 $) -3763 (|has| |#1| (-509)) (|has| |#1| (-333))) ((-34) |has| |#1| (-37 (-377 (-517)))) ((-91) |has| |#1| (-37 (-377 (-517)))) ((-97) . T) ((-106 (-377 (-517)) (-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-106 |#1| |#1|) . T) ((-106 |#2| |#2|) |has| |#1| (-333)) ((-106 $ $) -3763 (|has| |#1| (-509)) (|has| |#1| (-333)) (|has| |#1| (-156))) ((-123) . T) ((-132) -3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-132))) (|has| |#1| (-132))) ((-134) -3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-134))) (|has| |#1| (-134))) ((-557 (-787)) . 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T) ((-585 |#2|) |has| |#1| (-333)) ((-585 $) . T) ((-579 (-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-579 (-517)))) ((-579 |#2|) |has| |#1| (-333)) ((-650 (-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-650 |#1|) |has| |#1| (-156)) ((-650 |#2|) |has| |#1| (-333)) ((-650 $) -3763 (|has| |#1| (-509)) (|has| |#1| (-333))) ((-659) . T) ((-723) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-724) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-726) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-727) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-752) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-777) -12 (|has| |#1| (-333)) (|has| |#2| (-752))) ((-779) -3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-779))) (-12 (|has| |#1| (-333)) (|has| |#2| (-752)))) ((-822 (-1074)) -3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-822 (-1074)))) (-12 (|has| |#1| (-15 * (|#1| (-517) |#1|))) (|has| |#1| (-822 (-1074))))) ((-808 (-349)) -12 (|has| |#1| (-333)) (|has| |#2| (-808 (-349)))) ((-808 (-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-808 (-517)))) ((-806 |#2|) |has| |#1| (-333)) ((-831) -12 (|has| |#1| (-333)) (|has| |#2| (-831))) ((-890 |#1| (-517) (-989)) . T) ((-842) |has| |#1| (-333)) ((-909 |#2|) |has| |#1| (-333)) ((-918) |has| |#1| (-37 (-377 (-517)))) ((-937) -12 (|has| |#1| (-333)) (|has| |#2| (-937))) ((-952 (-377 (-517))) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-517)))) ((-952 (-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-517)))) ((-952 (-1074)) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-1074)))) ((-952 |#2|) . T) ((-967 (-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-967 |#1|) . T) ((-967 |#2|) |has| |#1| (-333)) ((-967 $) -3763 (|has| |#1| (-509)) (|has| |#1| (-333)) (|has| |#1| (-156))) ((-961) . T) ((-968) . T) ((-1015) . T) ((-1003) . T) ((-1050) -12 (|has| |#1| (-333)) (|has| |#2| (-1050))) ((-1095) |has| |#1| (-37 (-377 (-517)))) ((-1098) |has| |#1| (-37 (-377 (-517)))) ((-1109) |has| |#1| (-333)) ((-1113) |has| |#1| (-333)) ((-1115 |#1|) . T) ((-1133 |#1| (-517)) . 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T) ((-23) . T) ((-46 |#1| (-517)) . T) ((-25) . T) ((-37 (-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-37 |#1|) |has| |#1| (-156)) ((-37 |#2|) |has| |#1| (-333)) ((-37 $) -3782 (|has| |#1| (-509)) (|has| |#1| (-333))) ((-34) |has| |#1| (-37 (-377 (-517)))) ((-91) |has| |#1| (-37 (-377 (-517)))) ((-97) . T) ((-106 (-377 (-517)) (-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-106 |#1| |#1|) . T) ((-106 |#2| |#2|) |has| |#1| (-333)) ((-106 $ $) -3782 (|has| |#1| (-509)) (|has| |#1| (-333)) (|has| |#1| (-156))) ((-123) . T) ((-132) -3782 (-12 (|has| |#1| (-333)) (|has| |#2| (-132))) (|has| |#1| (-132))) ((-134) -3782 (-12 (|has| |#1| (-333)) (|has| |#2| (-134))) (|has| |#1| (-134))) ((-557 (-787)) . 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T) ((-585 |#2|) |has| |#1| (-333)) ((-585 $) . T) ((-579 (-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-579 (-517)))) ((-579 |#2|) |has| |#1| (-333)) ((-650 (-377 (-517))) -3782 (|has| |#1| (-333)) (|has| |#1| (-37 (-377 (-517))))) ((-650 |#1|) |has| |#1| (-156)) ((-650 |#2|) |has| |#1| (-333)) ((-650 $) -3782 (|has| |#1| (-509)) (|has| |#1| (-333))) ((-659) . 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26)) (** (($ $ (-843)) NIL) (($ $ (-703)) 40)) (* (($ (-843) $) NIL) (($ (-703) $) NIL) (($ (-517) $) 32) (($ $ $) 31))) (((-1180 |#1|) (-13 (-156) (-338) (-558 (-517)) (-1050)) (-843)) (T -1180)) NIL (-13 (-156) (-338) (-558 (-517)) (-1050)) @@ -4852,4 +4852,4 @@ NIL NIL NIL NIL -((-1185 3125227 3125232 3125237 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3125212 3125217 3125222 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3125197 3125202 3125207 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3125182 3125187 3125192 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3125167 3125172 3125177 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1180 3124297 3125042 3125119 "ZMOD" 3125124 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1179 3123407 3123571 3123780 "ZLINDEP" 3124129 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1178 3112811 3114556 3116508 "ZDSOLVE" 3121556 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1177 3112057 3112198 3112387 "YSTREAM" 3112657 NIL YSTREAM (NIL T) -7 NIL NIL) (-1176 3109826 3111362 3111565 "XRPOLY" 3111900 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1175 3106296 3107625 3108203 "XPR" 3109294 NIL XPR (NIL T T) -8 NIL NIL) (-1174 3104010 3105631 3105834 "XPOLY" 3106127 NIL XPOLY (NIL T) -8 NIL NIL) (-1173 3101823 3103201 3103256 "XPOLYC" 3103541 NIL XPOLYC (NIL T T) -9 NIL 3103654) (-1172 3098197 3100342 3100729 "XPBWPOLY" 3101482 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1171 3094080 3096393 3096436 "XF" 3097057 NIL XF (NIL T) -9 NIL 3097453) (-1170 3093701 3093789 3093958 "XF-" 3093963 NIL XF- (NIL T T) -8 NIL NIL) (-1169 3089082 3090381 3090436 "XFALG" 3092584 NIL XFALG (NIL T T) -9 NIL 3093369) (-1168 3088219 3088323 3088527 "XEXPPKG" 3088974 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1167 3086317 3088070 3088165 "XDPOLY" 3088170 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1166 3085196 3085806 3085849 "XALG" 3085911 NIL XALG (NIL T) -9 NIL 3086029) (-1165 3078672 3083180 3083673 "WUTSET" 3084788 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1164 3076488 3077295 3077644 "WP" 3078456 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1163 3075374 3075572 3075867 "WFFINTBS" 3076285 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1162 3073278 3073705 3074167 "WEIER" 3074946 NIL WEIER (NIL T) -7 NIL NIL) (-1161 3072426 3072850 3072893 "VSPACE" 3073029 NIL VSPACE (NIL T) -9 NIL 3073103) (-1160 3072264 3072291 3072382 "VSPACE-" 3072387 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1159 3072010 3072053 3072124 "VOID" 3072215 T VOID (NIL) -8 NIL NIL) (-1158 3070146 3070505 3070911 "VIEW" 3071626 T VIEW (NIL) -7 NIL NIL) (-1157 3066571 3067209 3067946 "VIEWDEF" 3069431 T VIEWDEF (NIL) -7 NIL NIL) (-1156 3055910 3058119 3060292 "VIEW3D" 3064420 T VIEW3D (NIL) -8 NIL NIL) (-1155 3048192 3049821 3051400 "VIEW2D" 3054353 T VIEW2D (NIL) -8 NIL NIL) (-1154 3043601 3047962 3048054 "VECTOR" 3048135 NIL VECTOR (NIL T) -8 NIL NIL) (-1153 3042178 3042437 3042755 "VECTOR2" 3043331 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1152 3035727 3039973 3040017 "VECTCAT" 3041005 NIL VECTCAT (NIL T) -9 NIL 3041582) (-1151 3034741 3034995 3035385 "VECTCAT-" 3035390 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1150 3034222 3034392 3034512 "VARIABLE" 3034656 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1149 3033059 3033213 3033473 "UTSODETL" 3034049 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1148 3030499 3030959 3031483 "UTSODE" 3032600 NIL UTSODE (NIL T T) -7 NIL NIL) (-1147 3022349 3028141 3028628 "UTS" 3030069 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1146 3013654 3019016 3019059 "UTSCAT" 3020160 NIL UTSCAT (NIL T) -9 NIL 3020910) (-1145 3011010 3011725 3012713 "UTSCAT-" 3012718 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1144 3010641 3010684 3010815 "UTS2" 3010961 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1143 3004917 3007482 3007526 "URAGG" 3009596 NIL URAGG (NIL T) -9 NIL 3010317) (-1142 3001856 3002719 3003842 "URAGG-" 3003847 NIL URAGG- (NIL T T) -8 NIL NIL) (-1141 2997542 3000473 3000944 "UPXSSING" 3001520 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1140 2989438 2996665 2996944 "UPXS" 2997320 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1139 2982470 2989343 2989414 "UPXSCONS" 2989419 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1138 2972698 2979525 2979587 "UPXSCCA" 2980236 NIL UPXSCCA (NIL T T) -9 NIL 2980477) (-1137 2972337 2972422 2972595 "UPXSCCA-" 2972600 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1136 2962494 2969094 2969137 "UPXSCAT" 2969780 NIL UPXSCAT (NIL T) -9 NIL 2970381) (-1135 2961928 2962007 2962184 "UPXS2" 2962409 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1134 2960582 2960835 2961186 "UPSQFREE" 2961671 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1133 2954436 2957488 2957543 "UPSCAT" 2958692 NIL UPSCAT (NIL T T) -9 NIL 2959459) (-1132 2953650 2953854 2954177 "UPSCAT-" 2954182 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1131 2939729 2947726 2947769 "UPOLYC" 2949847 NIL UPOLYC (NIL T) -9 NIL 2951061) (-1130 2931122 2933526 2936651 "UPOLYC-" 2936656 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1129 2930753 2930796 2930927 "UPOLYC2" 2931073 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1128 2922212 2930322 2930459 "UP" 2930663 NIL UP (NIL NIL T) -8 NIL NIL) (-1127 2921555 2921662 2921825 "UPMP" 2922101 NIL UPMP (NIL T T) -7 NIL NIL) (-1126 2921108 2921189 2921328 "UPDIVP" 2921468 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1125 2919676 2919925 2920241 "UPDECOMP" 2920857 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1124 2918911 2919023 2919208 "UPCDEN" 2919560 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1123 2918434 2918503 2918650 "UP2" 2918836 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1122 2916963 2917649 2917921 "UNISEG" 2918197 NIL UNISEG (NIL T) -8 NIL NIL) (-1121 2916180 2916307 2916511 "UNISEG2" 2916807 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1120 2915240 2915420 2915646 "UNIFACT" 2915996 NIL UNIFACT (NIL T) -7 NIL NIL) (-1119 2899141 2914423 2914672 "ULS" 2915048 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1118 2887109 2899046 2899117 "ULSCONS" 2899122 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1117 2869813 2881823 2881885 "ULSCCAT" 2882597 NIL ULSCCAT (NIL T T) -9 NIL 2882892) (-1116 2868864 2869109 2869496 "ULSCCAT-" 2869501 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1115 2858815 2865329 2865372 "ULSCAT" 2866228 NIL ULSCAT (NIL T) -9 NIL 2866950) (-1114 2858249 2858328 2858505 "ULS2" 2858730 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1113 2856646 2857613 2857644 "UFD" 2857856 T UFD (NIL) -9 NIL 2857970) (-1112 2856440 2856486 2856581 "UFD-" 2856586 NIL UFD- (NIL T) -8 NIL NIL) (-1111 2855522 2855705 2855921 "UDVO" 2856246 T UDVO (NIL) -7 NIL NIL) (-1110 2853340 2853749 2854219 "UDPO" 2855087 NIL UDPO (NIL T) -7 NIL NIL) (-1109 2853272 2853277 2853308 "TYPE" 2853313 T TYPE (NIL) -9 NIL NIL) (-1108 2852243 2852445 2852685 "TWOFACT" 2853066 NIL TWOFACT (NIL T) -7 NIL NIL) (-1107 2851185 2851522 2851783 "TUPLE" 2852017 NIL TUPLE (NIL T) -8 NIL NIL) (-1106 2848876 2849395 2849934 "TUBETOOL" 2850668 T TUBETOOL (NIL) -7 NIL NIL) (-1105 2847725 2847930 2848171 "TUBE" 2848669 NIL TUBE (NIL T) -8 NIL NIL) (-1104 2842451 2846705 2846986 "TS" 2847478 NIL TS (NIL T) -8 NIL NIL) (-1103 2831155 2835247 2835344 "TSETCAT" 2840578 NIL TSETCAT (NIL T T T T) -9 NIL 2842108) (-1102 2825891 2827488 2829378 "TSETCAT-" 2829383 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1101 2820162 2821008 2821946 "TRMANIP" 2825031 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1100 2819603 2819666 2819829 "TRIMAT" 2820094 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1099 2817409 2817646 2818009 "TRIGMNIP" 2819352 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1098 2816928 2817041 2817072 "TRIGCAT" 2817285 T TRIGCAT (NIL) -9 NIL NIL) (-1097 2816597 2816676 2816817 "TRIGCAT-" 2816822 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1096 2813502 2815457 2815737 "TREE" 2816352 NIL TREE (NIL T) -8 NIL NIL) (-1095 2812775 2813303 2813334 "TRANFUN" 2813369 T TRANFUN (NIL) -9 NIL 2813435) (-1094 2812054 2812245 2812525 "TRANFUN-" 2812530 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1093 2811858 2811890 2811951 "TOPSP" 2812015 T TOPSP (NIL) -7 NIL NIL) (-1092 2811210 2811325 2811478 "TOOLSIGN" 2811739 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1091 2809871 2810387 2810626 "TEXTFILE" 2810993 T TEXTFILE (NIL) -8 NIL NIL) (-1090 2807736 2808250 2808688 "TEX" 2809455 T TEX (NIL) -8 NIL NIL) (-1089 2807517 2807548 2807620 "TEX1" 2807699 NIL TEX1 (NIL T) -7 NIL NIL) (-1088 2807165 2807228 2807318 "TEMUTL" 2807449 T TEMUTL (NIL) -7 NIL NIL) (-1087 2805319 2805599 2805924 "TBCMPPK" 2806888 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1086 2796977 2803237 2803294 "TBAGG" 2803694 NIL TBAGG (NIL T T) -9 NIL 2803905) (-1085 2792047 2793535 2795289 "TBAGG-" 2795294 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1084 2791431 2791538 2791683 "TANEXP" 2791936 NIL TANEXP (NIL T) -7 NIL NIL) (-1083 2784944 2791288 2791381 "TABLE" 2791386 NIL TABLE (NIL T T) -8 NIL NIL) (-1082 2784357 2784455 2784593 "TABLEAU" 2784841 NIL TABLEAU (NIL T) -8 NIL NIL) (-1081 2778965 2780185 2781433 "TABLBUMP" 2783143 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1080 2775428 2776123 2776906 "SYSSOLP" 2778216 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1079 2774010 2774258 2774563 "SYNTAX" 2775145 T SYNTAX (NIL) -8 NIL NIL) (-1078 2771144 2771752 2772390 "SYMTAB" 2773394 T SYMTAB (NIL) -8 NIL NIL) (-1077 2766393 2767295 2768278 "SYMS" 2770183 T SYMS (NIL) -8 NIL NIL) (-1076 2763632 2765859 2766085 "SYMPOLY" 2766201 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1075 2763152 2763227 2763349 "SYMFUNC" 2763544 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1074 2759130 2760389 2761211 "SYMBOL" 2762352 T SYMBOL (NIL) -8 NIL NIL) (-1073 2752669 2754358 2756078 "SWITCH" 2757432 T SWITCH (NIL) -8 NIL NIL) (-1072 2745904 2751498 2751799 "SUTS" 2752425 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1071 2737799 2745027 2745306 "SUPXS" 2745682 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1070 2729332 2737420 2737545 "SUP" 2737708 NIL SUP (NIL T) -8 NIL NIL) (-1069 2728491 2728618 2728835 "SUPFRACF" 2729200 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1068 2728116 2728175 2728286 "SUP2" 2728426 NIL SUP2 (NIL T T) -7 NIL NIL) (-1067 2726542 2726814 2727174 "SUMRF" 2727817 NIL SUMRF (NIL T) -7 NIL NIL) (-1066 2725863 2725928 2726125 "SUMFS" 2726464 NIL SUMFS (NIL T T) -7 NIL NIL) (-1065 2709804 2725046 2725295 "SULS" 2725671 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1064 2709126 2709329 2709469 "SUCH" 2709712 NIL SUCH (NIL T T) -8 NIL NIL) (-1063 2703053 2704065 2705023 "SUBSPACE" 2708214 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1062 2702485 2702575 2702738 "SUBRESP" 2702942 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1061 2695854 2697150 2698461 "STTF" 2701221 NIL STTF (NIL T) -7 NIL NIL) (-1060 2690027 2691147 2692294 "STTFNC" 2694754 NIL STTFNC (NIL T) -7 NIL NIL) (-1059 2681382 2683249 2685040 "STTAYLOR" 2688270 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1058 2674638 2681246 2681329 "STRTBL" 2681334 NIL STRTBL (NIL T) -8 NIL NIL) (-1057 2670029 2674593 2674624 "STRING" 2674629 T STRING (NIL) -8 NIL NIL) (-1056 2664887 2669372 2669403 "STRICAT" 2669462 T STRICAT (NIL) -9 NIL 2669524) (-1055 2657612 2662414 2663032 "STREAM" 2664304 NIL STREAM (NIL T) -8 NIL NIL) (-1054 2657122 2657199 2657343 "STREAM3" 2657529 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1053 2656104 2656287 2656522 "STREAM2" 2656935 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1052 2655792 2655844 2655937 "STREAM1" 2656046 NIL STREAM1 (NIL T) -7 NIL NIL) (-1051 2654808 2654989 2655220 "STINPROD" 2655608 NIL STINPROD (NIL T) -7 NIL NIL) (-1050 2654386 2654570 2654601 "STEP" 2654681 T STEP (NIL) -9 NIL 2654759) (-1049 2647941 2654285 2654362 "STBL" 2654367 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1048 2643113 2647160 2647204 "STAGG" 2647357 NIL STAGG (NIL T) -9 NIL 2647446) (-1047 2640815 2641417 2642289 "STAGG-" 2642294 NIL STAGG- (NIL T T) -8 NIL NIL) (-1046 2639013 2640585 2640677 "STACK" 2640758 NIL STACK (NIL T) -8 NIL NIL) (-1045 2631744 2637160 2637615 "SREGSET" 2638643 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1044 2624184 2625552 2627064 "SRDCMPK" 2630350 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1043 2617127 2621594 2621625 "SRAGG" 2622928 T SRAGG (NIL) -9 NIL 2623536) (-1042 2616144 2616399 2616778 "SRAGG-" 2616783 NIL SRAGG- (NIL T) -8 NIL NIL) (-1041 2610601 2615071 2615494 "SQMATRIX" 2615767 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1040 2604359 2607321 2608047 "SPLTREE" 2609947 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1039 2600349 2601015 2601661 "SPLNODE" 2603785 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1038 2599395 2599628 2599659 "SPFCAT" 2600103 T SPFCAT (NIL) -9 NIL NIL) (-1037 2598132 2598342 2598606 "SPECOUT" 2599153 T SPECOUT (NIL) -7 NIL NIL) (-1036 2597893 2597933 2598002 "SPADPRSR" 2598085 T SPADPRSR (NIL) -7 NIL NIL) (-1035 2589915 2591662 2591705 "SPACEC" 2596028 NIL SPACEC (NIL T) -9 NIL 2597844) (-1034 2588087 2589848 2589896 "SPACE3" 2589901 NIL SPACE3 (NIL T) -8 NIL NIL) (-1033 2586841 2587012 2587302 "SORTPAK" 2587893 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1032 2584897 2585200 2585618 "SOLVETRA" 2586505 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1031 2583908 2584130 2584404 "SOLVESER" 2584670 NIL SOLVESER (NIL T) -7 NIL NIL) (-1030 2579128 2580009 2581011 "SOLVERAD" 2582960 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1029 2574943 2575552 2576281 "SOLVEFOR" 2578495 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1028 2569242 2574294 2574391 "SNTSCAT" 2574396 NIL SNTSCAT (NIL T T T T) -9 NIL 2574466) (-1027 2563349 2567575 2567964 "SMTS" 2568933 NIL SMTS (NIL T T T) -8 NIL NIL) (-1026 2557759 2563238 2563314 "SMP" 2563319 NIL SMP (NIL T T) -8 NIL NIL) (-1025 2555918 2556219 2556617 "SMITH" 2557456 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1024 2548885 2553081 2553184 "SMATCAT" 2554524 NIL SMATCAT (NIL NIL T T T) -9 NIL 2555070) (-1023 2545826 2546649 2547826 "SMATCAT-" 2547831 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1022 2543545 2545062 2545106 "SKAGG" 2545367 NIL SKAGG (NIL T) -9 NIL 2545502) (-1021 2539603 2542649 2542927 "SINT" 2543289 T SINT (NIL) -8 NIL NIL) (-1020 2539375 2539413 2539479 "SIMPAN" 2539559 T SIMPAN (NIL) -7 NIL NIL) (-1019 2538213 2538434 2538709 "SIGNRF" 2539134 NIL SIGNRF (NIL T) -7 NIL NIL) (-1018 2537022 2537173 2537463 "SIGNEF" 2538042 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1017 2534714 2535168 2535673 "SHP" 2536564 NIL SHP (NIL T NIL) -7 NIL NIL) (-1016 2528573 2534615 2534691 "SHDP" 2534696 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1015 2528062 2528254 2528285 "SGROUP" 2528437 T SGROUP (NIL) -9 NIL 2528524) (-1014 2527832 2527884 2527988 "SGROUP-" 2527993 NIL SGROUP- (NIL T) -8 NIL NIL) (-1013 2524668 2525365 2526088 "SGCF" 2527131 T SGCF (NIL) -7 NIL NIL) (-1012 2519066 2524118 2524215 "SFRTCAT" 2524220 NIL SFRTCAT (NIL T T T T) -9 NIL 2524258) (-1011 2512526 2513541 2514675 "SFRGCD" 2518049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1010 2505692 2506763 2507947 "SFQCMPK" 2511459 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1009 2505314 2505403 2505513 "SFORT" 2505633 NIL SFORT (NIL T T) -8 NIL NIL) (-1008 2504459 2505154 2505275 "SEXOF" 2505280 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1007 2503593 2504340 2504408 "SEX" 2504413 T SEX (NIL) -8 NIL NIL) (-1006 2498369 2499058 2499154 "SEXCAT" 2502925 NIL SEXCAT (NIL T T T T T) -9 NIL 2503544) (-1005 2495549 2498303 2498351 "SET" 2498356 NIL SET (NIL T) -8 NIL NIL) (-1004 2493800 2494262 2494567 "SETMN" 2495290 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1003 2493407 2493533 2493564 "SETCAT" 2493681 T SETCAT (NIL) -9 NIL 2493765) (-1002 2493187 2493239 2493338 "SETCAT-" 2493343 NIL SETCAT- (NIL T) -8 NIL NIL) (-1001 2489574 2491648 2491692 "SETAGG" 2492562 NIL SETAGG (NIL T) -9 NIL 2492902) (-1000 2489032 2489148 2489385 "SETAGG-" 2489390 NIL SETAGG- (NIL T T) -8 NIL NIL) (-999 2488242 2488535 2488595 "SEGXCAT" 2488878 NIL SEGXCAT (NIL T T) -9 NIL 2488997) (-998 2487308 2487918 2488094 "SEG" 2488099 NIL SEG (NIL T) -8 NIL NIL) (-997 2486225 2486438 2486480 "SEGCAT" 2487053 NIL SEGCAT (NIL T) -9 NIL 2487291) (-996 2485289 2485617 2485812 "SEGBIND" 2486063 NIL SEGBIND (NIL T) -8 NIL NIL) (-995 2484921 2484978 2485087 "SEGBIND2" 2485226 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-994 2484158 2484281 2484479 "SEG2" 2484769 NIL SEG2 (NIL T T) -7 NIL NIL) (-993 2483597 2484095 2484140 "SDVAR" 2484145 NIL SDVAR (NIL T) -8 NIL NIL) (-992 2475903 2483376 2483500 "SDPOL" 2483505 NIL SDPOL (NIL T) -8 NIL NIL) (-991 2474502 2474768 2475085 "SCPKG" 2475618 NIL SCPKG (NIL T) -7 NIL NIL) (-990 2473729 2473862 2474039 "SCACHE" 2474357 NIL SCACHE (NIL T) -7 NIL NIL) (-989 2473172 2473493 2473576 "SAOS" 2473666 T SAOS (NIL) -8 NIL NIL) (-988 2472740 2472775 2472946 "SAERFFC" 2473131 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-987 2466636 2472639 2472717 "SAE" 2472722 NIL SAE (NIL T T NIL) -8 NIL NIL) (-986 2466232 2466267 2466424 "SAEFACT" 2466595 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-985 2464558 2464872 2465271 "RURPK" 2465898 NIL RURPK (NIL T NIL) -7 NIL NIL) (-984 2463211 2463488 2463795 "RULESET" 2464394 NIL RULESET (NIL T T T) -8 NIL NIL) (-983 2460419 2460922 2461383 "RULE" 2462893 NIL RULE (NIL T T T) -8 NIL NIL) (-982 2460061 2460216 2460297 "RULECOLD" 2460371 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-981 2454953 2455747 2456663 "RSETGCD" 2459260 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-980 2444267 2449319 2449414 "RSETCAT" 2453479 NIL RSETCAT (NIL T T T T) -9 NIL 2454576) (-979 2442198 2442737 2443557 "RSETCAT-" 2443562 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-978 2434628 2436003 2437519 "RSDCMPK" 2440797 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-977 2432645 2433086 2433159 "RRCC" 2434235 NIL RRCC (NIL T T) -9 NIL 2434579) (-976 2431999 2432173 2432449 "RRCC-" 2432454 NIL RRCC- (NIL T T T) -8 NIL NIL) (-975 2406329 2415954 2416019 "RPOLCAT" 2426521 NIL RPOLCAT (NIL T T T) -9 NIL 2429668) (-974 2397833 2400171 2403289 "RPOLCAT-" 2403294 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-973 2388911 2396063 2396543 "ROUTINE" 2397373 T ROUTINE (NIL) -8 NIL NIL) (-972 2385616 2388467 2388614 "ROMAN" 2388784 T ROMAN (NIL) -8 NIL NIL) (-971 2383902 2384487 2384744 "ROIRC" 2385422 NIL ROIRC (NIL T T) -8 NIL NIL) (-970 2380259 2382563 2382592 "RNS" 2382888 T RNS (NIL) -9 NIL 2383158) (-969 2378773 2379156 2379687 "RNS-" 2379760 NIL RNS- (NIL T) -8 NIL NIL) (-968 2378198 2378606 2378635 "RNG" 2378640 T RNG (NIL) -9 NIL 2378661) (-967 2377595 2377957 2377998 "RMODULE" 2378058 NIL RMODULE (NIL T) -9 NIL 2378100) (-966 2376447 2376541 2376871 "RMCAT2" 2377496 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-965 2373165 2375634 2375953 "RMATRIX" 2376184 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-964 2366166 2368400 2368513 "RMATCAT" 2371822 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2372799) (-963 2365545 2365692 2365995 "RMATCAT-" 2366000 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-962 2365115 2365190 2365316 "RINTERP" 2365464 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-961 2364165 2364729 2364758 "RING" 2364868 T RING (NIL) -9 NIL 2364962) (-960 2363960 2364004 2364098 "RING-" 2364103 NIL RING- (NIL T) -8 NIL NIL) (-959 2362812 2363048 2363303 "RIDIST" 2363725 T RIDIST (NIL) -7 NIL NIL) (-958 2354134 2362286 2362489 "RGCHAIN" 2362661 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-957 2351139 2351753 2352421 "RF" 2353498 NIL RF (NIL T) -7 NIL NIL) (-956 2350788 2350851 2350952 "RFFACTOR" 2351070 NIL RFFACTOR (NIL T) -7 NIL NIL) (-955 2350516 2350551 2350646 "RFFACT" 2350747 NIL RFFACT (NIL T) -7 NIL NIL) (-954 2348646 2349010 2349390 "RFDIST" 2350156 T RFDIST (NIL) -7 NIL NIL) (-953 2348104 2348196 2348356 "RETSOL" 2348548 NIL RETSOL (NIL T T) -7 NIL NIL) (-952 2347696 2347776 2347818 "RETRACT" 2348008 NIL RETRACT (NIL T) -9 NIL NIL) (-951 2347548 2347573 2347657 "RETRACT-" 2347662 NIL RETRACT- (NIL T T) -8 NIL NIL) (-950 2340418 2347205 2347330 "RESULT" 2347443 T RESULT (NIL) -8 NIL NIL) (-949 2339003 2339692 2339889 "RESRING" 2340321 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-948 2338643 2338692 2338788 "RESLATC" 2338940 NIL RESLATC (NIL T) -7 NIL NIL) (-947 2338352 2338386 2338491 "REPSQ" 2338602 NIL REPSQ (NIL T) -7 NIL NIL) (-946 2335783 2336363 2336963 "REP" 2337772 T REP (NIL) -7 NIL NIL) (-945 2335484 2335518 2335627 "REPDB" 2335742 NIL REPDB (NIL T) -7 NIL NIL) (-944 2329437 2330816 2332032 "REP2" 2334300 NIL REP2 (NIL T) -7 NIL NIL) (-943 2325847 2326528 2327331 "REP1" 2328666 NIL REP1 (NIL T) -7 NIL NIL) (-942 2318593 2324008 2324460 "REGSET" 2325478 NIL REGSET (NIL T T T T) -8 NIL NIL) (-941 2317416 2317751 2317998 "REF" 2318379 NIL REF (NIL T) -8 NIL NIL) (-940 2316797 2316900 2317065 "REDORDER" 2317300 NIL REDORDER (NIL T T) -7 NIL NIL) (-939 2312766 2316031 2316252 "RECLOS" 2316628 NIL RECLOS (NIL T) -8 NIL NIL) (-938 2311823 2312004 2312217 "REALSOLV" 2312573 T REALSOLV (NIL) -7 NIL NIL) (-937 2311670 2311711 2311740 "REAL" 2311745 T REAL (NIL) -9 NIL 2311780) (-936 2308161 2308963 2309845 "REAL0Q" 2310835 NIL REAL0Q (NIL T) -7 NIL NIL) (-935 2303772 2304760 2305819 "REAL0" 2307142 NIL REAL0 (NIL T) -7 NIL NIL) (-934 2303180 2303252 2303457 "RDIV" 2303694 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-933 2302253 2302427 2302638 "RDIST" 2303002 NIL RDIST (NIL T) -7 NIL NIL) (-932 2300857 2301144 2301513 "RDETRS" 2301961 NIL RDETRS (NIL T T) -7 NIL NIL) (-931 2298678 2299132 2299667 "RDETR" 2300399 NIL RDETR (NIL T T) -7 NIL NIL) (-930 2297294 2297572 2297973 "RDEEFS" 2298394 NIL RDEEFS (NIL T T) -7 NIL NIL) (-929 2295794 2296100 2296529 "RDEEF" 2296982 NIL RDEEF (NIL T T) -7 NIL NIL) (-928 2290019 2292951 2292980 "RCFIELD" 2294257 T RCFIELD (NIL) -9 NIL 2294987) (-927 2288088 2288592 2289285 "RCFIELD-" 2289358 NIL RCFIELD- (NIL T) -8 NIL NIL) (-926 2284421 2286206 2286248 "RCAGG" 2287319 NIL RCAGG (NIL T) -9 NIL 2287782) (-925 2284052 2284146 2284306 "RCAGG-" 2284311 NIL RCAGG- (NIL T T) -8 NIL NIL) (-924 2283397 2283508 2283670 "RATRET" 2283936 NIL RATRET (NIL T) -7 NIL NIL) (-923 2282954 2283021 2283140 "RATFACT" 2283325 NIL RATFACT (NIL T) -7 NIL NIL) (-922 2282269 2282389 2282539 "RANDSRC" 2282824 T RANDSRC (NIL) -7 NIL NIL) (-921 2282006 2282050 2282121 "RADUTIL" 2282218 T RADUTIL (NIL) -7 NIL NIL) (-920 2275013 2280749 2281066 "RADIX" 2281721 NIL RADIX (NIL NIL) -8 NIL NIL) (-919 2266583 2274857 2274985 "RADFF" 2274990 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-918 2266234 2266309 2266338 "RADCAT" 2266495 T RADCAT (NIL) -9 NIL NIL) (-917 2266019 2266067 2266164 "RADCAT-" 2266169 NIL RADCAT- (NIL T) -8 NIL NIL) (-916 2264176 2265794 2265883 "QUEUE" 2265963 NIL QUEUE (NIL T) -8 NIL NIL) (-915 2260673 2264113 2264158 "QUAT" 2264163 NIL QUAT (NIL T) -8 NIL NIL) (-914 2260311 2260354 2260481 "QUATCT2" 2260624 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-913 2254065 2257445 2257486 "QUATCAT" 2258265 NIL QUATCAT (NIL T) -9 NIL 2259022) (-912 2250209 2251246 2252633 "QUATCAT-" 2252727 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-911 2247735 2249293 2249335 "QUAGG" 2249710 NIL QUAGG (NIL T) -9 NIL 2249885) (-910 2246660 2247133 2247305 "QFORM" 2247607 NIL QFORM (NIL NIL T) -8 NIL NIL) (-909 2237921 2243179 2243220 "QFCAT" 2243878 NIL QFCAT (NIL T) -9 NIL 2244859) (-908 2233493 2234694 2236285 "QFCAT-" 2236379 NIL QFCAT- (NIL T T) -8 NIL NIL) (-907 2233131 2233174 2233301 "QFCAT2" 2233444 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-906 2232591 2232701 2232831 "QEQUAT" 2233021 T QEQUAT (NIL) -8 NIL NIL) (-905 2225777 2226848 2228030 "QCMPACK" 2231524 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-904 2223357 2223778 2224204 "QALGSET" 2225434 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-903 2222602 2222776 2223008 "QALGSET2" 2223177 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-902 2221293 2221516 2221833 "PWFFINTB" 2222375 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-901 2219481 2219649 2220002 "PUSHVAR" 2221107 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-900 2215398 2216452 2216494 "PTRANFN" 2218378 NIL PTRANFN (NIL T) -9 NIL NIL) (-899 2213810 2214101 2214422 "PTPACK" 2215109 NIL PTPACK (NIL T) -7 NIL NIL) (-898 2213446 2213503 2213610 "PTFUNC2" 2213747 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-897 2207925 2212260 2212301 "PTCAT" 2212669 NIL PTCAT (NIL T) -9 NIL 2212831) (-896 2207583 2207618 2207742 "PSQFR" 2207884 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-895 2206178 2206476 2206810 "PSEUDLIN" 2207281 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-894 2192992 2195356 2197676 "PSETPK" 2203941 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-893 2186079 2188793 2188888 "PSETCAT" 2191869 NIL PSETCAT (NIL T T T T) -9 NIL 2192682) (-892 2183917 2184551 2185370 "PSETCAT-" 2185375 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-891 2183274 2183436 2183465 "PSCURVE" 2183730 T PSCURVE (NIL) -9 NIL 2183894) (-890 2179678 2181204 2181269 "PSCAT" 2182105 NIL PSCAT (NIL T T T) -9 NIL 2182345) (-889 2178742 2178958 2179357 "PSCAT-" 2179362 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-888 2177395 2178027 2178241 "PRTITION" 2178548 T PRTITION (NIL) -8 NIL NIL) (-887 2166495 2168701 2170888 "PRS" 2175258 NIL PRS (NIL T T) -7 NIL NIL) (-886 2164359 2165845 2165886 "PRQAGG" 2166069 NIL PRQAGG (NIL T) -9 NIL 2166171) (-885 2158165 2162557 2163361 "PRODUCT" 2163601 NIL PRODUCT (NIL T T) -8 NIL NIL) (-884 2155447 2157631 2157861 "PR" 2157979 NIL PR (NIL T T) -8 NIL NIL) (-883 2155243 2155275 2155334 "PRINT" 2155408 T PRINT (NIL) -7 NIL NIL) (-882 2154583 2154700 2154852 "PRIMES" 2155123 NIL PRIMES (NIL T) -7 NIL NIL) (-881 2152648 2153049 2153515 "PRIMELT" 2154162 NIL PRIMELT (NIL T) -7 NIL NIL) (-880 2152379 2152427 2152456 "PRIMCAT" 2152579 T PRIMCAT (NIL) -9 NIL NIL) (-879 2148540 2152317 2152362 "PRIMARR" 2152367 NIL PRIMARR (NIL T) -8 NIL NIL) (-878 2147547 2147725 2147953 "PRIMARR2" 2148358 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-877 2147190 2147246 2147357 "PREASSOC" 2147485 NIL PREASSOC (NIL T T) -7 NIL NIL) (-876 2146670 2146801 2146830 "PPCURVE" 2147033 T PPCURVE (NIL) -9 NIL 2147167) (-875 2144031 2144430 2145021 "POLYROOT" 2146252 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-874 2137939 2143639 2143797 "POLY" 2143905 NIL POLY (NIL T) -8 NIL NIL) (-873 2137324 2137382 2137615 "POLYLIFT" 2137875 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-872 2133609 2134058 2134686 "POLYCATQ" 2136869 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-871 2120617 2126014 2126079 "POLYCAT" 2129564 NIL POLYCAT (NIL T T T) -9 NIL 2131476) (-870 2114068 2115929 2118312 "POLYCAT-" 2118317 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-869 2113657 2113725 2113844 "POLY2UP" 2113994 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-868 2113293 2113350 2113457 "POLY2" 2113594 NIL POLY2 (NIL T T) -7 NIL NIL) (-867 2111980 2112219 2112494 "POLUTIL" 2113068 NIL POLUTIL (NIL T T) -7 NIL NIL) (-866 2110342 2110619 2110949 "POLTOPOL" 2111702 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-865 2105871 2110279 2110324 "POINT" 2110329 NIL POINT (NIL T) -8 NIL NIL) (-864 2104058 2104415 2104790 "PNTHEORY" 2105516 T PNTHEORY (NIL) -7 NIL NIL) (-863 2102486 2102783 2103192 "PMTOOLS" 2103756 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-862 2102079 2102157 2102274 "PMSYM" 2102402 NIL PMSYM (NIL T) -7 NIL NIL) (-861 2101589 2101658 2101832 "PMQFCAT" 2102004 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-860 2100944 2101054 2101210 "PMPRED" 2101466 NIL PMPRED (NIL T) -7 NIL NIL) (-859 2100340 2100426 2100587 "PMPREDFS" 2100845 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-858 2098988 2099196 2099579 "PMPLCAT" 2100103 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-857 2098520 2098599 2098751 "PMLSAGG" 2098903 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-856 2097997 2098073 2098253 "PMKERNEL" 2098438 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-855 2097614 2097689 2097802 "PMINS" 2097916 NIL PMINS (NIL T) -7 NIL NIL) (-854 2097044 2097113 2097328 "PMFS" 2097539 NIL PMFS (NIL T T T) -7 NIL NIL) (-853 2096275 2096393 2096597 "PMDOWN" 2096921 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-852 2095438 2095597 2095779 "PMASS" 2096113 T PMASS (NIL) -7 NIL NIL) (-851 2094712 2094823 2094986 "PMASSFS" 2095324 NIL PMASSFS (NIL T T) -7 NIL NIL) (-850 2094371 2094438 2094531 "PLOTTOOL" 2094639 T PLOTTOOL (NIL) -7 NIL NIL) (-849 2089072 2090238 2091365 "PLOT" 2093264 T PLOT (NIL) -8 NIL NIL) (-848 2084945 2085960 2086865 "PLOT3D" 2088187 T PLOT3D (NIL) -8 NIL NIL) (-847 2083869 2084043 2084275 "PLOT1" 2084752 NIL PLOT1 (NIL T) -7 NIL NIL) (-846 2059264 2063935 2068786 "PLEQN" 2079135 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-845 2058582 2058704 2058884 "PINTERP" 2059129 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-844 2058275 2058322 2058425 "PINTERPA" 2058529 NIL PINTERPA (NIL T T) -7 NIL NIL) (-843 2057502 2058069 2058162 "PI" 2058202 T PI (NIL) -8 NIL NIL) (-842 2055893 2056878 2056907 "PID" 2057089 T PID (NIL) -9 NIL 2057223) (-841 2055618 2055655 2055743 "PICOERCE" 2055850 NIL PICOERCE (NIL T) -7 NIL NIL) (-840 2054939 2055077 2055253 "PGROEB" 2055474 NIL PGROEB (NIL T) -7 NIL NIL) (-839 2050526 2051340 2052245 "PGE" 2054054 T PGE (NIL) -7 NIL NIL) (-838 2048650 2048896 2049262 "PGCD" 2050243 NIL PGCD (NIL T T T T) -7 NIL NIL) (-837 2047988 2048091 2048252 "PFRPAC" 2048534 NIL PFRPAC (NIL T) -7 NIL NIL) (-836 2044603 2046536 2046889 "PFR" 2047667 NIL PFR (NIL T) -8 NIL NIL) (-835 2042992 2043236 2043561 "PFOTOOLS" 2044350 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-834 2041525 2041764 2042115 "PFOQ" 2042749 NIL PFOQ (NIL T T T) -7 NIL NIL) (-833 2040002 2040214 2040576 "PFO" 2041309 NIL PFO (NIL T T T T T) -7 NIL NIL) (-832 2036525 2039891 2039960 "PF" 2039965 NIL PF (NIL NIL) -8 NIL NIL) (-831 2033954 2035235 2035264 "PFECAT" 2035849 T PFECAT (NIL) -9 NIL 2036232) (-830 2033399 2033553 2033767 "PFECAT-" 2033772 NIL PFECAT- (NIL T) -8 NIL NIL) (-829 2032003 2032254 2032555 "PFBRU" 2033148 NIL PFBRU (NIL T T) -7 NIL NIL) (-828 2029870 2030221 2030653 "PFBR" 2031654 NIL PFBR (NIL T T T T) -7 NIL NIL) (-827 2025726 2027250 2027924 "PERM" 2029229 NIL PERM (NIL T) -8 NIL NIL) (-826 2020993 2021933 2022803 "PERMGRP" 2024889 NIL PERMGRP (NIL T) -8 NIL NIL) (-825 2019065 2020058 2020100 "PERMCAT" 2020546 NIL PERMCAT (NIL T) -9 NIL 2020849) (-824 2018720 2018761 2018884 "PERMAN" 2019018 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-823 2016166 2018289 2018420 "PENDTREE" 2018622 NIL PENDTREE (NIL T) -8 NIL NIL) (-822 2014238 2015016 2015058 "PDRING" 2015715 NIL PDRING (NIL T) -9 NIL 2016000) (-821 2013341 2013559 2013921 "PDRING-" 2013926 NIL PDRING- (NIL T T) -8 NIL NIL) (-820 2010483 2011233 2011924 "PDEPROB" 2012670 T PDEPROB (NIL) -8 NIL NIL) (-819 2008054 2008550 2009099 "PDEPACK" 2009954 T PDEPACK (NIL) -7 NIL NIL) (-818 2006966 2007156 2007407 "PDECOMP" 2007853 NIL PDECOMP (NIL T T) -7 NIL NIL) (-817 2004577 2005392 2005421 "PDECAT" 2006206 T PDECAT (NIL) -9 NIL 2006917) (-816 2004330 2004363 2004452 "PCOMP" 2004538 NIL PCOMP (NIL T T) -7 NIL NIL) (-815 2002537 2003133 2003429 "PBWLB" 2004060 NIL PBWLB (NIL T) -8 NIL NIL) (-814 1995046 1996614 1997950 "PATTERN" 2001222 NIL PATTERN (NIL T) -8 NIL NIL) (-813 1994678 1994735 1994844 "PATTERN2" 1994983 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-812 1992435 1992823 1993280 "PATTERN1" 1994267 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-811 1989830 1990384 1990865 "PATRES" 1992000 NIL PATRES (NIL T T) -8 NIL NIL) (-810 1989394 1989461 1989593 "PATRES2" 1989757 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-809 1987291 1987691 1988096 "PATMATCH" 1989063 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-808 1986827 1987010 1987052 "PATMAB" 1987159 NIL PATMAB (NIL T) -9 NIL 1987242) (-807 1985372 1985681 1985939 "PATLRES" 1986632 NIL PATLRES (NIL T T T) -8 NIL NIL) (-806 1984919 1985042 1985084 "PATAB" 1985089 NIL PATAB (NIL T) -9 NIL 1985259) (-805 1982400 1982932 1983505 "PARTPERM" 1984366 T PARTPERM (NIL) -7 NIL NIL) (-804 1982021 1982084 1982186 "PARSURF" 1982331 NIL PARSURF (NIL T) -8 NIL NIL) (-803 1981653 1981710 1981819 "PARSU2" 1981958 NIL PARSU2 (NIL T T) -7 NIL NIL) (-802 1981274 1981337 1981439 "PARSCURV" 1981584 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980906 1980963 1981072 "PARSC2" 1981211 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980545 1980603 1980700 "PARPCURV" 1980842 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1980177 1980234 1980343 "PARPC2" 1980482 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1979697 1979783 1979902 "PAN2EXPR" 1980078 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978503 1978818 1979046 "PALETTE" 1979489 T PALETTE (NIL) -8 NIL NIL) (-796 1972353 1977762 1977956 "PADICRC" 1978358 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965561 1971699 1971883 "PADICRAT" 1972201 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963865 1965498 1965543 "PADIC" 1965548 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1961069 1962643 1962684 "PADICCT" 1963265 NIL PADICCT (NIL NIL) -9 NIL 1963547) (-792 1960026 1960226 1960494 "PADEPAC" 1960856 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1959238 1959371 1959577 "PADE" 1959888 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1957253 1958085 1958398 "OWP" 1959008 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956362 1956858 1957030 "OVAR" 1957121 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1955626 1955747 1955908 "OUT" 1956221 T OUT (NIL) -7 NIL NIL) (-787 1944672 1946851 1949021 "OUTFORM" 1953476 T OUTFORM (NIL) -8 NIL NIL) (-786 1944080 1944401 1944490 "OSI" 1944603 T OSI (NIL) -8 NIL NIL) (-785 1942827 1943054 1943338 "ORTHPOL" 1943828 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1940198 1942488 1942626 "OREUP" 1942770 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937594 1939891 1940017 "ORESUP" 1940140 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1935133 1935633 1936191 "OREPCTO" 1937085 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1929046 1931252 1931293 "OREPCAT" 1933614 NIL OREPCAT (NIL T) -9 NIL 1934713) (-780 1926194 1926976 1928033 "OREPCAT-" 1928038 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925371 1925643 1925672 "ORDSET" 1925981 T ORDSET (NIL) -9 NIL 1926145) (-778 1924890 1925012 1925205 "ORDSET-" 1925210 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923503 1924304 1924333 "ORDRING" 1924535 T ORDRING (NIL) -9 NIL 1924659) (-776 1923148 1923242 1923386 "ORDRING-" 1923391 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922523 1923004 1923033 "ORDMON" 1923038 T ORDMON (NIL) -9 NIL 1923059) (-774 1921685 1921832 1922027 "ORDFUNS" 1922372 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1921196 1921555 1921584 "ORDFIN" 1921589 T ORDFIN (NIL) -9 NIL 1921610) (-772 1917714 1919788 1920194 "ORDCOMP" 1920823 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916980 1917107 1917293 "ORDCOMP2" 1917574 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1913488 1914370 1915207 "OPTPROB" 1916163 T OPTPROB (NIL) -8 NIL NIL) (-769 1910330 1910959 1911653 "OPTPACK" 1912814 T OPTPACK (NIL) -7 NIL NIL) (-768 1908055 1908791 1908820 "OPTCAT" 1909635 T OPTCAT (NIL) -9 NIL 1910281) (-767 1907823 1907862 1907928 "OPQUERY" 1908009 T OPQUERY (NIL) -7 NIL NIL) (-766 1904965 1906156 1906653 "OP" 1907358 NIL OP (NIL T) -8 NIL NIL) (-765 1901736 1903768 1904134 "ONECOMP" 1904632 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1901041 1901156 1901330 "ONECOMP2" 1901608 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1900460 1900566 1900696 "OMSERVER" 1900931 T OMSERVER (NIL) -7 NIL NIL) (-762 1897348 1899900 1899941 "OMSAGG" 1900002 NIL OMSAGG (NIL T) -9 NIL 1900066) (-761 1895971 1896234 1896516 "OMPKG" 1897086 T OMPKG (NIL) -7 NIL NIL) (-760 1895400 1895503 1895532 "OM" 1895831 T OM (NIL) -9 NIL NIL) (-759 1893941 1894954 1895121 "OMLO" 1895282 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1892871 1893018 1893244 "OMEXPR" 1893767 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1892189 1892417 1892553 "OMERR" 1892755 T OMERR (NIL) -8 NIL NIL) (-756 1891367 1891610 1891770 "OMERRK" 1892049 T OMERRK (NIL) -8 NIL NIL) (-755 1890845 1891044 1891152 "OMENC" 1891279 T OMENC (NIL) -8 NIL NIL) (-754 1884740 1885925 1887096 "OMDEV" 1889694 T OMDEV (NIL) -8 NIL NIL) (-753 1883809 1883980 1884174 "OMCONN" 1884566 T OMCONN (NIL) -8 NIL NIL) (-752 1882424 1883410 1883439 "OINTDOM" 1883444 T OINTDOM (NIL) -9 NIL 1883465) (-751 1878186 1879416 1880131 "OFMONOID" 1881741 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877624 1878123 1878168 "ODVAR" 1878173 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1874751 1877123 1877307 "ODR" 1877500 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1867057 1874530 1874654 "ODPOL" 1874659 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1860886 1866929 1867034 "ODP" 1867039 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1859652 1859867 1860142 "ODETOOLS" 1860660 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1856621 1857277 1857993 "ODESYS" 1858985 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1851527 1852435 1853457 "ODERTRIC" 1855697 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1850953 1851035 1851229 "ODERED" 1851439 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1847855 1848403 1849078 "ODERAT" 1850376 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1844823 1845287 1845883 "ODEPRRIC" 1847384 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1842694 1843261 1843770 "ODEPROB" 1844334 T ODEPROB (NIL) -8 NIL NIL) (-739 1839226 1839709 1840355 "ODEPRIM" 1842173 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1838479 1838581 1838839 "ODEPAL" 1839118 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1834681 1835462 1836316 "ODEPACK" 1837645 T ODEPACK (NIL) -7 NIL NIL) (-736 1833718 1833825 1834053 "ODEINT" 1834570 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1827819 1829244 1830691 "ODEIFTBL" 1832291 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1823163 1823949 1824907 "ODEEF" 1826978 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822500 1822589 1822818 "ODECONST" 1823068 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1820657 1821290 1821319 "ODECAT" 1821922 T ODECAT (NIL) -9 NIL 1822451) (-731 1817529 1820369 1820488 "OCT" 1820570 NIL OCT (NIL T) -8 NIL NIL) (-730 1817167 1817210 1817337 "OCTCT2" 1817480 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1812008 1814446 1814487 "OC" 1815583 NIL OC (NIL T) -9 NIL 1816432) (-728 1809235 1809983 1810973 "OC-" 1811067 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808613 1809055 1809084 "OCAMON" 1809089 T OCAMON (NIL) -9 NIL 1809110) (-726 1808066 1808473 1808502 "OASGP" 1808507 T OASGP (NIL) -9 NIL 1808527) (-725 1807353 1807816 1807845 "OAMONS" 1807885 T OAMONS (NIL) -9 NIL 1807928) (-724 1806793 1807200 1807229 "OAMON" 1807234 T OAMON (NIL) -9 NIL 1807254) (-723 1806097 1806589 1806618 "OAGROUP" 1806623 T OAGROUP (NIL) -9 NIL 1806643) (-722 1805787 1805837 1805925 "NUMTUBE" 1806041 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1799360 1800878 1802414 "NUMQUAD" 1804271 T NUMQUAD (NIL) -7 NIL NIL) (-720 1795116 1796104 1797129 "NUMODE" 1798355 T NUMODE (NIL) -7 NIL NIL) (-719 1792531 1793373 1793402 "NUMINT" 1794315 T NUMINT (NIL) -9 NIL 1795067) (-718 1791479 1791676 1791894 "NUMFMT" 1792333 T NUMFMT (NIL) -7 NIL NIL) (-717 1777874 1780811 1783333 "NUMERIC" 1788996 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1772274 1777326 1777421 "NTSCAT" 1777426 NIL NTSCAT (NIL T T T T) -9 NIL 1777464) (-715 1771470 1771635 1771827 "NTPOLFN" 1772114 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1759328 1768314 1769123 "NSUP" 1770693 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758964 1759021 1759128 "NSUP2" 1759265 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1748926 1758743 1758873 "NSMP" 1758878 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1747358 1747659 1748016 "NREP" 1748614 NIL NREP (NIL T) -7 NIL NIL) (-710 1745949 1746201 1746559 "NPCOEF" 1747101 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1745015 1745130 1745346 "NORMRETR" 1745830 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1743068 1743358 1743765 "NORMPK" 1744723 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1742753 1742781 1742905 "NORMMA" 1743034 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1742580 1742710 1742739 "NONE" 1742744 T NONE (NIL) -8 NIL NIL) (-705 1742369 1742398 1742467 "NONE1" 1742544 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1741854 1741916 1742101 "NODE1" 1742301 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1740148 1741017 1741272 "NNI" 1741619 T NNI (NIL) -8 NIL NIL) (-702 1738568 1738881 1739245 "NLINSOL" 1739816 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1734760 1735721 1736637 "NIPROB" 1737672 T NIPROB (NIL) -8 NIL NIL) (-700 1733517 1733751 1734053 "NFINTBAS" 1734522 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1732225 1732456 1732737 "NCODIV" 1733285 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731987 1732024 1732099 "NCNTFRAC" 1732182 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1730167 1730531 1730951 "NCEP" 1731612 NIL NCEP (NIL T) -7 NIL NIL) (-696 1729078 1729817 1729846 "NASRING" 1729956 T NASRING (NIL) -9 NIL 1730030) (-695 1728873 1728917 1729011 "NASRING-" 1729016 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1728026 1728525 1728554 "NARNG" 1728671 T NARNG (NIL) -9 NIL 1728762) (-693 1727718 1727785 1727919 "NARNG-" 1727924 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1726597 1726804 1727039 "NAGSP" 1727503 T NAGSP (NIL) -7 NIL NIL) (-691 1718021 1719667 1721302 "NAGS" 1724982 T NAGS (NIL) -7 NIL NIL) (-690 1716585 1716889 1717216 "NAGF07" 1717714 T NAGF07 (NIL) -7 NIL NIL) (-689 1711167 1712447 1713743 "NAGF04" 1715309 T NAGF04 (NIL) -7 NIL NIL) (-688 1704199 1705797 1707414 "NAGF02" 1709570 T NAGF02 (NIL) -7 NIL NIL) (-687 1699463 1700553 1701660 "NAGF01" 1703112 T NAGF01 (NIL) -7 NIL NIL) (-686 1693123 1694681 1696258 "NAGE04" 1697906 T NAGE04 (NIL) -7 NIL NIL) (-685 1684364 1686467 1688579 "NAGE02" 1691031 T NAGE02 (NIL) -7 NIL NIL) (-684 1680357 1681294 1682248 "NAGE01" 1683430 T NAGE01 (NIL) -7 NIL NIL) (-683 1678164 1678695 1679250 "NAGD03" 1679822 T NAGD03 (NIL) -7 NIL NIL) (-682 1669950 1671869 1673814 "NAGD02" 1676239 T NAGD02 (NIL) -7 NIL NIL) (-681 1663809 1665222 1666650 "NAGD01" 1668542 T NAGD01 (NIL) -7 NIL NIL) (-680 1660066 1660876 1661701 "NAGC06" 1663004 T NAGC06 (NIL) -7 NIL NIL) (-679 1658543 1658872 1659225 "NAGC05" 1659733 T NAGC05 (NIL) -7 NIL NIL) (-678 1657927 1658044 1658186 "NAGC02" 1658421 T NAGC02 (NIL) -7 NIL NIL) (-677 1656988 1657545 1657586 "NAALG" 1657665 NIL NAALG (NIL T) -9 NIL 1657726) (-676 1656823 1656852 1656942 "NAALG-" 1656947 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650773 1651881 1653068 "MULTSQFR" 1655719 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1650092 1650167 1650351 "MULTFACT" 1650685 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1643234 1647145 1647198 "MTSCAT" 1648258 NIL MTSCAT (NIL T T) -9 NIL 1648771) (-672 1642946 1643000 1643092 "MTHING" 1643174 NIL MTHING (NIL T) -7 NIL NIL) (-671 1642738 1642771 1642831 "MSYSCMD" 1642906 T MSYSCMD (NIL) -7 NIL NIL) (-670 1638850 1641493 1641813 "MSET" 1642451 NIL MSET (NIL T) -8 NIL NIL) (-669 1635945 1638411 1638453 "MSETAGG" 1638458 NIL MSETAGG (NIL T) -9 NIL 1638492) (-668 1631813 1633355 1634090 "MRING" 1635254 NIL MRING (NIL T T) -8 NIL NIL) (-667 1631383 1631450 1631579 "MRF2" 1631740 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1631001 1631036 1631180 "MRATFAC" 1631342 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1628613 1628908 1629339 "MPRFF" 1630706 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1622633 1628468 1628564 "MPOLY" 1628569 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1622123 1622158 1622366 "MPCPF" 1622592 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1621639 1621682 1621865 "MPC3" 1622074 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1620840 1620921 1621140 "MPC2" 1621554 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1619141 1619478 1619868 "MONOTOOL" 1620500 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1618265 1618600 1618629 "MONOID" 1618906 T MONOID (NIL) -9 NIL 1619078) (-658 1617643 1617806 1618049 "MONOID-" 1618054 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608579 1614565 1614625 "MONOGEN" 1615299 NIL MONOGEN (NIL T T) -9 NIL 1615752) (-656 1605797 1606532 1607532 "MONOGEN-" 1607651 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604656 1605076 1605105 "MONADWU" 1605497 T MONADWU (NIL) -9 NIL 1605735) (-654 1604028 1604187 1604435 "MONADWU-" 1604440 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603413 1603631 1603660 "MONAD" 1603867 T MONAD (NIL) -9 NIL 1603979) (-652 1603098 1603176 1603308 "MONAD-" 1603313 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601349 1602011 1602290 "MOEBIUS" 1602851 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600742 1601120 1601161 "MODULE" 1601166 NIL MODULE (NIL T) -9 NIL 1601192) (-649 1600310 1600406 1600596 "MODULE-" 1600601 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597981 1598676 1599002 "MODRING" 1600135 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594943 1596108 1596622 "MODOP" 1597516 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1593130 1593582 1593923 "MODMONOM" 1594742 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582852 1591338 1591758 "MODMON" 1592760 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579978 1581696 1581972 "MODFIELD" 1582727 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579504 1579547 1579726 "MMAP" 1579929 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577741 1578518 1578559 "MLO" 1578976 NIL MLO (NIL T) -9 NIL 1579216) (-641 1575108 1575623 1576225 "MLIFT" 1577222 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574499 1574583 1574737 "MKUCFUNC" 1575019 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1574098 1574168 1574291 "MKRECORD" 1574422 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1573146 1573307 1573535 "MKFUNC" 1573909 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572534 1572638 1572794 "MKFLCFN" 1573029 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571960 1572327 1572416 "MKCHSET" 1572478 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1571237 1571339 1571524 "MKBCFUNC" 1571853 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567921 1570791 1570927 "MINT" 1571121 T MINT (NIL) -8 NIL NIL) (-633 1566733 1566976 1567253 "MHROWRED" 1567676 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1562004 1565178 1565602 "MFLOAT" 1566329 T MFLOAT (NIL) -8 NIL NIL) (-631 1561361 1561437 1561608 "MFINFACT" 1561916 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557708 1558547 1559422 "MESH" 1560506 T MESH (NIL) -7 NIL NIL) (-629 1556098 1556410 1556763 "MDDFACT" 1557395 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552946 1555257 1555299 "MDAGG" 1555554 NIL MDAGG (NIL T) -9 NIL 1555697) (-627 1542644 1552239 1552446 "MCMPLX" 1552759 T MCMPLX (NIL) -8 NIL NIL) (-626 1541785 1541931 1542131 "MCDEN" 1542493 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539675 1539945 1540325 "MCALCFN" 1541515 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1537297 1537820 1538381 "MATSTOR" 1539146 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1533315 1536676 1536921 "MATRIX" 1537084 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1529090 1529794 1530527 "MATLIN" 1532675 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1519299 1522431 1522508 "MATCAT" 1527346 NIL MATCAT (NIL T T T) -9 NIL 1528757) (-620 1515664 1516677 1518032 "MATCAT-" 1518037 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1514266 1514419 1514750 "MATCAT2" 1515499 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1512378 1512702 1513086 "MAPPKG3" 1513941 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1511359 1511532 1511754 "MAPPKG2" 1512202 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509858 1510142 1510469 "MAPPKG1" 1511065 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509469 1509527 1509650 "MAPHACK3" 1509794 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1509061 1509122 1509236 "MAPHACK2" 1509401 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508499 1508602 1508744 "MAPHACK1" 1508952 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506607 1507201 1507504 "MAGMA" 1508228 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1503090 1504853 1505312 "M3D" 1506181 NIL M3D (NIL T) -8 NIL NIL) (-610 1497248 1501457 1501499 "LZSTAGG" 1502281 NIL LZSTAGG (NIL T) -9 NIL 1502576) (-609 1493222 1494379 1495836 "LZSTAGG-" 1495841 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1490338 1491115 1491601 "LWORD" 1492768 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483498 1490109 1490243 "LSQM" 1490248 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482722 1482861 1483089 "LSPP" 1483353 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480534 1480835 1481291 "LSMP" 1482411 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1477313 1477987 1478717 "LSMP1" 1479836 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1471236 1476478 1476520 "LSAGG" 1476582 NIL LSAGG (NIL T) -9 NIL 1476660) (-602 1467931 1468855 1470068 "LSAGG-" 1470073 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465557 1467075 1467324 "LPOLY" 1467726 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1465139 1465224 1465347 "LPEFRAC" 1465466 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463488 1464235 1464487 "LO" 1464972 NIL LO (NIL T T T) -8 NIL NIL) (-598 1463141 1463253 1463282 "LOGIC" 1463393 T LOGIC (NIL) -9 NIL 1463473) (-597 1463003 1463026 1463097 "LOGIC-" 1463102 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1462196 1462336 1462529 "LODOOPS" 1462859 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459614 1462113 1462178 "LODO" 1462183 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1458162 1458397 1458747 "LODOF" 1459362 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454582 1457018 1457059 "LODOCAT" 1457491 NIL LODOCAT (NIL T) -9 NIL 1457701) (-592 1454316 1454374 1454500 "LODOCAT-" 1454505 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451630 1454157 1454275 "LODO2" 1454280 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1449059 1451567 1451612 "LODO1" 1451617 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447922 1448087 1448398 "LODEEF" 1448882 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1443206 1446050 1446092 "LNAGG" 1447039 NIL LNAGG (NIL T) -9 NIL 1447482) (-587 1442353 1442567 1442909 "LNAGG-" 1442914 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438518 1439280 1439918 "LMOPS" 1441769 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437915 1438277 1438318 "LMODULE" 1438378 NIL LMODULE (NIL T) -9 NIL 1438420) (-584 1435167 1437560 1437683 "LMDICT" 1437825 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1428398 1434117 1434413 "LIST" 1434904 NIL LIST (NIL T) -8 NIL NIL) (-582 1427923 1427997 1428136 "LIST3" 1428318 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426930 1427108 1427336 "LIST2" 1427741 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1425064 1425376 1425775 "LIST2MAP" 1426577 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423776 1424456 1424497 "LINEXP" 1424750 NIL LINEXP (NIL T) -9 NIL 1424898) (-578 1422423 1422683 1422980 "LINDEP" 1423528 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1419190 1419909 1420686 "LIMITRF" 1421678 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417471 1417765 1418180 "LIMITPS" 1418885 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411930 1416986 1417212 "LIE" 1417294 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410981 1411424 1411465 "LIECAT" 1411605 NIL LIECAT (NIL T) -9 NIL 1411755) (-573 1410822 1410849 1410937 "LIECAT-" 1410942 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1403446 1410271 1410436 "LIB" 1410677 T LIB (NIL) -8 NIL NIL) (-571 1399083 1399964 1400899 "LGROBP" 1402563 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396953 1397226 1397587 "LF" 1398805 NIL LF (NIL T T) -7 NIL NIL) (-569 1395793 1396484 1396513 "LFCAT" 1396720 T LFCAT (NIL) -9 NIL 1396859) (-568 1392705 1393331 1394017 "LEXTRIPK" 1395159 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1389411 1390275 1390778 "LEXP" 1392285 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387809 1388122 1388523 "LEADCDET" 1389093 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1387005 1387079 1387306 "LAZM3PK" 1387730 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381928 1385090 1385624 "LAUPOL" 1386521 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381495 1381539 1381706 "LAPLACE" 1381878 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1379425 1380598 1380848 "LA" 1381329 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378487 1379081 1379122 "LALG" 1379183 NIL LALG (NIL T) -9 NIL 1379241) (-560 1378202 1378261 1378396 "LALG-" 1378401 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1377112 1377299 1377596 "KOVACIC" 1378002 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376946 1376970 1377012 "KONVERT" 1377074 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376780 1376804 1376846 "KOERCE" 1376908 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374516 1375276 1375668 "KERNEL" 1376420 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1374018 1374099 1374229 "KERNEL2" 1374430 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367633 1372315 1372370 "KDAGG" 1372747 NIL KDAGG (NIL T T) -9 NIL 1372953) (-553 1367162 1367286 1367491 "KDAGG-" 1367496 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360337 1366823 1366978 "KAFILE" 1367040 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354796 1359852 1360078 "JORDAN" 1360160 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1351105 1353005 1353060 "IXAGG" 1353989 NIL IXAGG (NIL T T) -9 NIL 1354444) (-549 1350024 1350330 1350749 "IXAGG-" 1350754 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345615 1349946 1350005 "IVECTOR" 1350010 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344381 1344618 1344884 "ITUPLE" 1345382 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342817 1342994 1343300 "ITRIGMNP" 1344203 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341562 1341766 1342049 "ITFUN3" 1342593 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1341194 1341251 1341360 "ITFUN2" 1341499 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338998 1340069 1340365 "ITAYLOR" 1340930 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327992 1333186 1334344 "ISUPS" 1337872 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1327100 1327239 1327474 "ISUMP" 1327840 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322364 1326901 1326980 "ISTRING" 1327053 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321577 1321658 1321873 "IRURPK" 1322278 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320513 1320714 1320954 "IRSN" 1321357 T IRSN (NIL) -7 NIL NIL) (-537 1318550 1318905 1319339 "IRRF2F" 1320152 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318297 1318335 1318411 "IRREDFFX" 1318506 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316912 1317171 1317470 "IROOT" 1318030 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313554 1314605 1315293 "IR" 1316256 NIL IR (NIL T) -8 NIL NIL) (-533 1311167 1311662 1312228 "IR2" 1313032 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1310243 1310356 1310576 "IR2F" 1311050 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1310034 1310068 1310128 "IPRNTPK" 1310203 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306588 1309923 1309992 "IPF" 1309997 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304905 1306513 1306570 "IPADIC" 1306575 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304404 1304462 1304651 "INVLAPLA" 1304841 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1294053 1296406 1298792 "INTTR" 1302068 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290415 1291156 1292012 "INTTOOLS" 1293246 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1290001 1290092 1290209 "INTSLPE" 1290318 T INTSLPE (NIL) -7 NIL NIL) (-524 1287951 1289924 1289983 "INTRVL" 1289988 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285558 1286070 1286644 "INTRF" 1287436 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284973 1285070 1285211 "INTRET" 1285456 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282975 1283364 1283833 "INTRAT" 1284581 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1280216 1280799 1281420 "INTPM" 1282464 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276927 1277526 1278269 "INTPAF" 1279603 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1272210 1273146 1274171 "INTPACK" 1275922 T INTPACK (NIL) -7 NIL NIL) (-517 1269064 1271939 1272066 "INT" 1272103 T INT (NIL) -8 NIL NIL) (-516 1268316 1268468 1268676 "INTHERTR" 1268906 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267755 1267835 1268023 "INTHERAL" 1268230 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265601 1266044 1266501 "INTHEORY" 1267318 T INTHEORY (NIL) -7 NIL NIL) (-513 1256926 1258546 1260323 "INTG0" 1263954 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237523 1242307 1247111 "INTFTBL" 1252142 T INTFTBL (NIL) -8 NIL NIL) (-511 1236772 1236910 1237083 "INTFACT" 1237382 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1234163 1234609 1235172 "INTEF" 1236326 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232624 1233373 1233402 "INTDOM" 1233703 T INTDOM (NIL) -9 NIL 1233910) (-508 1231993 1232167 1232409 "INTDOM-" 1232414 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228485 1230417 1230472 "INTCAT" 1231271 NIL INTCAT (NIL T) -9 NIL 1231590) (-506 1227958 1228060 1228188 "INTBIT" 1228377 T INTBIT (NIL) -7 NIL NIL) (-505 1226633 1226787 1227100 "INTALG" 1227803 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1226090 1226180 1226350 "INTAF" 1226537 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219556 1225900 1226040 "INTABL" 1226045 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214506 1217235 1217264 "INS" 1218232 T INS (NIL) -9 NIL 1218913) (-501 1211746 1212517 1213491 "INS-" 1213564 NIL INS- (NIL T) -8 NIL NIL) (-500 1210525 1210752 1211049 "INPSIGN" 1211499 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209643 1209760 1209957 "INPRODPF" 1210405 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208537 1208654 1208891 "INPRODFF" 1209523 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207537 1207689 1207949 "INNMFACT" 1208373 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206734 1206831 1207019 "INMODGCD" 1207436 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1205243 1205487 1205811 "INFSP" 1206479 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204427 1204544 1204727 "INFPROD0" 1205123 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201437 1202596 1203087 "INFORM" 1203944 T INFORM (NIL) -8 NIL NIL) (-492 1201047 1201107 1201205 "INFORM1" 1201372 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200570 1200659 1200773 "INFINITY" 1200953 T INFINITY (NIL) -7 NIL NIL) (-490 1199188 1199436 1199757 "INEP" 1200318 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198464 1199085 1199150 "INDE" 1199155 NIL INDE (NIL T) -8 NIL NIL) (-488 1198028 1198096 1198213 "INCRMAPS" 1198391 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1193339 1194264 1195208 "INBFF" 1197116 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189840 1193184 1193287 "IMATRIX" 1193292 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188554 1188677 1188991 "IMATQF" 1189697 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186776 1187003 1187339 "IMATLIN" 1188311 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181402 1186700 1186758 "ILIST" 1186763 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1179361 1181262 1181375 "IIARRAY2" 1181380 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174729 1179272 1179336 "IFF" 1179341 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169778 1174021 1174209 "IFARRAY" 1174586 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168985 1169682 1169755 "IFAMON" 1169760 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168568 1168633 1168688 "IEVALAB" 1168895 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1168243 1168311 1168471 "IEVALAB-" 1168476 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167901 1168157 1168220 "IDPO" 1168225 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1167178 1167790 1167865 "IDPOAMS" 1167870 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166512 1167067 1167142 "IDPOAM" 1167147 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165597 1165847 1165901 "IDPC" 1166314 NIL IDPC (NIL T T) -9 NIL 1166463) (-472 1165093 1165489 1165562 "IDPAM" 1165567 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164496 1164985 1165058 "IDPAG" 1165063 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160751 1161599 1162494 "IDECOMP" 1163653 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153627 1154676 1155722 "IDEAL" 1159788 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152791 1152903 1153102 "ICDEN" 1153511 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151890 1152271 1152418 "ICARD" 1152664 T ICARD (NIL) -8 NIL NIL) (-466 1149962 1150275 1150678 "IBPTOOLS" 1151567 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145576 1149582 1149695 "IBITS" 1149881 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1142299 1142875 1143570 "IBATOOL" 1144993 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1140079 1140540 1141073 "IBACHIN" 1141834 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137962 1139925 1140028 "IARRAY2" 1140033 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1134121 1137888 1137945 "IARRAY1" 1137950 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1128061 1132539 1133017 "IAN" 1133663 T IAN (NIL) -8 NIL NIL) (-459 1127572 1127629 1127802 "IALGFACT" 1127998 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1127099 1127212 1127241 "HYPCAT" 1127448 T HYPCAT (NIL) -9 NIL NIL) (-457 1126637 1126754 1126940 "HYPCAT-" 1126945 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1123323 1124654 1124696 "HOAGG" 1125677 NIL HOAGG (NIL T) -9 NIL 1126349) (-455 1121917 1122316 1122842 "HOAGG-" 1122847 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115748 1121358 1121524 "HEXADEC" 1121771 T HEXADEC (NIL) -8 NIL NIL) (-453 1114496 1114718 1114981 "HEUGCD" 1115525 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113599 1114333 1114463 "HELLFDIV" 1114468 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111833 1113376 1113464 "HEAP" 1113543 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105706 1111748 1111810 "HDP" 1111815 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099418 1105343 1105494 "HDMP" 1105607 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098743 1098882 1099046 "HB" 1099274 T HB (NIL) -7 NIL NIL) (-447 1092252 1098589 1098693 "HASHTBL" 1098698 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1090005 1091880 1092059 "HACKPI" 1092093 T HACKPI (NIL) -8 NIL NIL) (-445 1085701 1089859 1089971 "GTSET" 1089976 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1079239 1085579 1085677 "GSTBL" 1085682 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071477 1078277 1078540 "GSERIES" 1079031 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070499 1070952 1070981 "GROUP" 1071242 T GROUP (NIL) -9 NIL 1071401) (-441 1069615 1069838 1070182 "GROUP-" 1070187 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067984 1068303 1068690 "GROEBSOL" 1069292 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066924 1067186 1067238 "GRMOD" 1067767 NIL GRMOD (NIL T T) -9 NIL 1067935) (-438 1066692 1066728 1066856 "GRMOD-" 1066861 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1062032 1063054 1064051 "GRIMAGE" 1065715 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060499 1060759 1061083 "GRDEF" 1061728 T GRDEF (NIL) -7 NIL NIL) (-435 1059943 1060059 1060200 "GRAY" 1060378 T GRAY (NIL) -7 NIL NIL) (-434 1059176 1059556 1059608 "GRALG" 1059761 NIL GRALG (NIL T T) -9 NIL 1059853) (-433 1058837 1058910 1059073 "GRALG-" 1059078 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055645 1058426 1058602 "GPOLSET" 1058744 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1055001 1055058 1055315 "GOSPER" 1055582 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050760 1051439 1051965 "GMODPOL" 1054700 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049765 1049949 1050187 "GHENSEL" 1050572 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043831 1044674 1045700 "GENUPS" 1048849 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043528 1043579 1043668 "GENUFACT" 1043774 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042940 1043017 1043182 "GENPGCD" 1043446 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1042414 1042449 1042662 "GENMFACT" 1042899 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040982 1041237 1041544 "GENEEZ" 1042157 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034856 1040595 1040756 "GDMP" 1040905 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1024237 1028629 1029734 "GCNAALG" 1033840 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022658 1023530 1023559 "GCDDOM" 1023814 T GCDDOM (NIL) -9 NIL 1023971) (-420 1022128 1022255 1022470 "GCDDOM-" 1022475 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020802 1020987 1021290 "GB" 1021908 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1009422 1011748 1014140 "GBINTERN" 1018493 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1007259 1007551 1007972 "GBF" 1009097 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1006040 1006205 1006472 "GBEUCLID" 1007075 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1005389 1005514 1005663 "GAUSSFAC" 1005911 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003768 1004070 1004382 "GALUTIL" 1005109 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1002085 1002359 1002682 "GALPOLYU" 1003495 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999474 999764 1000169 "GALFACTU" 1001782 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 991280 992779 994387 "GALFACT" 997906 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988667 989325 989354 "FVFUN" 990510 T FVFUN (NIL) -9 NIL 991230) (-409 987932 988114 988143 "FVC" 988434 T FVC (NIL) -9 NIL 988617) (-408 987574 987729 987810 "FUNCTION" 987884 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 985244 985795 986284 "FT" 987105 T FT (NIL) -8 NIL NIL) (-406 984062 984545 984748 "FTEM" 985061 T FTEM (NIL) -8 NIL NIL) (-405 982329 982617 983018 "FSUPFACT" 983755 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980726 981015 981347 "FST" 982017 T FST (NIL) -8 NIL NIL) (-403 979901 980007 980201 "FSRED" 980608 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978582 978837 979190 "FSPRMELT" 979617 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975667 976105 976604 "FSPECF" 978145 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 958004 966561 966602 "FS" 970440 NIL FS (NIL T) -9 NIL 972711) (-399 946654 949644 953700 "FS-" 953997 NIL FS- (NIL T T) -8 NIL NIL) (-398 946170 946224 946400 "FSINT" 946595 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944455 945167 945468 "FSERIES" 945951 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943473 943589 943819 "FSCINT" 944335 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939709 942419 942461 "FSAGG" 942831 NIL FSAGG (NIL T) -9 NIL 943088) (-394 937471 938072 938868 "FSAGG-" 938963 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936513 936656 936883 "FSAGG2" 937324 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 934172 934451 935004 "FS2UPS" 936231 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933758 933801 933954 "FS2" 934123 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932618 932789 933097 "FS2EXPXP" 933583 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 932044 932159 932311 "FRUTIL" 932498 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923481 927559 928907 "FR" 930728 NIL FR (NIL T) -8 NIL NIL) (-387 918558 921201 921242 "FRNAALG" 922638 NIL FRNAALG (NIL T) -9 NIL 923244) (-386 914237 915307 916582 "FRNAALG-" 917332 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913875 913918 914045 "FRNAAF2" 914188 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 912242 912734 913027 "FRMOD" 913689 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909965 910633 910949 "FRIDEAL" 912033 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 909164 909251 909538 "FRIDEAL2" 909872 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 908423 908831 908873 "FRETRCT" 908878 NIL FRETRCT (NIL T) -9 NIL 909047) (-380 907535 907766 908117 "FRETRCT-" 908122 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904744 905964 906024 "FRAMALG" 906906 NIL FRAMALG (NIL T T) -9 NIL 907198) (-378 902877 903333 903963 "FRAMALG-" 904186 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896789 902362 902633 "FRAC" 902638 NIL FRAC (NIL T) -8 NIL NIL) (-376 896425 896482 896589 "FRAC2" 896726 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 896061 896118 896225 "FR2" 896362 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890690 893603 893632 "FPS" 894751 T FPS (NIL) -9 NIL 895304) (-373 890139 890248 890412 "FPS-" 890558 NIL FPS- (NIL T) -8 NIL NIL) (-372 887540 889237 889266 "FPC" 889491 T FPC (NIL) -9 NIL 889633) (-371 887333 887373 887470 "FPC-" 887475 NIL FPC- (NIL T) -8 NIL NIL) (-370 886213 886823 886865 "FPATMAB" 886870 NIL FPATMAB (NIL T) -9 NIL 887020) (-369 883913 884389 884815 "FPARFRAC" 885850 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 879308 879805 880487 "FORTRAN" 883345 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 877024 877524 878063 "FORT" 878789 T FORT (NIL) -7 NIL NIL) (-366 874699 875261 875290 "FORTFN" 876350 T FORTFN (NIL) -9 NIL 876974) (-365 874462 874512 874541 "FORTCAT" 874600 T FORTCAT (NIL) -9 NIL 874662) (-364 872522 873005 873404 "FORMULA" 874083 T FORMULA (NIL) -8 NIL NIL) (-363 872310 872340 872409 "FORMULA1" 872486 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871833 871885 872058 "FORDER" 872252 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870929 871093 871286 "FOP" 871660 T FOP (NIL) -7 NIL NIL) (-360 869537 870209 870383 "FNLA" 870811 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 868205 868594 868623 "FNCAT" 869195 T FNCAT (NIL) -9 NIL 869488) (-358 867771 868164 868192 "FNAME" 868197 T FNAME (NIL) -8 NIL NIL) (-357 866430 867403 867432 "FMTC" 867437 T FMTC (NIL) -9 NIL 867472) (-356 862750 863957 864584 "FMONOID" 865836 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861972 862495 862642 "FM" 862647 NIL FM (NIL T T) -8 NIL NIL) (-354 859395 860041 860070 "FMFUN" 861214 T FMFUN (NIL) -9 NIL 861922) (-353 858663 858844 858873 "FMC" 859163 T FMC (NIL) -9 NIL 859345) (-352 855893 856727 856781 "FMCAT" 857963 NIL FMCAT (NIL T T) -9 NIL 858456) (-351 854788 855661 855760 "FM1" 855838 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852562 852978 853472 "FLOATRP" 854339 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 846049 850218 850848 "FLOAT" 851952 T FLOAT (NIL) -8 NIL NIL) (-348 843487 843987 844565 "FLOATCP" 845516 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 842276 843124 843165 "FLINEXP" 843170 NIL FLINEXP (NIL T) -9 NIL 843262) (-346 841431 841666 841993 "FLINEXP-" 841998 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840507 840651 840875 "FLASORT" 841283 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837725 838567 838620 "FLALG" 839847 NIL FLALG (NIL T T) -9 NIL 840314) (-343 831516 835212 835254 "FLAGG" 836516 NIL FLAGG (NIL T) -9 NIL 837164) (-342 830242 830581 831071 "FLAGG-" 831076 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 829284 829427 829654 "FLAGG2" 830095 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 826259 827277 827337 "FINRALG" 828465 NIL FINRALG (NIL T T) -9 NIL 828970) (-339 825419 825648 825987 "FINRALG-" 825992 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824825 825038 825067 "FINITE" 825263 T FINITE (NIL) -9 NIL 825370) (-337 817285 819446 819487 "FINAALG" 823154 NIL FINAALG (NIL T) -9 NIL 824606) (-336 812626 813667 814811 "FINAALG-" 816190 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 812021 812381 812484 "FILE" 812556 NIL FILE (NIL T) -8 NIL NIL) (-334 810705 811017 811072 "FILECAT" 811756 NIL FILECAT (NIL T T) -9 NIL 811972) (-333 808520 810076 810105 "FIELD" 810145 T FIELD (NIL) -9 NIL 810225) (-332 807140 807525 808036 "FIELD-" 808041 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804955 805777 806123 "FGROUP" 806827 NIL FGROUP (NIL T) -8 NIL NIL) (-330 804045 804209 804429 "FGLMICPK" 804787 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799847 803970 804027 "FFX" 804032 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799448 799509 799644 "FFSLPE" 799780 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795444 796220 797016 "FFPOLY" 798684 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794948 794984 795193 "FFPOLY2" 795402 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790770 794867 794930 "FFP" 794935 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 786138 790681 790745 "FF" 790750 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 781234 785481 785671 "FFNBX" 785992 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 776144 780369 780627 "FFNBP" 781088 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770747 775428 775639 "FFNB" 775977 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769579 769777 770092 "FFINTBAS" 770544 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765755 767995 768024 "FFIELDC" 768644 T FFIELDC (NIL) -9 NIL 769020) (-318 764418 764788 765285 "FFIELDC-" 765290 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763988 764033 764157 "FFHOM" 764360 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761686 762170 762687 "FFF" 763503 NIL FFF (NIL T) -7 NIL NIL) (-315 757274 761428 761529 "FFCGX" 761629 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752876 757006 757113 "FFCGP" 757217 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 748029 752603 752711 "FFCG" 752812 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729828 738951 739038 "FFCAT" 744203 NIL FFCAT (NIL T T T) -9 NIL 745688) (-311 725026 726073 727387 "FFCAT-" 728617 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724437 724480 724715 "FFCAT2" 724977 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713641 717431 718646 "FEXPR" 723294 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712643 713078 713120 "FEVALAB" 713204 NIL FEVALAB (NIL T) -9 NIL 713462) (-307 711802 712012 712350 "FEVALAB-" 712355 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710395 711185 711388 "FDIV" 711701 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707461 708176 708292 "FDIVCAT" 709860 NIL FDIVCAT (NIL T T T T) -9 NIL 710297) (-304 707223 707250 707420 "FDIVCAT-" 707425 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706443 706530 706807 "FDIV2" 707130 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 705136 705393 705680 "FCPAK1" 706176 T FCPAK1 (NIL) -7 NIL NIL) (-301 704264 704636 704777 "FCOMP" 705027 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687904 691316 694876 "FC" 700724 T FC (NIL) -8 NIL NIL) (-299 680453 684499 684540 "FAXF" 686342 NIL FAXF (NIL T) -9 NIL 687032) (-298 677732 678387 679212 "FAXF-" 679677 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672838 677108 677284 "FARRAY" 677589 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668184 670255 670308 "FAMR" 671320 NIL FAMR (NIL T T) -9 NIL 671777) (-295 667075 667377 667811 "FAMR-" 667816 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666271 666997 667050 "FAMONOID" 667055 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 664104 664788 664842 "FAMONC" 665783 NIL FAMONC (NIL T T) -9 NIL 666167) (-292 662798 663860 663996 "FAGROUP" 664001 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660601 660920 661322 "FACUTIL" 662479 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659700 659885 660107 "FACTFUNC" 660411 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 652023 658951 659163 "EXPUPXS" 659556 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649522 650058 650640 "EXPRTUBE" 651461 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645716 646308 647045 "EXPRODE" 648861 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630884 644381 644804 "EXPR" 645325 NIL EXPR (NIL T) -8 NIL NIL) (-285 625312 625899 626711 "EXPR2UPS" 630182 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624948 625005 625112 "EXPR2" 625249 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616302 624085 624380 "EXPEXPAN" 624786 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 616129 616259 616288 "EXIT" 616293 T EXIT (NIL) -8 NIL NIL) (-281 615756 615818 615931 "EVALCYC" 616061 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615296 615414 615456 "EVALAB" 615626 NIL EVALAB (NIL T) -9 NIL 615730) (-279 614777 614899 615120 "EVALAB-" 615125 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612239 613551 613580 "EUCDOM" 614135 T EUCDOM (NIL) -9 NIL 614485) (-277 610644 611086 611676 "EUCDOM-" 611681 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598257 600996 603727 "ESTOOLS" 607933 T ESTOOLS (NIL) -7 NIL NIL) (-275 597893 597950 598057 "ESTOOLS2" 598194 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597644 597686 597766 "ESTOOLS1" 597845 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591583 593307 593336 "ES" 596100 T ES (NIL) -9 NIL 597504) (-272 586531 587817 589634 "ES-" 589798 NIL ES- (NIL T) -8 NIL NIL) (-271 582938 583690 584462 "ESCONT" 585779 T ESCONT (NIL) -7 NIL NIL) (-270 582683 582715 582797 "ESCONT1" 582900 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582358 582408 582508 "ES2" 582627 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581988 582046 582155 "ES1" 582294 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581204 581333 581509 "ERROR" 581832 T ERROR (NIL) -7 NIL NIL) (-266 574719 581063 581154 "EQTBL" 581159 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 567184 570065 571498 "EQ" 573319 NIL -3015 (NIL T) -8 NIL NIL) (-264 566816 566873 566982 "EQ2" 567121 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 562108 563154 564247 "EP" 565755 NIL EP (NIL T) -7 NIL NIL) (-262 561267 561831 561860 "ENTIRER" 561865 T ENTIRER (NIL) -9 NIL 561910) (-261 557723 559222 559592 "EMR" 561066 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556867 557052 557107 "ELTAGG" 557487 NIL ELTAGG (NIL T T) -9 NIL 557697) (-259 556586 556648 556789 "ELTAGG-" 556794 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556374 556403 556458 "ELTAB" 556542 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555500 555646 555845 "ELFUTS" 556225 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555241 555297 555326 "ELEMFUN" 555431 T ELEMFUN (NIL) -9 NIL NIL) (-255 555111 555132 555200 "ELEMFUN-" 555205 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 550007 553210 553252 "ELAGG" 554192 NIL ELAGG (NIL T) -9 NIL 554653) (-253 548292 548726 549389 "ELAGG-" 549394 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 541162 542961 543787 "EFUPXS" 547569 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534614 536415 537224 "EFULS" 540439 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 532045 532403 532881 "EFSTRUC" 534246 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 521117 522682 524242 "EF" 530560 NIL EF (NIL T T) -7 NIL NIL) (-248 520218 520602 520751 "EAB" 520988 T EAB (NIL) -8 NIL NIL) (-247 519431 520177 520205 "E04UCFA" 520210 T E04UCFA (NIL) -8 NIL NIL) (-246 518644 519390 519418 "E04NAFA" 519423 T E04NAFA (NIL) -8 NIL NIL) (-245 517857 518603 518631 "E04MBFA" 518636 T E04MBFA (NIL) -8 NIL NIL) (-244 517070 517816 517844 "E04JAFA" 517849 T E04JAFA (NIL) -8 NIL NIL) (-243 516285 517029 517057 "E04GCFA" 517062 T E04GCFA (NIL) -8 NIL NIL) (-242 515500 516244 516272 "E04FDFA" 516277 T E04FDFA (NIL) -8 NIL NIL) (-241 514713 515459 515487 "E04DGFA" 515492 T E04DGFA (NIL) -8 NIL NIL) (-240 508899 510243 511605 "E04AGNT" 513371 T E04AGNT (NIL) -7 NIL NIL) (-239 507625 508105 508146 "DVARCAT" 508621 NIL DVARCAT (NIL T) -9 NIL 508819) (-238 506829 507041 507355 "DVARCAT-" 507360 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499691 506631 506758 "DSMP" 506763 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494517 495648 496712 "DROPT" 498647 T DROPT (NIL) -8 NIL NIL) (-235 494182 494241 494339 "DROPT1" 494452 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489304 490428 491563 "DROPT0" 493067 T DROPT0 (NIL) -7 NIL NIL) (-233 487649 487974 488360 "DRAWPT" 488938 T DRAWPT (NIL) -7 NIL NIL) (-232 482324 483223 484278 "DRAW" 486647 NIL DRAW (NIL T) -7 NIL NIL) (-231 481965 482016 482132 "DRAWHACK" 482267 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480710 480975 481262 "DRAWCX" 481698 T DRAWCX (NIL) -7 NIL NIL) (-229 480228 480296 480446 "DRAWCURV" 480636 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470832 472754 474833 "DRAWCFUN" 478169 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467651 469527 469569 "DQAGG" 470198 NIL DQAGG (NIL T) -9 NIL 470471) (-226 456111 462849 462932 "DPOLCAT" 464770 NIL DPOLCAT (NIL T T T T) -9 NIL 465313) (-225 450951 452297 454254 "DPOLCAT-" 454259 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 445035 450813 450910 "DPMO" 450915 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 439022 444816 444982 "DPMM" 444987 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438784 438835 438909 "DOMAIN" 438968 T DOMAIN (NIL) -8 NIL NIL) (-221 432496 438421 438572 "DMP" 438685 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 432096 432152 432296 "DLP" 432434 NIL DLP (NIL T) -7 NIL NIL) (-219 425746 431197 431424 "DLIST" 431901 NIL DLIST (NIL T) -8 NIL NIL) (-218 422599 424602 424644 "DLAGG" 425194 NIL DLAGG (NIL T) -9 NIL 425422) (-217 421261 421953 421982 "DIVRING" 422132 T DIVRING (NIL) -9 NIL 422240) (-216 420249 420502 420895 "DIVRING-" 420900 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 418351 418708 419114 "DISPLAY" 419863 T DISPLAY (NIL) -7 NIL NIL) (-214 412246 418265 418328 "DIRPROD" 418333 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 411094 411297 411562 "DIRPROD2" 412039 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400738 406737 406791 "DIRPCAT" 407199 NIL DIRPCAT (NIL NIL T) -9 NIL 408015) (-211 398064 398706 399587 "DIRPCAT-" 399924 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 397351 397511 397697 "DIOSP" 397898 T DIOSP (NIL) -7 NIL NIL) (-209 394060 396264 396306 "DIOPS" 396740 NIL DIOPS (NIL T) -9 NIL 396968) (-208 393609 393723 393914 "DIOPS-" 393919 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392480 393118 393147 "DIFRING" 393334 T DIFRING (NIL) -9 NIL 393443) (-206 392126 392203 392355 "DIFRING-" 392360 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389917 391199 391240 "DIFEXT" 391599 NIL DIFEXT (NIL T) -9 NIL 391890) (-204 388203 388631 389296 "DIFEXT-" 389301 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385531 387735 387777 "DIAGG" 387782 NIL DIAGG (NIL T) -9 NIL 387802) (-202 384915 385072 385324 "DIAGG-" 385329 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 380386 383874 384151 "DHMATRIX" 384684 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375998 376907 377917 "DFSFUN" 379396 T DFSFUN (NIL) -7 NIL NIL) (-199 370784 374712 375077 "DFLOAT" 375653 T DFLOAT (NIL) -8 NIL NIL) (-198 369017 369298 369693 "DFINTTLS" 370492 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 366050 367052 367450 "DERHAM" 368684 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363905 365825 365914 "DEQUEUE" 365994 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 363123 363256 363451 "DEGRED" 363767 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359539 360280 361128 "DEFINTRF" 362355 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 357078 357545 358141 "DEFINTEF" 359060 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350909 356519 356685 "DECIMAL" 356932 T DECIMAL (NIL) -8 NIL NIL) (-191 348421 348879 349385 "DDFACT" 350453 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 348017 348060 348211 "DBLRESP" 348372 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345727 346061 346430 "DBASE" 347775 NIL DBASE (NIL T) -8 NIL NIL) (-188 344862 345686 345714 "D03FAFA" 345719 T D03FAFA (NIL) -8 NIL NIL) (-187 343998 344821 344849 "D03EEFA" 344854 T D03EEFA (NIL) -8 NIL NIL) (-186 341948 342414 342903 "D03AGNT" 343529 T D03AGNT (NIL) -7 NIL NIL) (-185 341266 341907 341935 "D02EJFA" 341940 T D02EJFA (NIL) -8 NIL NIL) (-184 340584 341225 341253 "D02CJFA" 341258 T D02CJFA (NIL) -8 NIL NIL) (-183 339902 340543 340571 "D02BHFA" 340576 T D02BHFA (NIL) -8 NIL NIL) (-182 339220 339861 339889 "D02BBFA" 339894 T D02BBFA (NIL) -8 NIL NIL) (-181 332419 334006 335612 "D02AGNT" 337634 T D02AGNT (NIL) -7 NIL NIL) (-180 330200 330719 331262 "D01WGTS" 331896 T D01WGTS (NIL) -7 NIL NIL) (-179 329307 330159 330187 "D01TRNS" 330192 T D01TRNS (NIL) -8 NIL NIL) (-178 328414 329266 329294 "D01GBFA" 329299 T D01GBFA (NIL) -8 NIL NIL) (-177 327521 328373 328401 "D01FCFA" 328406 T D01FCFA (NIL) -8 NIL NIL) (-176 326628 327480 327508 "D01ASFA" 327513 T D01ASFA (NIL) -8 NIL NIL) (-175 325735 326587 326615 "D01AQFA" 326620 T D01AQFA (NIL) -8 NIL NIL) (-174 324842 325694 325722 "D01APFA" 325727 T D01APFA (NIL) -8 NIL NIL) (-173 323949 324801 324829 "D01ANFA" 324834 T D01ANFA (NIL) -8 NIL NIL) (-172 323056 323908 323936 "D01AMFA" 323941 T D01AMFA (NIL) -8 NIL NIL) (-171 322163 323015 323043 "D01ALFA" 323048 T D01ALFA (NIL) -8 NIL NIL) (-170 321270 322122 322150 "D01AKFA" 322155 T D01AKFA (NIL) -8 NIL NIL) (-169 320377 321229 321257 "D01AJFA" 321262 T D01AJFA (NIL) -8 NIL NIL) (-168 313709 315251 316803 "D01AGNT" 318845 T D01AGNT (NIL) -7 NIL NIL) (-167 313046 313174 313326 "CYCLOTOM" 313577 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309781 310494 311221 "CYCLES" 312339 T CYCLES (NIL) -7 NIL NIL) (-165 309093 309227 309398 "CVMP" 309642 NIL CVMP (NIL T) -7 NIL NIL) (-164 306875 307132 307507 "CTRIGMNP" 308821 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 306249 306348 306501 "CSTTOOLS" 306772 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 302048 302705 303463 "CRFP" 305561 NIL CRFP (NIL T T) -7 NIL NIL) (-161 301095 301280 301508 "CRAPACK" 301852 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 300481 300582 300785 "CPMATCH" 300972 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 300206 300234 300340 "CPIMA" 300447 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 296570 297242 297960 "COORDSYS" 299541 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 292431 294573 295065 "CONTFRAC" 296110 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291584 292148 292177 "COMRING" 292182 T COMRING (NIL) -9 NIL 292233) (-155 290665 290942 291126 "COMPPROP" 291420 T COMPPROP (NIL) -8 NIL NIL) (-154 290326 290361 290489 "COMPLPAT" 290624 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 280309 290137 290245 "COMPLEX" 290250 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279945 280002 280109 "COMPLEX2" 280246 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279663 279698 279796 "COMPFACT" 279904 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263943 274237 274278 "COMPCAT" 275280 NIL COMPCAT (NIL T) -9 NIL 276656) (-149 253459 256382 260009 "COMPCAT-" 260365 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 253190 253218 253320 "COMMUPC" 253425 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252985 253018 253077 "COMMONOP" 253151 T COMMONOP (NIL) -7 NIL NIL) (-146 252568 252736 252823 "COMM" 252918 T COMM (NIL) -8 NIL NIL) (-145 251822 252014 252043 "COMBOPC" 252379 T COMBOPC (NIL) -9 NIL 252552) (-144 250718 250928 251170 "COMBINAT" 251612 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246924 247495 248133 "COMBF" 250142 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245710 246040 246275 "COLOR" 246709 T COLOR (NIL) -8 NIL NIL) (-141 245350 245397 245522 "CMPLXRT" 245657 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240908 241922 242988 "CLIP" 244304 T CLIP (NIL) -7 NIL NIL) (-139 239246 240016 240254 "CLIF" 240736 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 235477 237395 237437 "CLAGG" 238366 NIL CLAGG (NIL T) -9 NIL 238899) (-137 233899 234356 234939 "CLAGG-" 234944 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 233443 233528 233668 "CINTSLPE" 233808 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230944 231415 231963 "CHVAR" 232971 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 230166 230730 230759 "CHARZ" 230764 T CHARZ (NIL) -9 NIL 230778) (-133 229920 229960 230038 "CHARPOL" 230120 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 229026 229623 229652 "CHARNZ" 229699 T CHARNZ (NIL) -9 NIL 229754) (-131 227049 227716 228051 "CHAR" 228711 T CHAR (NIL) -8 NIL NIL) (-130 226774 226835 226864 "CFCAT" 226975 T CFCAT (NIL) -9 NIL NIL) (-129 226019 226130 226312 "CDEN" 226658 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 222011 225172 225452 "CCLASS" 225759 T CCLASS (NIL) -8 NIL NIL) (-127 217064 218040 218793 "CARTEN" 221314 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 216172 216320 216541 "CARTEN2" 216911 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 214469 215324 215580 "CARD" 215936 T CARD (NIL) -8 NIL NIL) (-124 213841 214169 214198 "CACHSET" 214330 T CACHSET (NIL) -9 NIL 214407) (-123 213337 213633 213662 "CABMON" 213712 T CABMON (NIL) -9 NIL 213768) (-122 210900 213029 213136 "BTREE" 213263 NIL BTREE (NIL T) -8 NIL NIL) (-121 208404 210548 210670 "BTOURN" 210810 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205828 207875 207917 "BTCAT" 207985 NIL BTCAT (NIL T) -9 NIL 208062) (-119 205495 205575 205724 "BTCAT-" 205729 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200685 204556 204585 "BTAGG" 204841 T BTAGG (NIL) -9 NIL 205020) (-117 200108 200252 200482 "BTAGG-" 200487 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 197158 199386 199601 "BSTREE" 199925 NIL BSTREE (NIL T) -8 NIL NIL) (-115 196296 196422 196606 "BRILL" 197014 NIL BRILL (NIL T) -7 NIL NIL) (-114 193004 195025 195067 "BRAGG" 195716 NIL BRAGG (NIL T) -9 NIL 195972) (-113 191533 191939 192494 "BRAGG-" 192499 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184741 190879 191063 "BPADICRT" 191381 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 183045 184678 184723 "BPADIC" 184728 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182745 182775 182888 "BOUNDZRO" 183009 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 178260 179351 180218 "BOP" 181898 T BOP (NIL) -8 NIL NIL) (-108 175883 176327 176846 "BOP1" 177774 NIL BOP1 (NIL T) -7 NIL NIL) (-107 174236 174926 175220 "BOOLEAN" 175609 T BOOLEAN (NIL) -8 NIL NIL) (-106 173602 173980 174033 "BMODULE" 174038 NIL BMODULE (NIL T T) -9 NIL 174102) (-105 169412 173400 173473 "BITS" 173549 T BITS (NIL) -8 NIL NIL) (-104 168509 168944 169096 "BINFILE" 169280 T BINFILE (NIL) -8 NIL NIL) (-103 162344 167953 168118 "BINARY" 168364 T BINARY (NIL) -8 NIL NIL) (-102 160177 161599 161641 "BGAGG" 161901 NIL BGAGG (NIL T) -9 NIL 162038) (-101 160008 160040 160131 "BGAGG-" 160136 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 159106 159392 159597 "BFUNCT" 159823 T BFUNCT (NIL) -8 NIL NIL) (-99 157809 157987 158271 "BEZOUT" 158931 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154340 156669 156997 "BBTREE" 157512 NIL BBTREE (NIL T) -8 NIL NIL) (-97 154077 154130 154157 "BASTYPE" 154274 T BASTYPE (NIL) -9 NIL NIL) (-96 153933 153961 154031 "BASTYPE-" 154036 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153371 153447 153597 "BALFACT" 153844 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 152193 152790 152975 "AUTOMOR" 153216 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151918 151923 151950 "ATTREG" 151955 T ATTREG (NIL) -9 NIL NIL) (-92 150197 150615 150967 "ATTRBUT" 151584 T ATTRBUT (NIL) -8 NIL NIL) (-91 149732 149845 149872 "ATRIG" 150073 T ATRIG (NIL) -9 NIL NIL) (-90 149541 149582 149669 "ATRIG-" 149674 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147744 149317 149405 "ASTACK" 149484 NIL ASTACK (NIL T) -8 NIL NIL) (-88 146251 146548 146912 "ASSOCEQ" 147427 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 145283 145910 146034 "ASP9" 146158 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 145047 145231 145270 "ASP8" 145275 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143917 144652 144794 "ASP80" 144936 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142816 143552 143684 "ASP7" 143816 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141772 142493 142611 "ASP78" 142729 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140743 141452 141569 "ASP77" 141686 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139658 140381 140512 "ASP74" 140643 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138559 139293 139425 "ASP73" 139557 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137514 138236 138354 "ASP6" 138472 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136463 137191 137309 "ASP55" 137427 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135413 136137 136256 "ASP50" 136375 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134501 135114 135224 "ASP4" 135334 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133589 134202 134312 "ASP49" 134422 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132374 133128 133296 "ASP42" 133478 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 131152 131907 132077 "ASP41" 132261 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 130104 130829 130947 "ASP35" 131065 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129869 130052 130091 "ASP34" 130096 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129606 129673 129749 "ASP33" 129824 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128502 129241 129373 "ASP31" 129505 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 128267 128450 128489 "ASP30" 128494 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 128002 128071 128147 "ASP29" 128222 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127767 127950 127989 "ASP28" 127994 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127532 127715 127754 "ASP27" 127759 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126616 127230 127341 "ASP24" 127452 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125533 126257 126387 "ASP20" 126517 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124621 125234 125344 "ASP1" 125454 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123565 124295 124414 "ASP19" 124533 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 123302 123369 123445 "ASP12" 123520 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 122155 122901 123045 "ASP10" 123189 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 120060 121999 122090 "ARRAY2" 122095 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115882 119708 119822 "ARRAY1" 119977 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114914 115087 115308 "ARRAY12" 115705 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 109279 111144 111220 "ARR2CAT" 113850 NIL ARR2CAT (NIL T T T) -9 NIL 114608) (-54 106713 107457 108411 "ARR2CAT-" 108416 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105473 105623 105926 "APPRULE" 106551 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 105126 105174 105292 "APPLYORE" 105419 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 104100 104391 104586 "ANY" 104949 T ANY (NIL) -8 NIL NIL) (-50 103378 103501 103658 "ANY1" 103974 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100910 101828 102153 "ANTISYM" 103103 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100737 100869 100896 "ANON" 100901 T ANON (NIL) -8 NIL NIL) (-47 94814 99282 99733 "AN" 100304 T AN (NIL) -8 NIL NIL) (-46 91126 92524 92575 "AMR" 93314 NIL AMR (NIL T T) -9 NIL 93907) (-45 90239 90460 90822 "AMR-" 90827 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74801 90156 90217 "ALIST" 90222 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71638 74395 74564 "ALGSC" 74719 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 68196 68750 69356 "ALGPKG" 71079 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 67473 67574 67758 "ALGMFACT" 68082 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 63230 63911 64561 "ALGMANIP" 67001 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 54549 62856 63006 "ALGFF" 63163 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53745 53876 54055 "ALGFACT" 54407 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52735 53345 53384 "ALGEBRA" 53444 NIL ALGEBRA (NIL T) -9 NIL 53502) (-36 52453 52512 52644 "ALGEBRA-" 52649 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34174 49899 49952 "ALAGG" 50088 NIL ALAGG (NIL T T) -9 NIL 50249) (-34 33709 33822 33849 "AHYP" 34050 T AHYP (NIL) -9 NIL NIL) (-33 32640 32888 32915 "AGG" 33414 T AGG (NIL) -9 NIL 33692) (-32 32074 32236 32450 "AGG-" 32455 NIL AGG- (NIL T) -8 NIL NIL) (-31 29763 30181 30597 "AF" 31718 NIL AF (NIL T T) -7 NIL NIL) (-30 29041 29295 29449 "ACPLOT" 29627 T ACPLOT (NIL) -8 NIL NIL) (-29 18460 26406 26458 "ACFS" 27169 NIL ACFS (NIL T) -9 NIL 27408) (-28 16474 16964 17739 "ACFS-" 17744 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12694 14650 14677 "ACF" 15556 T ACF (NIL) -9 NIL 15968) (-26 11398 11732 12225 "ACF-" 12230 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11192 "ABELSG" 11284 T ABELSG (NIL) -9 NIL 11349) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10232 10493 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9896 9980 10118 "ABELMON-" 10123 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9230 9576 9603 "ABELGRP" 9728 T ABELGRP (NIL) -9 NIL 9810) (-20 8693 8822 9038 "ABELGRP-" 9043 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8029 8069 "A1AGG" 8074 NIL A1AGG (NIL T) -9 NIL 8114) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-1185 3125904 3125909 3125914 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3125889 3125894 3125899 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3125874 3125879 3125884 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3125859 3125864 3125869 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3125844 3125849 3125854 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1180 3124974 3125719 3125796 "ZMOD" 3125801 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1179 3124084 3124248 3124457 "ZLINDEP" 3124806 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1178 3113488 3115233 3117185 "ZDSOLVE" 3122233 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1177 3112734 3112875 3113064 "YSTREAM" 3113334 NIL YSTREAM (NIL T) -7 NIL NIL) (-1176 3110503 3112039 3112242 "XRPOLY" 3112577 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1175 3106965 3108294 3108876 "XPR" 3109967 NIL XPR (NIL T T) -8 NIL NIL) (-1174 3104679 3106300 3106503 "XPOLY" 3106796 NIL XPOLY (NIL T) -8 NIL NIL) (-1173 3102492 3103870 3103925 "XPOLYC" 3104210 NIL XPOLYC (NIL T T) -9 NIL 3104323) (-1172 3098864 3101009 3101397 "XPBWPOLY" 3102150 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1171 3094744 3097057 3097100 "XF" 3097721 NIL XF (NIL T) -9 NIL 3098120) (-1170 3094365 3094453 3094622 "XF-" 3094627 NIL XF- (NIL T T) -8 NIL NIL) (-1169 3089744 3091043 3091098 "XFALG" 3093246 NIL XFALG (NIL T T) -9 NIL 3094033) (-1168 3088881 3088985 3089189 "XEXPPKG" 3089636 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1167 3086979 3088732 3088827 "XDPOLY" 3088832 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1166 3085857 3086467 3086510 "XALG" 3086572 NIL XALG (NIL T) -9 NIL 3086691) (-1165 3079333 3083841 3084334 "WUTSET" 3085449 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1164 3077145 3077952 3078303 "WP" 3079115 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1163 3076031 3076229 3076524 "WFFINTBS" 3076942 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1162 3073935 3074362 3074824 "WEIER" 3075603 NIL WEIER (NIL T) -7 NIL NIL) (-1161 3073083 3073507 3073550 "VSPACE" 3073686 NIL VSPACE (NIL T) -9 NIL 3073760) (-1160 3072921 3072948 3073039 "VSPACE-" 3073044 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1159 3072667 3072710 3072781 "VOID" 3072872 T VOID (NIL) -8 NIL NIL) (-1158 3070803 3071162 3071568 "VIEW" 3072283 T VIEW (NIL) -7 NIL NIL) (-1157 3067228 3067866 3068603 "VIEWDEF" 3070088 T VIEWDEF (NIL) -7 NIL NIL) (-1156 3056567 3058776 3060949 "VIEW3D" 3065077 T VIEW3D (NIL) -8 NIL NIL) (-1155 3048849 3050478 3052057 "VIEW2D" 3055010 T VIEW2D (NIL) -8 NIL NIL) (-1154 3044258 3048619 3048711 "VECTOR" 3048792 NIL VECTOR (NIL T) -8 NIL NIL) (-1153 3042835 3043094 3043412 "VECTOR2" 3043988 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1152 3036377 3040623 3040667 "VECTCAT" 3041655 NIL VECTCAT (NIL T) -9 NIL 3042239) (-1151 3035391 3035645 3036035 "VECTCAT-" 3036040 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1150 3034872 3035042 3035162 "VARIABLE" 3035306 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1149 3033707 3033861 3034122 "UTSODETL" 3034698 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1148 3031147 3031607 3032131 "UTSODE" 3033248 NIL UTSODE (NIL T T) -7 NIL NIL) (-1147 3022995 3028787 3029275 "UTS" 3030716 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1146 3014293 3019655 3019698 "UTSCAT" 3020799 NIL UTSCAT (NIL T) -9 NIL 3021556) (-1145 3011649 3012364 3013352 "UTSCAT-" 3013357 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1144 3011280 3011323 3011454 "UTS2" 3011600 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1143 3005555 3008120 3008164 "URAGG" 3010234 NIL URAGG (NIL T) -9 NIL 3010956) (-1142 3002494 3003357 3004480 "URAGG-" 3004485 NIL URAGG- (NIL T T) -8 NIL NIL) (-1141 2998180 3001111 3001582 "UPXSSING" 3002158 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1140 2990074 2997301 2997581 "UPXS" 2997957 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1139 2983106 2989979 2990050 "UPXSCONS" 2990055 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1138 2973334 2980161 2980223 "UPXSCCA" 2980872 NIL UPXSCCA (NIL T T) -9 NIL 2981113) (-1137 2972973 2973058 2973231 "UPXSCCA-" 2973236 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1136 2963123 2969723 2969766 "UPXSCAT" 2970409 NIL UPXSCAT (NIL T) -9 NIL 2971017) (-1135 2962557 2962636 2962813 "UPXS2" 2963038 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1134 2961211 2961464 2961815 "UPSQFREE" 2962300 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1133 2955059 2958111 2958166 "UPSCAT" 2959315 NIL UPSCAT (NIL T T) -9 NIL 2960088) (-1132 2954273 2954477 2954800 "UPSCAT-" 2954805 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1131 2940346 2948343 2948386 "UPOLYC" 2950464 NIL UPOLYC (NIL T) -9 NIL 2951684) (-1130 2931739 2934143 2937268 "UPOLYC-" 2937273 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1129 2931370 2931413 2931544 "UPOLYC2" 2931690 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1128 2922829 2930939 2931076 "UP" 2931280 NIL UP (NIL NIL T) -8 NIL NIL) (-1127 2922172 2922279 2922442 "UPMP" 2922718 NIL UPMP (NIL T T) -7 NIL NIL) (-1126 2921725 2921806 2921945 "UPDIVP" 2922085 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1125 2920293 2920542 2920858 "UPDECOMP" 2921474 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1124 2919528 2919640 2919825 "UPCDEN" 2920177 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1123 2919051 2919120 2919267 "UP2" 2919453 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1122 2917576 2918262 2918536 "UNISEG" 2918812 NIL UNISEG (NIL T) -8 NIL NIL) (-1121 2916791 2916918 2917123 "UNISEG2" 2917419 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1120 2915851 2916031 2916257 "UNIFACT" 2916607 NIL UNIFACT (NIL T) -7 NIL NIL) (-1119 2899750 2915032 2915282 "ULS" 2915658 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1118 2887718 2899655 2899726 "ULSCONS" 2899731 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1117 2870421 2882431 2882493 "ULSCCAT" 2883205 NIL ULSCCAT (NIL T T) -9 NIL 2883501) (-1116 2869472 2869717 2870104 "ULSCCAT-" 2870109 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1115 2859415 2865929 2865972 "ULSCAT" 2866828 NIL ULSCAT (NIL T) -9 NIL 2867558) (-1114 2858849 2858928 2859105 "ULS2" 2859330 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1113 2857246 2858213 2858244 "UFD" 2858456 T UFD (NIL) -9 NIL 2858570) (-1112 2857040 2857086 2857181 "UFD-" 2857186 NIL UFD- (NIL T) -8 NIL NIL) (-1111 2856122 2856305 2856521 "UDVO" 2856846 T UDVO (NIL) -7 NIL NIL) (-1110 2853938 2854347 2854818 "UDPO" 2855686 NIL UDPO (NIL T) -7 NIL NIL) (-1109 2853870 2853875 2853906 "TYPE" 2853911 T TYPE (NIL) -9 NIL NIL) (-1108 2852841 2853043 2853283 "TWOFACT" 2853664 NIL TWOFACT (NIL T) -7 NIL NIL) (-1107 2851779 2852116 2852379 "TUPLE" 2852613 NIL TUPLE (NIL T) -8 NIL NIL) (-1106 2849470 2849989 2850528 "TUBETOOL" 2851262 T TUBETOOL (NIL) -7 NIL NIL) (-1105 2848319 2848524 2848765 "TUBE" 2849263 NIL TUBE (NIL T) -8 NIL NIL) (-1104 2843043 2847297 2847579 "TS" 2848071 NIL TS (NIL T) -8 NIL NIL) (-1103 2831746 2835838 2835935 "TSETCAT" 2841169 NIL TSETCAT (NIL T T T T) -9 NIL 2842700) (-1102 2826482 2828079 2829969 "TSETCAT-" 2829974 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1101 2820745 2821591 2822533 "TRMANIP" 2825618 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1100 2820186 2820249 2820412 "TRIMAT" 2820677 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1099 2817992 2818229 2818592 "TRIGMNIP" 2819935 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1098 2817511 2817624 2817655 "TRIGCAT" 2817868 T TRIGCAT (NIL) -9 NIL NIL) (-1097 2817180 2817259 2817400 "TRIGCAT-" 2817405 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1096 2814085 2816040 2816320 "TREE" 2816935 NIL TREE (NIL T) -8 NIL NIL) (-1095 2813358 2813886 2813917 "TRANFUN" 2813952 T TRANFUN (NIL) -9 NIL 2814018) (-1094 2812637 2812828 2813108 "TRANFUN-" 2813113 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1093 2812441 2812473 2812534 "TOPSP" 2812598 T TOPSP (NIL) -7 NIL NIL) (-1092 2811793 2811908 2812061 "TOOLSIGN" 2812322 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1091 2810454 2810970 2811209 "TEXTFILE" 2811576 T TEXTFILE (NIL) -8 NIL NIL) (-1090 2808319 2808833 2809271 "TEX" 2810038 T TEX (NIL) -8 NIL NIL) (-1089 2808100 2808131 2808203 "TEX1" 2808282 NIL TEX1 (NIL T) -7 NIL NIL) (-1088 2807748 2807811 2807901 "TEMUTL" 2808032 T TEMUTL (NIL) -7 NIL NIL) (-1087 2805902 2806182 2806507 "TBCMPPK" 2807471 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1086 2797560 2803820 2803877 "TBAGG" 2804277 NIL TBAGG (NIL T T) -9 NIL 2804488) (-1085 2792630 2794118 2795872 "TBAGG-" 2795877 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1084 2792014 2792121 2792266 "TANEXP" 2792519 NIL TANEXP (NIL T) -7 NIL NIL) (-1083 2785527 2791871 2791964 "TABLE" 2791969 NIL TABLE (NIL T T) -8 NIL NIL) (-1082 2784940 2785038 2785176 "TABLEAU" 2785424 NIL TABLEAU (NIL T) -8 NIL NIL) (-1081 2779548 2780768 2782016 "TABLBUMP" 2783726 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1080 2776011 2776706 2777489 "SYSSOLP" 2778799 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1079 2774593 2774841 2775146 "SYNTAX" 2775728 T SYNTAX (NIL) -8 NIL NIL) (-1078 2771727 2772335 2772973 "SYMTAB" 2773977 T SYMTAB (NIL) -8 NIL NIL) (-1077 2766976 2767878 2768861 "SYMS" 2770766 T SYMS (NIL) -8 NIL NIL) (-1076 2764209 2766436 2766665 "SYMPOLY" 2766781 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1075 2763729 2763804 2763926 "SYMFUNC" 2764121 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1074 2759707 2760966 2761788 "SYMBOL" 2762929 T SYMBOL (NIL) -8 NIL NIL) (-1073 2753246 2754935 2756655 "SWITCH" 2758009 T SWITCH (NIL) -8 NIL NIL) (-1072 2746479 2752073 2752375 "SUTS" 2753001 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1071 2738372 2745600 2745880 "SUPXS" 2746256 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1070 2729905 2737993 2738118 "SUP" 2738281 NIL SUP (NIL T) -8 NIL NIL) (-1069 2729064 2729191 2729408 "SUPFRACF" 2729773 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1068 2728689 2728748 2728859 "SUP2" 2728999 NIL SUP2 (NIL T T) -7 NIL NIL) (-1067 2727115 2727387 2727747 "SUMRF" 2728390 NIL SUMRF (NIL T) -7 NIL NIL) (-1066 2726436 2726501 2726698 "SUMFS" 2727037 NIL SUMFS (NIL T T) -7 NIL NIL) (-1065 2710375 2725617 2725867 "SULS" 2726243 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1064 2709697 2709900 2710040 "SUCH" 2710283 NIL SUCH (NIL T T) -8 NIL NIL) (-1063 2703624 2704636 2705594 "SUBSPACE" 2708785 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1062 2703054 2703144 2703308 "SUBRESP" 2703512 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1061 2696423 2697719 2699030 "STTF" 2701790 NIL STTF (NIL T) -7 NIL NIL) (-1060 2690596 2691716 2692863 "STTFNC" 2695323 NIL STTFNC (NIL T) -7 NIL NIL) (-1059 2681947 2683814 2685607 "STTAYLOR" 2688837 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1058 2675203 2681811 2681894 "STRTBL" 2681899 NIL STRTBL (NIL T) -8 NIL NIL) (-1057 2670594 2675158 2675189 "STRING" 2675194 T STRING (NIL) -8 NIL NIL) (-1056 2665452 2669937 2669968 "STRICAT" 2670027 T STRICAT (NIL) -9 NIL 2670089) (-1055 2658173 2662975 2663595 "STREAM" 2664867 NIL STREAM (NIL T) -8 NIL NIL) (-1054 2657683 2657760 2657904 "STREAM3" 2658090 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1053 2656665 2656848 2657083 "STREAM2" 2657496 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1052 2656353 2656405 2656498 "STREAM1" 2656607 NIL STREAM1 (NIL T) -7 NIL NIL) (-1051 2655369 2655550 2655781 "STINPROD" 2656169 NIL STINPROD (NIL T) -7 NIL NIL) (-1050 2654947 2655131 2655162 "STEP" 2655242 T STEP (NIL) -9 NIL 2655320) (-1049 2648502 2654846 2654923 "STBL" 2654928 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1048 2643674 2647721 2647765 "STAGG" 2647918 NIL STAGG (NIL T) -9 NIL 2648007) (-1047 2641376 2641978 2642850 "STAGG-" 2642855 NIL STAGG- (NIL T T) -8 NIL NIL) (-1046 2639574 2641146 2641238 "STACK" 2641319 NIL STACK (NIL T) -8 NIL NIL) (-1045 2632305 2637721 2638176 "SREGSET" 2639204 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1044 2624745 2626113 2627625 "SRDCMPK" 2630911 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1043 2617688 2622155 2622186 "SRAGG" 2623489 T SRAGG (NIL) -9 NIL 2624097) (-1042 2616705 2616960 2617339 "SRAGG-" 2617344 NIL SRAGG- (NIL T) -8 NIL NIL) (-1041 2611154 2615624 2616051 "SQMATRIX" 2616324 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1040 2604912 2607874 2608600 "SPLTREE" 2610500 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1039 2600902 2601568 2602214 "SPLNODE" 2604338 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1038 2599948 2600181 2600212 "SPFCAT" 2600656 T SPFCAT (NIL) -9 NIL NIL) (-1037 2598685 2598895 2599159 "SPECOUT" 2599706 T SPECOUT (NIL) -7 NIL NIL) (-1036 2598446 2598486 2598555 "SPADPRSR" 2598638 T SPADPRSR (NIL) -7 NIL NIL) (-1035 2590468 2592215 2592258 "SPACEC" 2596581 NIL SPACEC (NIL T) -9 NIL 2598397) (-1034 2588640 2590401 2590449 "SPACE3" 2590454 NIL SPACE3 (NIL T) -8 NIL NIL) (-1033 2587392 2587563 2587854 "SORTPAK" 2588445 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1032 2585448 2585751 2586169 "SOLVETRA" 2587056 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1031 2584459 2584681 2584955 "SOLVESER" 2585221 NIL SOLVESER (NIL T) -7 NIL NIL) (-1030 2579679 2580560 2581562 "SOLVERAD" 2583511 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1029 2575494 2576103 2576832 "SOLVEFOR" 2579046 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1028 2569793 2574845 2574942 "SNTSCAT" 2574947 NIL SNTSCAT (NIL T T T T) -9 NIL 2575017) (-1027 2563898 2568124 2568514 "SMTS" 2569483 NIL SMTS (NIL T T T) -8 NIL NIL) (-1026 2558308 2563787 2563863 "SMP" 2563868 NIL SMP (NIL T T) -8 NIL NIL) (-1025 2556467 2556768 2557166 "SMITH" 2558005 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1024 2549431 2553627 2553730 "SMATCAT" 2555070 NIL SMATCAT (NIL NIL T T T) -9 NIL 2555619) (-1023 2546372 2547195 2548372 "SMATCAT-" 2548377 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1022 2544091 2545608 2545652 "SKAGG" 2545913 NIL SKAGG (NIL T) -9 NIL 2546048) (-1021 2540149 2543195 2543473 "SINT" 2543835 T SINT (NIL) -8 NIL NIL) (-1020 2539921 2539959 2540025 "SIMPAN" 2540105 T SIMPAN (NIL) -7 NIL NIL) (-1019 2538759 2538980 2539255 "SIGNRF" 2539680 NIL SIGNRF (NIL T) -7 NIL NIL) (-1018 2537568 2537719 2538009 "SIGNEF" 2538588 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1017 2535258 2535712 2536218 "SHP" 2537109 NIL SHP (NIL T NIL) -7 NIL NIL) (-1016 2529117 2535159 2535235 "SHDP" 2535240 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1015 2528606 2528798 2528829 "SGROUP" 2528981 T SGROUP (NIL) -9 NIL 2529068) (-1014 2528376 2528428 2528532 "SGROUP-" 2528537 NIL SGROUP- (NIL T) -8 NIL NIL) (-1013 2525212 2525909 2526632 "SGCF" 2527675 T SGCF (NIL) -7 NIL NIL) (-1012 2519610 2524662 2524759 "SFRTCAT" 2524764 NIL SFRTCAT (NIL T T T T) -9 NIL 2524802) (-1011 2513070 2514085 2515219 "SFRGCD" 2518593 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1010 2506236 2507307 2508491 "SFQCMPK" 2512003 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1009 2505858 2505947 2506057 "SFORT" 2506177 NIL SFORT (NIL T T) -8 NIL NIL) (-1008 2505003 2505698 2505819 "SEXOF" 2505824 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1007 2504137 2504884 2504952 "SEX" 2504957 T SEX (NIL) -8 NIL NIL) (-1006 2498913 2499602 2499698 "SEXCAT" 2503469 NIL SEXCAT (NIL T T T T T) -9 NIL 2504088) (-1005 2496093 2498847 2498895 "SET" 2498900 NIL SET (NIL T) -8 NIL NIL) (-1004 2494344 2494806 2495111 "SETMN" 2495834 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1003 2493951 2494077 2494108 "SETCAT" 2494225 T SETCAT (NIL) -9 NIL 2494309) (-1002 2493731 2493783 2493882 "SETCAT-" 2493887 NIL SETCAT- (NIL T) -8 NIL NIL) (-1001 2490118 2492192 2492236 "SETAGG" 2493106 NIL SETAGG (NIL T) -9 NIL 2493446) (-1000 2489576 2489692 2489929 "SETAGG-" 2489934 NIL SETAGG- (NIL T T) -8 NIL NIL) (-999 2488786 2489079 2489139 "SEGXCAT" 2489422 NIL SEGXCAT (NIL T T) -9 NIL 2489541) (-998 2487848 2488458 2488636 "SEG" 2488641 NIL SEG (NIL T) -8 NIL NIL) (-997 2486765 2486978 2487020 "SEGCAT" 2487593 NIL SEGCAT (NIL T) -9 NIL 2487831) (-996 2485827 2486155 2486351 "SEGBIND" 2486602 NIL SEGBIND (NIL T) -8 NIL NIL) (-995 2485459 2485516 2485625 "SEGBIND2" 2485764 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-994 2484694 2484817 2485016 "SEG2" 2485306 NIL SEG2 (NIL T T) -7 NIL NIL) (-993 2484133 2484631 2484676 "SDVAR" 2484681 NIL SDVAR (NIL T) -8 NIL NIL) (-992 2476439 2483912 2484036 "SDPOL" 2484041 NIL SDPOL (NIL T) -8 NIL NIL) (-991 2475038 2475304 2475621 "SCPKG" 2476154 NIL SCPKG (NIL T) -7 NIL NIL) (-990 2474265 2474398 2474575 "SCACHE" 2474893 NIL SCACHE (NIL T) -7 NIL NIL) (-989 2473708 2474029 2474112 "SAOS" 2474202 T SAOS (NIL) -8 NIL NIL) (-988 2473276 2473311 2473482 "SAERFFC" 2473667 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-987 2467172 2473175 2473253 "SAE" 2473258 NIL SAE (NIL T T NIL) -8 NIL NIL) (-986 2466768 2466803 2466960 "SAEFACT" 2467131 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-985 2465094 2465408 2465807 "RURPK" 2466434 NIL RURPK (NIL T NIL) -7 NIL NIL) (-984 2463747 2464024 2464331 "RULESET" 2464930 NIL RULESET (NIL T T T) -8 NIL NIL) (-983 2460955 2461458 2461919 "RULE" 2463429 NIL RULE (NIL T T T) -8 NIL NIL) (-982 2460597 2460752 2460833 "RULECOLD" 2460907 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-981 2455489 2456283 2457199 "RSETGCD" 2459796 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-980 2444803 2449855 2449950 "RSETCAT" 2454015 NIL RSETCAT (NIL T T T T) -9 NIL 2455112) (-979 2442734 2443273 2444093 "RSETCAT-" 2444098 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-978 2435164 2436539 2438055 "RSDCMPK" 2441333 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-977 2433181 2433622 2433695 "RRCC" 2434771 NIL RRCC (NIL T T) -9 NIL 2435115) (-976 2432535 2432709 2432985 "RRCC-" 2432990 NIL RRCC- (NIL T T T) -8 NIL NIL) (-975 2406854 2416479 2416544 "RPOLCAT" 2427046 NIL RPOLCAT (NIL T T T) -9 NIL 2430204) (-974 2398358 2400696 2403814 "RPOLCAT-" 2403819 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-973 2389436 2396588 2397068 "ROUTINE" 2397898 T ROUTINE (NIL) -8 NIL NIL) (-972 2386141 2388992 2389139 "ROMAN" 2389309 T ROMAN (NIL) -8 NIL NIL) (-971 2384427 2385012 2385269 "ROIRC" 2385947 NIL ROIRC (NIL T T) -8 NIL NIL) (-970 2380784 2383088 2383117 "RNS" 2383413 T RNS (NIL) -9 NIL 2383683) (-969 2379298 2379681 2380212 "RNS-" 2380285 NIL RNS- (NIL T) -8 NIL NIL) (-968 2378723 2379131 2379160 "RNG" 2379165 T RNG (NIL) -9 NIL 2379186) (-967 2378120 2378482 2378523 "RMODULE" 2378583 NIL RMODULE (NIL T) -9 NIL 2378625) (-966 2376972 2377066 2377396 "RMCAT2" 2378021 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-965 2373686 2376155 2376476 "RMATRIX" 2376707 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-964 2366682 2368916 2369029 "RMATCAT" 2372338 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2373320) (-963 2366061 2366208 2366511 "RMATCAT-" 2366516 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-962 2365631 2365706 2365832 "RINTERP" 2365980 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-961 2364681 2365245 2365274 "RING" 2365384 T RING (NIL) -9 NIL 2365478) (-960 2364476 2364520 2364614 "RING-" 2364619 NIL RING- (NIL T) -8 NIL NIL) (-959 2363328 2363564 2363819 "RIDIST" 2364241 T RIDIST (NIL) -7 NIL NIL) (-958 2354650 2362802 2363005 "RGCHAIN" 2363177 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-957 2351655 2352269 2352937 "RF" 2354014 NIL RF (NIL T) -7 NIL NIL) (-956 2351304 2351367 2351468 "RFFACTOR" 2351586 NIL RFFACTOR (NIL T) -7 NIL NIL) (-955 2351032 2351067 2351162 "RFFACT" 2351263 NIL RFFACT (NIL T) -7 NIL NIL) (-954 2349162 2349526 2349906 "RFDIST" 2350672 T RFDIST (NIL) -7 NIL NIL) (-953 2348620 2348712 2348872 "RETSOL" 2349064 NIL RETSOL (NIL T T) -7 NIL NIL) (-952 2348212 2348292 2348334 "RETRACT" 2348524 NIL RETRACT (NIL T) -9 NIL NIL) (-951 2348064 2348089 2348173 "RETRACT-" 2348178 NIL RETRACT- (NIL T T) -8 NIL NIL) (-950 2340934 2347721 2347846 "RESULT" 2347959 T RESULT (NIL) -8 NIL NIL) (-949 2339519 2340208 2340405 "RESRING" 2340837 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-948 2339159 2339208 2339304 "RESLATC" 2339456 NIL RESLATC (NIL T) -7 NIL NIL) (-947 2338868 2338902 2339007 "REPSQ" 2339118 NIL REPSQ (NIL T) -7 NIL NIL) (-946 2336299 2336879 2337479 "REP" 2338288 T REP (NIL) -7 NIL NIL) (-945 2336000 2336034 2336143 "REPDB" 2336258 NIL REPDB (NIL T) -7 NIL NIL) (-944 2329945 2331324 2332544 "REP2" 2334812 NIL REP2 (NIL T) -7 NIL NIL) (-943 2326351 2327032 2327837 "REP1" 2329172 NIL REP1 (NIL T) -7 NIL NIL) (-942 2319097 2324512 2324964 "REGSET" 2325982 NIL REGSET (NIL T T T T) -8 NIL NIL) (-941 2317918 2318253 2318501 "REF" 2318882 NIL REF (NIL T) -8 NIL NIL) (-940 2317299 2317402 2317567 "REDORDER" 2317802 NIL REDORDER (NIL T T) -7 NIL NIL) (-939 2313268 2316533 2316754 "RECLOS" 2317130 NIL RECLOS (NIL T) -8 NIL NIL) (-938 2312325 2312506 2312719 "REALSOLV" 2313075 T REALSOLV (NIL) -7 NIL NIL) (-937 2312172 2312213 2312242 "REAL" 2312247 T REAL (NIL) -9 NIL 2312282) (-936 2308663 2309465 2310347 "REAL0Q" 2311337 NIL REAL0Q (NIL T) -7 NIL NIL) (-935 2304274 2305262 2306321 "REAL0" 2307644 NIL REAL0 (NIL T) -7 NIL NIL) (-934 2303682 2303754 2303959 "RDIV" 2304196 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-933 2302755 2302929 2303140 "RDIST" 2303504 NIL RDIST (NIL T) -7 NIL NIL) (-932 2301359 2301646 2302015 "RDETRS" 2302463 NIL RDETRS (NIL T T) -7 NIL NIL) (-931 2299180 2299634 2300169 "RDETR" 2300901 NIL RDETR (NIL T T) -7 NIL NIL) (-930 2297796 2298074 2298475 "RDEEFS" 2298896 NIL RDEEFS (NIL T T) -7 NIL NIL) (-929 2296296 2296602 2297031 "RDEEF" 2297484 NIL RDEEF (NIL T T) -7 NIL NIL) (-928 2290521 2293453 2293482 "RCFIELD" 2294759 T RCFIELD (NIL) -9 NIL 2295489) (-927 2288590 2289094 2289787 "RCFIELD-" 2289860 NIL RCFIELD- (NIL T) -8 NIL NIL) (-926 2284921 2286706 2286748 "RCAGG" 2287819 NIL RCAGG (NIL T) -9 NIL 2288284) (-925 2284552 2284646 2284806 "RCAGG-" 2284811 NIL RCAGG- (NIL T T) -8 NIL NIL) (-924 2283897 2284008 2284170 "RATRET" 2284436 NIL RATRET (NIL T) -7 NIL NIL) (-923 2283454 2283521 2283640 "RATFACT" 2283825 NIL RATFACT (NIL T) -7 NIL NIL) (-922 2282769 2282889 2283039 "RANDSRC" 2283324 T RANDSRC (NIL) -7 NIL NIL) (-921 2282506 2282550 2282621 "RADUTIL" 2282718 T RADUTIL (NIL) -7 NIL NIL) (-920 2275513 2281249 2281566 "RADIX" 2282221 NIL RADIX (NIL NIL) -8 NIL NIL) (-919 2267083 2275357 2275485 "RADFF" 2275490 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-918 2266734 2266809 2266838 "RADCAT" 2266995 T RADCAT (NIL) -9 NIL NIL) (-917 2266519 2266567 2266664 "RADCAT-" 2266669 NIL RADCAT- (NIL T) -8 NIL NIL) (-916 2264676 2266294 2266383 "QUEUE" 2266463 NIL QUEUE (NIL T) -8 NIL NIL) (-915 2261173 2264613 2264658 "QUAT" 2264663 NIL QUAT (NIL T) -8 NIL NIL) (-914 2260811 2260854 2260981 "QUATCT2" 2261124 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-913 2254557 2257937 2257978 "QUATCAT" 2258757 NIL QUATCAT (NIL T) -9 NIL 2259522) (-912 2250701 2251738 2253125 "QUATCAT-" 2253219 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-911 2248227 2249785 2249827 "QUAGG" 2250202 NIL QUAGG (NIL T) -9 NIL 2250377) (-910 2247152 2247625 2247797 "QFORM" 2248099 NIL QFORM (NIL NIL T) -8 NIL NIL) (-909 2238401 2243659 2243700 "QFCAT" 2244358 NIL QFCAT (NIL T) -9 NIL 2245351) (-908 2233973 2235174 2236765 "QFCAT-" 2236859 NIL QFCAT- (NIL T T) -8 NIL NIL) (-907 2233611 2233654 2233781 "QFCAT2" 2233924 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-906 2233071 2233181 2233311 "QEQUAT" 2233501 T QEQUAT (NIL) -8 NIL NIL) (-905 2226257 2227328 2228510 "QCMPACK" 2232004 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-904 2223833 2224254 2224682 "QALGSET" 2225912 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-903 2223078 2223252 2223484 "QALGSET2" 2223653 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-902 2221769 2221992 2222309 "PWFFINTB" 2222851 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-901 2219957 2220125 2220478 "PUSHVAR" 2221583 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-900 2215874 2216928 2216970 "PTRANFN" 2218854 NIL PTRANFN (NIL T) -9 NIL NIL) (-899 2214286 2214577 2214898 "PTPACK" 2215585 NIL PTPACK (NIL T) -7 NIL NIL) (-898 2213922 2213979 2214086 "PTFUNC2" 2214223 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-897 2208401 2212736 2212777 "PTCAT" 2213145 NIL PTCAT (NIL T) -9 NIL 2213307) (-896 2208059 2208094 2208218 "PSQFR" 2208360 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-895 2206654 2206952 2207286 "PSEUDLIN" 2207757 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-894 2193462 2195826 2198149 "PSETPK" 2204414 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-893 2186548 2189262 2189357 "PSETCAT" 2192338 NIL PSETCAT (NIL T T T T) -9 NIL 2193152) (-892 2184386 2185020 2185839 "PSETCAT-" 2185844 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-891 2183743 2183905 2183934 "PSCURVE" 2184199 T PSCURVE (NIL) -9 NIL 2184363) (-890 2180147 2181673 2181738 "PSCAT" 2182574 NIL PSCAT (NIL T T T) -9 NIL 2182814) (-889 2179211 2179427 2179826 "PSCAT-" 2179831 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-888 2177864 2178496 2178710 "PRTITION" 2179017 T PRTITION (NIL) -8 NIL NIL) (-887 2166962 2169168 2171356 "PRS" 2175726 NIL PRS (NIL T T) -7 NIL NIL) (-886 2164826 2166312 2166353 "PRQAGG" 2166536 NIL PRQAGG (NIL T) -9 NIL 2166638) (-885 2158600 2162992 2163812 "PRODUCT" 2164052 NIL PRODUCT (NIL T T) -8 NIL NIL) (-884 2155876 2158060 2158293 "PR" 2158411 NIL PR (NIL T T) -8 NIL NIL) (-883 2155672 2155704 2155763 "PRINT" 2155837 T PRINT (NIL) -7 NIL NIL) (-882 2155012 2155129 2155281 "PRIMES" 2155552 NIL PRIMES (NIL T) -7 NIL NIL) (-881 2153077 2153478 2153944 "PRIMELT" 2154591 NIL PRIMELT (NIL T) -7 NIL NIL) (-880 2152808 2152856 2152885 "PRIMCAT" 2153008 T PRIMCAT (NIL) -9 NIL NIL) (-879 2148969 2152746 2152791 "PRIMARR" 2152796 NIL PRIMARR (NIL T) -8 NIL NIL) (-878 2147976 2148154 2148382 "PRIMARR2" 2148787 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-877 2147619 2147675 2147786 "PREASSOC" 2147914 NIL PREASSOC (NIL T T) -7 NIL NIL) (-876 2147099 2147230 2147259 "PPCURVE" 2147462 T PPCURVE (NIL) -9 NIL 2147596) (-875 2144458 2144857 2145449 "POLYROOT" 2146680 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-874 2138364 2144064 2144223 "POLY" 2144331 NIL POLY (NIL T) -8 NIL NIL) (-873 2137749 2137807 2138040 "POLYLIFT" 2138300 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-872 2134034 2134483 2135111 "POLYCATQ" 2137294 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-871 2121027 2126424 2126489 "POLYCAT" 2129974 NIL POLYCAT (NIL T T T) -9 NIL 2131901) (-870 2114478 2116339 2118722 "POLYCAT-" 2118727 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-869 2114067 2114135 2114254 "POLY2UP" 2114404 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-868 2113703 2113760 2113867 "POLY2" 2114004 NIL POLY2 (NIL T T) -7 NIL NIL) (-867 2112388 2112627 2112903 "POLUTIL" 2113477 NIL POLUTIL (NIL T T) -7 NIL NIL) (-866 2110750 2111027 2111357 "POLTOPOL" 2112110 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-865 2106279 2110687 2110732 "POINT" 2110737 NIL POINT (NIL T) -8 NIL NIL) (-864 2104466 2104823 2105198 "PNTHEORY" 2105924 T PNTHEORY (NIL) -7 NIL NIL) (-863 2102894 2103191 2103600 "PMTOOLS" 2104164 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-862 2102487 2102565 2102682 "PMSYM" 2102810 NIL PMSYM (NIL T) -7 NIL NIL) (-861 2101997 2102066 2102240 "PMQFCAT" 2102412 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-860 2101352 2101462 2101618 "PMPRED" 2101874 NIL PMPRED (NIL T) -7 NIL NIL) (-859 2100748 2100834 2100995 "PMPREDFS" 2101253 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-858 2099394 2099602 2099986 "PMPLCAT" 2100510 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-857 2098926 2099005 2099157 "PMLSAGG" 2099309 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-856 2098403 2098479 2098659 "PMKERNEL" 2098844 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-855 2098020 2098095 2098208 "PMINS" 2098322 NIL PMINS (NIL T) -7 NIL NIL) (-854 2097450 2097519 2097734 "PMFS" 2097945 NIL PMFS (NIL T T T) -7 NIL NIL) (-853 2096681 2096799 2097003 "PMDOWN" 2097327 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-852 2095844 2096003 2096185 "PMASS" 2096519 T PMASS (NIL) -7 NIL NIL) (-851 2095118 2095229 2095392 "PMASSFS" 2095730 NIL PMASSFS (NIL T T) -7 NIL NIL) (-850 2094777 2094844 2094937 "PLOTTOOL" 2095045 T PLOTTOOL (NIL) -7 NIL NIL) (-849 2089478 2090644 2091771 "PLOT" 2093670 T PLOT (NIL) -8 NIL NIL) (-848 2085351 2086366 2087271 "PLOT3D" 2088593 T PLOT3D (NIL) -8 NIL NIL) (-847 2084275 2084449 2084681 "PLOT1" 2085158 NIL PLOT1 (NIL T) -7 NIL NIL) (-846 2059670 2064341 2069192 "PLEQN" 2079541 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-845 2058988 2059110 2059290 "PINTERP" 2059535 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-844 2058681 2058728 2058831 "PINTERPA" 2058935 NIL PINTERPA (NIL T T) -7 NIL NIL) (-843 2057908 2058475 2058568 "PI" 2058608 T PI (NIL) -8 NIL NIL) (-842 2056299 2057284 2057313 "PID" 2057495 T PID (NIL) -9 NIL 2057629) (-841 2056024 2056061 2056149 "PICOERCE" 2056256 NIL PICOERCE (NIL T) -7 NIL NIL) (-840 2055345 2055483 2055659 "PGROEB" 2055880 NIL PGROEB (NIL T) -7 NIL NIL) (-839 2050932 2051746 2052651 "PGE" 2054460 T PGE (NIL) -7 NIL NIL) (-838 2049056 2049302 2049668 "PGCD" 2050649 NIL PGCD (NIL T T T T) -7 NIL NIL) (-837 2048394 2048497 2048658 "PFRPAC" 2048940 NIL PFRPAC (NIL T) -7 NIL NIL) (-836 2045009 2046942 2047295 "PFR" 2048073 NIL PFR (NIL T) -8 NIL NIL) (-835 2043398 2043642 2043967 "PFOTOOLS" 2044756 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-834 2041931 2042170 2042521 "PFOQ" 2043155 NIL PFOQ (NIL T T T) -7 NIL NIL) (-833 2040408 2040620 2040982 "PFO" 2041715 NIL PFO (NIL T T T T T) -7 NIL NIL) (-832 2036931 2040297 2040366 "PF" 2040371 NIL PF (NIL NIL) -8 NIL NIL) (-831 2034359 2035640 2035669 "PFECAT" 2036254 T PFECAT (NIL) -9 NIL 2036638) (-830 2033804 2033958 2034172 "PFECAT-" 2034177 NIL PFECAT- (NIL T) -8 NIL NIL) (-829 2032408 2032659 2032960 "PFBRU" 2033553 NIL PFBRU (NIL T T) -7 NIL NIL) (-828 2030275 2030626 2031058 "PFBR" 2032059 NIL PFBR (NIL T T T T) -7 NIL NIL) (-827 2026127 2027651 2028327 "PERM" 2029632 NIL PERM (NIL T) -8 NIL NIL) (-826 2021394 2022334 2023204 "PERMGRP" 2025290 NIL PERMGRP (NIL T) -8 NIL NIL) (-825 2019464 2020457 2020499 "PERMCAT" 2020945 NIL PERMCAT (NIL T) -9 NIL 2021250) (-824 2019119 2019160 2019283 "PERMAN" 2019417 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-823 2016565 2018688 2018819 "PENDTREE" 2019021 NIL PENDTREE (NIL T) -8 NIL NIL) (-822 2014637 2015415 2015457 "PDRING" 2016114 NIL PDRING (NIL T) -9 NIL 2016399) (-821 2013740 2013958 2014320 "PDRING-" 2014325 NIL PDRING- (NIL T T) -8 NIL NIL) (-820 2010882 2011632 2012323 "PDEPROB" 2013069 T PDEPROB (NIL) -8 NIL NIL) (-819 2008453 2008949 2009498 "PDEPACK" 2010353 T PDEPACK (NIL) -7 NIL NIL) (-818 2007365 2007555 2007806 "PDECOMP" 2008252 NIL PDECOMP (NIL T T) -7 NIL NIL) (-817 2004976 2005791 2005820 "PDECAT" 2006605 T PDECAT (NIL) -9 NIL 2007316) (-816 2004729 2004762 2004851 "PCOMP" 2004937 NIL PCOMP (NIL T T) -7 NIL NIL) (-815 2002936 2003532 2003828 "PBWLB" 2004459 NIL PBWLB (NIL T) -8 NIL NIL) (-814 1995445 1997013 1998349 "PATTERN" 2001621 NIL PATTERN (NIL T) -8 NIL NIL) (-813 1995077 1995134 1995243 "PATTERN2" 1995382 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-812 1992834 1993222 1993679 "PATTERN1" 1994666 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-811 1990229 1990783 1991264 "PATRES" 1992399 NIL PATRES (NIL T T) -8 NIL NIL) (-810 1989793 1989860 1989992 "PATRES2" 1990156 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-809 1987690 1988090 1988495 "PATMATCH" 1989462 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-808 1987226 1987409 1987451 "PATMAB" 1987558 NIL PATMAB (NIL T) -9 NIL 1987641) (-807 1985771 1986080 1986338 "PATLRES" 1987031 NIL PATLRES (NIL T T T) -8 NIL NIL) (-806 1985316 1985439 1985481 "PATAB" 1985486 NIL PATAB (NIL T) -9 NIL 1985658) (-805 1982797 1983329 1983902 "PARTPERM" 1984763 T PARTPERM (NIL) -7 NIL NIL) (-804 1982418 1982481 1982583 "PARSURF" 1982728 NIL PARSURF (NIL T) -8 NIL NIL) (-803 1982050 1982107 1982216 "PARSU2" 1982355 NIL PARSU2 (NIL T T) -7 NIL NIL) (-802 1981671 1981734 1981836 "PARSCURV" 1981981 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1981303 1981360 1981469 "PARSC2" 1981608 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980942 1981000 1981097 "PARPCURV" 1981239 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1980574 1980631 1980740 "PARPC2" 1980879 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1980094 1980180 1980299 "PAN2EXPR" 1980475 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978900 1979215 1979443 "PALETTE" 1979886 T PALETTE (NIL) -8 NIL NIL) (-796 1972750 1978159 1978353 "PADICRC" 1978755 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965958 1972096 1972280 "PADICRAT" 1972598 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1964262 1965895 1965940 "PADIC" 1965945 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1961466 1963040 1963081 "PADICCT" 1963662 NIL PADICCT (NIL NIL) -9 NIL 1963944) (-792 1960423 1960623 1960891 "PADEPAC" 1961253 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1959635 1959768 1959974 "PADE" 1960285 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1957646 1958478 1958793 "OWP" 1959403 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956755 1957251 1957423 "OVAR" 1957514 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1956019 1956140 1956301 "OUT" 1956614 T OUT (NIL) -7 NIL NIL) (-787 1945065 1947244 1949414 "OUTFORM" 1953869 T OUTFORM (NIL) -8 NIL NIL) (-786 1944473 1944794 1944883 "OSI" 1944996 T OSI (NIL) -8 NIL NIL) (-785 1943218 1943445 1943730 "ORTHPOL" 1944220 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1940589 1942879 1943017 "OREUP" 1943161 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937985 1940282 1940408 "ORESUP" 1940531 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1935520 1936020 1936580 "OREPCTO" 1937474 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1929429 1931635 1931676 "OREPCAT" 1933997 NIL OREPCAT (NIL T) -9 NIL 1935100) (-780 1926577 1927359 1928416 "OREPCAT-" 1928421 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925754 1926026 1926055 "ORDSET" 1926364 T ORDSET (NIL) -9 NIL 1926528) (-778 1925273 1925395 1925588 "ORDSET-" 1925593 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923886 1924687 1924716 "ORDRING" 1924918 T ORDRING (NIL) -9 NIL 1925042) (-776 1923531 1923625 1923769 "ORDRING-" 1923774 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922906 1923387 1923416 "ORDMON" 1923421 T ORDMON (NIL) -9 NIL 1923442) (-774 1922068 1922215 1922410 "ORDFUNS" 1922755 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1921579 1921938 1921967 "ORDFIN" 1921972 T ORDFIN (NIL) -9 NIL 1921993) (-772 1918091 1920165 1920574 "ORDCOMP" 1921203 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1917357 1917484 1917670 "ORDCOMP2" 1917951 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1913865 1914747 1915584 "OPTPROB" 1916540 T OPTPROB (NIL) -8 NIL NIL) (-769 1910707 1911336 1912030 "OPTPACK" 1913191 T OPTPACK (NIL) -7 NIL NIL) (-768 1908432 1909168 1909197 "OPTCAT" 1910012 T OPTCAT (NIL) -9 NIL 1910658) (-767 1908200 1908239 1908305 "OPQUERY" 1908386 T OPQUERY (NIL) -7 NIL NIL) (-766 1905336 1906527 1907027 "OP" 1907732 NIL OP (NIL T) -8 NIL NIL) (-765 1902101 1904133 1904502 "ONECOMP" 1905000 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1901406 1901521 1901695 "ONECOMP2" 1901973 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1900825 1900931 1901061 "OMSERVER" 1901296 T OMSERVER (NIL) -7 NIL NIL) (-762 1897713 1900265 1900306 "OMSAGG" 1900367 NIL OMSAGG (NIL T) -9 NIL 1900431) (-761 1896336 1896599 1896881 "OMPKG" 1897451 T OMPKG (NIL) -7 NIL NIL) (-760 1895765 1895868 1895897 "OM" 1896196 T OM (NIL) -9 NIL NIL) (-759 1894304 1895317 1895485 "OMLO" 1895646 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1893234 1893381 1893607 "OMEXPR" 1894130 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1892552 1892780 1892916 "OMERR" 1893118 T OMERR (NIL) -8 NIL NIL) (-756 1891730 1891973 1892133 "OMERRK" 1892412 T OMERRK (NIL) -8 NIL NIL) (-755 1891208 1891407 1891515 "OMENC" 1891642 T OMENC (NIL) -8 NIL NIL) (-754 1885103 1886288 1887459 "OMDEV" 1890057 T OMDEV (NIL) -8 NIL NIL) (-753 1884172 1884343 1884537 "OMCONN" 1884929 T OMCONN (NIL) -8 NIL NIL) (-752 1882787 1883773 1883802 "OINTDOM" 1883807 T OINTDOM (NIL) -9 NIL 1883828) (-751 1878549 1879779 1880494 "OFMONOID" 1882104 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877987 1878486 1878531 "ODVAR" 1878536 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1875112 1877484 1877669 "ODR" 1877862 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1867418 1874891 1875015 "ODPOL" 1875020 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1861247 1867290 1867395 "ODP" 1867400 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1860013 1860228 1860503 "ODETOOLS" 1861021 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1856982 1857638 1858354 "ODESYS" 1859346 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1851886 1852794 1853817 "ODERTRIC" 1856057 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1851312 1851394 1851588 "ODERED" 1851798 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1848214 1848762 1849437 "ODERAT" 1850735 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1845182 1845646 1846242 "ODEPRRIC" 1847743 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1843053 1843620 1844129 "ODEPROB" 1844693 T ODEPROB (NIL) -8 NIL NIL) (-739 1839585 1840068 1840714 "ODEPRIM" 1842532 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1838838 1838940 1839198 "ODEPAL" 1839477 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1835040 1835821 1836675 "ODEPACK" 1838004 T ODEPACK (NIL) -7 NIL NIL) (-736 1834077 1834184 1834412 "ODEINT" 1834929 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1828178 1829603 1831050 "ODEIFTBL" 1832650 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1823522 1824308 1825266 "ODEEF" 1827337 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822859 1822948 1823177 "ODECONST" 1823427 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1821016 1821649 1821678 "ODECAT" 1822281 T ODECAT (NIL) -9 NIL 1822810) (-731 1817888 1820728 1820847 "OCT" 1820929 NIL OCT (NIL T) -8 NIL NIL) (-730 1817526 1817569 1817696 "OCTCT2" 1817839 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1812359 1814797 1814838 "OC" 1815934 NIL OC (NIL T) -9 NIL 1816791) (-728 1809586 1810334 1811324 "OC-" 1811418 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808964 1809406 1809435 "OCAMON" 1809440 T OCAMON (NIL) -9 NIL 1809461) (-726 1808417 1808824 1808853 "OASGP" 1808858 T OASGP (NIL) -9 NIL 1808878) (-725 1807704 1808167 1808196 "OAMONS" 1808236 T OAMONS (NIL) -9 NIL 1808279) (-724 1807144 1807551 1807580 "OAMON" 1807585 T OAMON (NIL) -9 NIL 1807605) (-723 1806448 1806940 1806969 "OAGROUP" 1806974 T OAGROUP (NIL) -9 NIL 1806994) (-722 1806138 1806188 1806276 "NUMTUBE" 1806392 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1799711 1801229 1802765 "NUMQUAD" 1804622 T NUMQUAD (NIL) -7 NIL NIL) (-720 1795467 1796455 1797480 "NUMODE" 1798706 T NUMODE (NIL) -7 NIL NIL) (-719 1792882 1793724 1793753 "NUMINT" 1794666 T NUMINT (NIL) -9 NIL 1795418) (-718 1791830 1792027 1792245 "NUMFMT" 1792684 T NUMFMT (NIL) -7 NIL NIL) (-717 1778209 1781146 1783676 "NUMERIC" 1789339 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1772609 1777661 1777756 "NTSCAT" 1777761 NIL NTSCAT (NIL T T T T) -9 NIL 1777799) (-715 1771803 1771968 1772161 "NTPOLFN" 1772448 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1759659 1768645 1769455 "NSUP" 1771025 NIL NSUP (NIL T) -8 NIL NIL) (-713 1759295 1759352 1759459 "NSUP2" 1759596 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1749257 1759074 1759204 "NSMP" 1759209 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1747689 1747990 1748347 "NREP" 1748945 NIL NREP (NIL T) -7 NIL NIL) (-710 1746280 1746532 1746890 "NPCOEF" 1747432 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1745346 1745461 1745677 "NORMRETR" 1746161 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1743399 1743689 1744096 "NORMPK" 1745054 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1743084 1743112 1743236 "NORMMA" 1743365 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1742911 1743041 1743070 "NONE" 1743075 T NONE (NIL) -8 NIL NIL) (-705 1742700 1742729 1742798 "NONE1" 1742875 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1742185 1742247 1742432 "NODE1" 1742632 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1740479 1741348 1741603 "NNI" 1741950 T NNI (NIL) -8 NIL NIL) (-702 1738899 1739212 1739576 "NLINSOL" 1740147 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1735091 1736052 1736968 "NIPROB" 1738003 T NIPROB (NIL) -8 NIL NIL) (-700 1733848 1734082 1734384 "NFINTBAS" 1734853 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1732556 1732787 1733068 "NCODIV" 1733616 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1732318 1732355 1732430 "NCNTFRAC" 1732513 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1730498 1730862 1731282 "NCEP" 1731943 NIL NCEP (NIL T) -7 NIL NIL) (-696 1729409 1730148 1730177 "NASRING" 1730287 T NASRING (NIL) -9 NIL 1730361) (-695 1729204 1729248 1729342 "NASRING-" 1729347 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1728357 1728856 1728885 "NARNG" 1729002 T NARNG (NIL) -9 NIL 1729093) (-693 1728049 1728116 1728250 "NARNG-" 1728255 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1726928 1727135 1727370 "NAGSP" 1727834 T NAGSP (NIL) -7 NIL NIL) (-691 1718352 1719998 1721633 "NAGS" 1725313 T NAGS (NIL) -7 NIL NIL) (-690 1716916 1717220 1717547 "NAGF07" 1718045 T NAGF07 (NIL) -7 NIL NIL) (-689 1711498 1712778 1714074 "NAGF04" 1715640 T NAGF04 (NIL) -7 NIL NIL) (-688 1704530 1706128 1707745 "NAGF02" 1709901 T NAGF02 (NIL) -7 NIL NIL) (-687 1699794 1700884 1701991 "NAGF01" 1703443 T NAGF01 (NIL) -7 NIL NIL) (-686 1693454 1695012 1696589 "NAGE04" 1698237 T NAGE04 (NIL) -7 NIL NIL) (-685 1684695 1686798 1688910 "NAGE02" 1691362 T NAGE02 (NIL) -7 NIL NIL) (-684 1680688 1681625 1682579 "NAGE01" 1683761 T NAGE01 (NIL) -7 NIL NIL) (-683 1678495 1679026 1679581 "NAGD03" 1680153 T NAGD03 (NIL) -7 NIL NIL) (-682 1670281 1672200 1674145 "NAGD02" 1676570 T NAGD02 (NIL) -7 NIL NIL) (-681 1664140 1665553 1666981 "NAGD01" 1668873 T NAGD01 (NIL) -7 NIL NIL) (-680 1660397 1661207 1662032 "NAGC06" 1663335 T NAGC06 (NIL) -7 NIL NIL) (-679 1658874 1659203 1659556 "NAGC05" 1660064 T NAGC05 (NIL) -7 NIL NIL) (-678 1658258 1658375 1658517 "NAGC02" 1658752 T NAGC02 (NIL) -7 NIL NIL) (-677 1657319 1657876 1657917 "NAALG" 1657996 NIL NAALG (NIL T) -9 NIL 1658057) (-676 1657154 1657183 1657273 "NAALG-" 1657278 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1651104 1652212 1653399 "MULTSQFR" 1656050 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1650423 1650498 1650682 "MULTFACT" 1651016 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1643564 1647475 1647528 "MTSCAT" 1648588 NIL MTSCAT (NIL T T) -9 NIL 1649102) (-672 1643276 1643330 1643422 "MTHING" 1643504 NIL MTHING (NIL T) -7 NIL NIL) (-671 1643068 1643101 1643161 "MSYSCMD" 1643236 T MSYSCMD (NIL) -7 NIL NIL) (-670 1639180 1641823 1642143 "MSET" 1642781 NIL MSET (NIL T) -8 NIL NIL) (-669 1636275 1638741 1638783 "MSETAGG" 1638788 NIL MSETAGG (NIL T) -9 NIL 1638822) (-668 1632131 1633673 1634414 "MRING" 1635578 NIL MRING (NIL T T) -8 NIL NIL) (-667 1631701 1631768 1631897 "MRF2" 1632058 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1631319 1631354 1631498 "MRATFAC" 1631660 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1628931 1629226 1629657 "MPRFF" 1631024 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1622951 1628786 1628882 "MPOLY" 1628887 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1622441 1622476 1622684 "MPCPF" 1622910 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1621957 1622000 1622183 "MPC3" 1622392 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1621158 1621239 1621458 "MPC2" 1621872 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1619459 1619796 1620186 "MONOTOOL" 1620818 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1618583 1618918 1618947 "MONOID" 1619224 T MONOID (NIL) -9 NIL 1619396) (-658 1617961 1618124 1618367 "MONOID-" 1618372 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608894 1614880 1614940 "MONOGEN" 1615614 NIL MONOGEN (NIL T T) -9 NIL 1616070) (-656 1606112 1606847 1607847 "MONOGEN-" 1607966 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604971 1605391 1605420 "MONADWU" 1605812 T MONADWU (NIL) -9 NIL 1606050) (-654 1604343 1604502 1604750 "MONADWU-" 1604755 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603728 1603946 1603975 "MONAD" 1604182 T MONAD (NIL) -9 NIL 1604294) (-652 1603413 1603491 1603623 "MONAD-" 1603628 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601664 1602326 1602605 "MOEBIUS" 1603166 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1601057 1601435 1601476 "MODULE" 1601481 NIL MODULE (NIL T) -9 NIL 1601507) (-649 1600625 1600721 1600911 "MODULE-" 1600916 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1598296 1598991 1599317 "MODRING" 1600450 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1595252 1596417 1596934 "MODOP" 1597828 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1593439 1593891 1594232 "MODMONOM" 1595051 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1583157 1591643 1592065 "MODMON" 1593067 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1580283 1582001 1582277 "MODFIELD" 1583032 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579809 1579852 1580031 "MMAP" 1580234 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1578045 1578822 1578863 "MLO" 1579280 NIL MLO (NIL T) -9 NIL 1579521) (-641 1575412 1575927 1576529 "MLIFT" 1577526 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574803 1574887 1575041 "MKUCFUNC" 1575323 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1574402 1574472 1574595 "MKRECORD" 1574726 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1573450 1573611 1573839 "MKFUNC" 1574213 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572838 1572942 1573098 "MKFLCFN" 1573333 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1572264 1572631 1572720 "MKCHSET" 1572782 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1571541 1571643 1571828 "MKBCFUNC" 1572157 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1568225 1571095 1571231 "MINT" 1571425 T MINT (NIL) -8 NIL NIL) (-633 1567037 1567280 1567557 "MHROWRED" 1567980 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1562308 1565482 1565906 "MFLOAT" 1566633 T MFLOAT (NIL) -8 NIL NIL) (-631 1561665 1561741 1561912 "MFINFACT" 1562220 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1558012 1558851 1559726 "MESH" 1560810 T MESH (NIL) -7 NIL NIL) (-629 1556402 1556714 1557067 "MDDFACT" 1557699 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1553250 1555561 1555603 "MDAGG" 1555858 NIL MDAGG (NIL T) -9 NIL 1556001) (-627 1542948 1552543 1552750 "MCMPLX" 1553063 T MCMPLX (NIL) -8 NIL NIL) (-626 1542089 1542235 1542435 "MCDEN" 1542797 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539979 1540249 1540629 "MCALCFN" 1541819 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1537601 1538124 1538685 "MATSTOR" 1539450 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1533615 1536976 1537223 "MATRIX" 1537386 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1529384 1530088 1530824 "MATLIN" 1532972 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1519587 1522719 1522796 "MATCAT" 1527634 NIL MATCAT (NIL T T T) -9 NIL 1529051) (-620 1515952 1516965 1518320 "MATCAT-" 1518325 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1514554 1514707 1515038 "MATCAT2" 1515787 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1512666 1512990 1513374 "MAPPKG3" 1514229 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1511647 1511820 1512042 "MAPPKG2" 1512490 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1510146 1510430 1510757 "MAPPKG1" 1511353 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509757 1509815 1509938 "MAPHACK3" 1510082 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1509349 1509410 1509524 "MAPHACK2" 1509689 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508787 1508890 1509032 "MAPHACK1" 1509240 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506895 1507489 1507792 "MAGMA" 1508516 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1503376 1505139 1505599 "M3D" 1506468 NIL M3D (NIL T) -8 NIL NIL) (-610 1497534 1501743 1501785 "LZSTAGG" 1502567 NIL LZSTAGG (NIL T) -9 NIL 1502862) (-609 1493508 1494665 1496122 "LZSTAGG-" 1496127 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1490624 1491401 1491887 "LWORD" 1493054 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483784 1490395 1490529 "LSQM" 1490534 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1483008 1483147 1483375 "LSPP" 1483639 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480820 1481121 1481577 "LSMP" 1482697 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1477599 1478273 1479003 "LSMP1" 1480122 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1471522 1476764 1476806 "LSAGG" 1476868 NIL LSAGG (NIL T) -9 NIL 1476946) (-602 1468217 1469141 1470354 "LSAGG-" 1470359 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465843 1467361 1467610 "LPOLY" 1468012 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1465425 1465510 1465633 "LPEFRAC" 1465752 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463772 1464519 1464772 "LO" 1465257 NIL LO (NIL T T T) -8 NIL NIL) (-598 1463425 1463537 1463566 "LOGIC" 1463677 T LOGIC (NIL) -9 NIL 1463757) (-597 1463287 1463310 1463381 "LOGIC-" 1463386 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1462480 1462620 1462813 "LODOOPS" 1463143 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459898 1462397 1462462 "LODO" 1462467 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1458444 1458679 1459030 "LODOF" 1459645 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454863 1457299 1457340 "LODOCAT" 1457772 NIL LODOCAT (NIL T) -9 NIL 1457983) (-592 1454597 1454655 1454781 "LODOCAT-" 1454786 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451911 1454438 1454556 "LODO2" 1454561 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1449340 1451848 1451893 "LODO1" 1451898 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1448203 1448368 1448679 "LODEEF" 1449163 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1443486 1446330 1446372 "LNAGG" 1447319 NIL LNAGG (NIL T) -9 NIL 1447763) (-587 1442633 1442847 1443189 "LNAGG-" 1443194 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438798 1439560 1440198 "LMOPS" 1442049 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1438195 1438557 1438598 "LMODULE" 1438658 NIL LMODULE (NIL T) -9 NIL 1438700) (-584 1435447 1437840 1437963 "LMDICT" 1438105 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1428674 1434393 1434691 "LIST" 1435182 NIL LIST (NIL T) -8 NIL NIL) (-582 1428199 1428273 1428412 "LIST3" 1428594 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1427206 1427384 1427612 "LIST2" 1428017 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1425340 1425652 1426051 "LIST2MAP" 1426853 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1424052 1424732 1424773 "LINEXP" 1425026 NIL LINEXP (NIL T) -9 NIL 1425174) (-578 1422699 1422959 1423256 "LINDEP" 1423804 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1419466 1420185 1420962 "LIMITRF" 1421954 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417747 1418041 1418456 "LIMITPS" 1419161 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1412202 1417258 1417486 "LIE" 1417568 NIL LIE (NIL T T) -8 NIL NIL) (-574 1411252 1411695 1411736 "LIECAT" 1411876 NIL LIECAT (NIL T) -9 NIL 1412027) (-573 1411093 1411120 1411208 "LIECAT-" 1411213 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1403717 1410542 1410707 "LIB" 1410948 T LIB (NIL) -8 NIL NIL) (-571 1399354 1400235 1401170 "LGROBP" 1402834 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1397224 1397497 1397858 "LF" 1399076 NIL LF (NIL T T) -7 NIL NIL) (-569 1396064 1396755 1396784 "LFCAT" 1396991 T LFCAT (NIL) -9 NIL 1397130) (-568 1392976 1393602 1394288 "LEXTRIPK" 1395430 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1389682 1390546 1391049 "LEXP" 1392556 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1388080 1388393 1388794 "LEADCDET" 1389364 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1387276 1387350 1387577 "LAZM3PK" 1388001 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1382193 1385355 1385892 "LAUPOL" 1386789 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381760 1381804 1381971 "LAPLACE" 1382143 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1379688 1380861 1381112 "LA" 1381593 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378750 1379344 1379385 "LALG" 1379446 NIL LALG (NIL T) -9 NIL 1379504) (-560 1378465 1378524 1378659 "LALG-" 1378664 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1377375 1377562 1377859 "KOVACIC" 1378265 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1377209 1377233 1377275 "KONVERT" 1377337 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1377043 1377067 1377109 "KOERCE" 1377171 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374777 1375537 1375930 "KERNEL" 1376682 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1374279 1374360 1374490 "KERNEL2" 1374691 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367894 1372576 1372631 "KDAGG" 1373008 NIL KDAGG (NIL T T) -9 NIL 1373214) (-553 1367423 1367547 1367752 "KDAGG-" 1367757 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360598 1367084 1367239 "KAFILE" 1367301 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1355053 1360109 1360337 "JORDAN" 1360419 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1351358 1353258 1353313 "IXAGG" 1354242 NIL IXAGG (NIL T T) -9 NIL 1354701) (-549 1350277 1350583 1351002 "IXAGG-" 1351007 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345868 1350199 1350258 "IVECTOR" 1350263 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344634 1344871 1345137 "ITUPLE" 1345635 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1343070 1343247 1343553 "ITRIGMNP" 1344456 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341815 1342019 1342302 "ITFUN3" 1342846 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1341447 1341504 1341613 "ITFUN2" 1341752 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1339249 1340320 1340617 "ITAYLOR" 1341182 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1328241 1333435 1334594 "ISUPS" 1338122 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1327349 1327488 1327723 "ISUMP" 1328089 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322613 1327150 1327229 "ISTRING" 1327302 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321826 1321907 1322122 "IRURPK" 1322527 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320762 1320963 1321203 "IRSN" 1321606 T IRSN (NIL) -7 NIL NIL) (-537 1318797 1319152 1319587 "IRRF2F" 1320400 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318544 1318582 1318658 "IRREDFFX" 1318753 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1317159 1317418 1317717 "IROOT" 1318277 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313797 1314848 1315538 "IR" 1316501 NIL IR (NIL T) -8 NIL NIL) (-533 1311410 1311905 1312471 "IR2" 1313275 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1310486 1310599 1310819 "IR2F" 1311293 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1310277 1310311 1310371 "IPRNTPK" 1310446 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306831 1310166 1310235 "IPF" 1310240 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1305148 1306756 1306813 "IPADIC" 1306818 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304647 1304705 1304894 "INVLAPLA" 1305084 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1294296 1296649 1299035 "INTTR" 1302311 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290644 1291385 1292248 "INTTOOLS" 1293482 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1290230 1290321 1290438 "INTSLPE" 1290547 T INTSLPE (NIL) -7 NIL NIL) (-524 1288180 1290153 1290212 "INTRVL" 1290217 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285787 1286299 1286873 "INTRF" 1287665 NIL INTRF (NIL T) -7 NIL NIL) (-522 1285202 1285299 1285440 "INTRET" 1285685 NIL INTRET (NIL T) -7 NIL NIL) (-521 1283204 1283593 1284062 "INTRAT" 1284810 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1280437 1281020 1281645 "INTPM" 1282689 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1277146 1277745 1278489 "INTPAF" 1279823 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1272429 1273365 1274390 "INTPACK" 1276141 T INTPACK (NIL) -7 NIL NIL) (-517 1269283 1272158 1272285 "INT" 1272322 T INT (NIL) -8 NIL NIL) (-516 1268535 1268687 1268895 "INTHERTR" 1269125 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267974 1268054 1268242 "INTHERAL" 1268449 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265820 1266263 1266720 "INTHEORY" 1267537 T INTHEORY (NIL) -7 NIL NIL) (-513 1257143 1258763 1260541 "INTG0" 1264172 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237740 1242524 1247328 "INTFTBL" 1252359 T INTFTBL (NIL) -8 NIL NIL) (-511 1236989 1237127 1237300 "INTFACT" 1237599 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1234380 1234826 1235389 "INTEF" 1236543 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232841 1233590 1233619 "INTDOM" 1233920 T INTDOM (NIL) -9 NIL 1234127) (-508 1232210 1232384 1232626 "INTDOM-" 1232631 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228702 1230634 1230689 "INTCAT" 1231488 NIL INTCAT (NIL T) -9 NIL 1231807) (-506 1228175 1228277 1228405 "INTBIT" 1228594 T INTBIT (NIL) -7 NIL NIL) (-505 1226850 1227004 1227317 "INTALG" 1228020 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1226307 1226397 1226567 "INTAF" 1226754 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219773 1226117 1226257 "INTABL" 1226262 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214723 1217452 1217481 "INS" 1218449 T INS (NIL) -9 NIL 1219130) (-501 1211963 1212734 1213708 "INS-" 1213781 NIL INS- (NIL T) -8 NIL NIL) (-500 1210742 1210969 1211266 "INPSIGN" 1211716 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209860 1209977 1210174 "INPRODPF" 1210622 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208754 1208871 1209108 "INPRODFF" 1209740 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207754 1207906 1208166 "INNMFACT" 1208590 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206951 1207048 1207236 "INMODGCD" 1207653 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1205460 1205704 1206028 "INFSP" 1206696 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204644 1204761 1204944 "INFPROD0" 1205340 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201654 1202813 1203304 "INFORM" 1204161 T INFORM (NIL) -8 NIL NIL) (-492 1201264 1201324 1201422 "INFORM1" 1201589 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200787 1200876 1200990 "INFINITY" 1201170 T INFINITY (NIL) -7 NIL NIL) (-490 1199405 1199653 1199974 "INEP" 1200535 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198681 1199302 1199367 "INDE" 1199372 NIL INDE (NIL T) -8 NIL NIL) (-488 1198245 1198313 1198430 "INCRMAPS" 1198608 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1193556 1194481 1195425 "INBFF" 1197333 NIL INBFF (NIL T) -7 NIL NIL) (-486 1190057 1193401 1193504 "IMATRIX" 1193509 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188769 1188892 1189207 "IMATQF" 1189913 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186989 1187216 1187553 "IMATLIN" 1188525 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181615 1186913 1186971 "ILIST" 1186976 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1179574 1181475 1181588 "IIARRAY2" 1181593 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174942 1179485 1179549 "IFF" 1179554 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169991 1174234 1174422 "IFARRAY" 1174799 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1169198 1169895 1169968 "IFAMON" 1169973 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168781 1168846 1168901 "IEVALAB" 1169108 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1168456 1168524 1168684 "IEVALAB-" 1168689 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1168114 1168370 1168433 "IDPO" 1168438 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1167391 1168003 1168078 "IDPOAMS" 1168083 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166725 1167280 1167355 "IDPOAM" 1167360 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165810 1166060 1166114 "IDPC" 1166527 NIL IDPC (NIL T T) -9 NIL 1166676) (-472 1165306 1165702 1165775 "IDPAM" 1165780 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164709 1165198 1165271 "IDPAG" 1165276 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160964 1161812 1162707 "IDECOMP" 1163866 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153838 1154887 1155934 "IDEAL" 1160000 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1153002 1153114 1153313 "ICDEN" 1153722 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1152101 1152482 1152629 "ICARD" 1152875 T ICARD (NIL) -8 NIL NIL) (-466 1150173 1150486 1150889 "IBPTOOLS" 1151778 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145787 1149793 1149906 "IBITS" 1150092 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1142510 1143086 1143781 "IBATOOL" 1145204 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1140290 1140751 1141284 "IBACHIN" 1142045 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1138173 1140136 1140239 "IARRAY2" 1140244 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1134332 1138099 1138156 "IARRAY1" 1138161 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1128272 1132750 1133228 "IAN" 1133874 T IAN (NIL) -8 NIL NIL) (-459 1127783 1127840 1128013 "IALGFACT" 1128209 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1127310 1127423 1127452 "HYPCAT" 1127659 T HYPCAT (NIL) -9 NIL NIL) (-457 1126848 1126965 1127151 "HYPCAT-" 1127156 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1123527 1124858 1124900 "HOAGG" 1125881 NIL HOAGG (NIL T) -9 NIL 1126560) (-455 1122121 1122520 1123046 "HOAGG-" 1123051 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115952 1121562 1121728 "HEXADEC" 1121975 T HEXADEC (NIL) -8 NIL NIL) (-453 1114700 1114922 1115185 "HEUGCD" 1115729 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113803 1114537 1114667 "HELLFDIV" 1114672 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1112037 1113580 1113668 "HEAP" 1113747 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105910 1111952 1112014 "HDP" 1112019 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099622 1105547 1105698 "HDMP" 1105811 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098947 1099086 1099250 "HB" 1099478 T HB (NIL) -7 NIL NIL) (-447 1092456 1098793 1098897 "HASHTBL" 1098902 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1090209 1092084 1092263 "HACKPI" 1092297 T HACKPI (NIL) -8 NIL NIL) (-445 1085905 1090063 1090175 "GTSET" 1090180 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1079443 1085783 1085881 "GSTBL" 1085886 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071679 1078479 1078743 "GSERIES" 1079234 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070701 1071154 1071183 "GROUP" 1071444 T GROUP (NIL) -9 NIL 1071603) (-441 1069817 1070040 1070384 "GROUP-" 1070389 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1068186 1068505 1068892 "GROEBSOL" 1069494 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1067126 1067388 1067440 "GRMOD" 1067969 NIL GRMOD (NIL T T) -9 NIL 1068137) (-438 1066894 1066930 1067058 "GRMOD-" 1067063 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1062234 1063256 1064253 "GRIMAGE" 1065917 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060701 1060961 1061285 "GRDEF" 1061930 T GRDEF (NIL) -7 NIL NIL) (-435 1060145 1060261 1060402 "GRAY" 1060580 T GRAY (NIL) -7 NIL NIL) (-434 1059378 1059758 1059810 "GRALG" 1059963 NIL GRALG (NIL T T) -9 NIL 1060055) (-433 1059039 1059112 1059275 "GRALG-" 1059280 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055847 1058628 1058804 "GPOLSET" 1058946 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1055203 1055260 1055517 "GOSPER" 1055784 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050962 1051641 1052167 "GMODPOL" 1054902 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049967 1050151 1050389 "GHENSEL" 1050774 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1044033 1044876 1045902 "GENUPS" 1049051 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043730 1043781 1043870 "GENUFACT" 1043976 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1043142 1043219 1043384 "GENPGCD" 1043648 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1042616 1042651 1042864 "GENMFACT" 1043101 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1041184 1041439 1041746 "GENEEZ" 1042359 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1035058 1040797 1040958 "GDMP" 1041107 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1024437 1028829 1029935 "GCNAALG" 1034041 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022858 1023730 1023759 "GCDDOM" 1024014 T GCDDOM (NIL) -9 NIL 1024171) (-420 1022328 1022455 1022670 "GCDDOM-" 1022675 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1021000 1021185 1021489 "GB" 1022107 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1009620 1011946 1014338 "GBINTERN" 1018691 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1007457 1007749 1008170 "GBF" 1009295 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1006238 1006403 1006670 "GBEUCLID" 1007273 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1005587 1005712 1005861 "GAUSSFAC" 1006109 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003964 1004266 1004579 "GALUTIL" 1005306 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1002281 1002555 1002878 "GALPOLYU" 1003691 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999670 999960 1000365 "GALFACTU" 1001978 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 991476 992975 994583 "GALFACT" 998102 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988863 989521 989550 "FVFUN" 990706 T FVFUN (NIL) -9 NIL 991426) (-409 988128 988310 988339 "FVC" 988630 T FVC (NIL) -9 NIL 988813) (-408 987770 987925 988006 "FUNCTION" 988080 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 985440 985991 986480 "FT" 987301 T FT (NIL) -8 NIL NIL) (-406 984258 984741 984944 "FTEM" 985257 T FTEM (NIL) -8 NIL NIL) (-405 982523 982811 983213 "FSUPFACT" 983950 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980920 981209 981541 "FST" 982211 T FST (NIL) -8 NIL NIL) (-403 980095 980201 980395 "FSRED" 980802 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978774 979029 979383 "FSPRMELT" 979810 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975859 976297 976796 "FSPECF" 978337 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 958185 966742 966783 "FS" 970621 NIL FS (NIL T) -9 NIL 972903) (-399 946835 949825 953881 "FS-" 954178 NIL FS- (NIL T T) -8 NIL NIL) (-398 946351 946405 946581 "FSINT" 946776 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944632 945344 945647 "FSERIES" 946130 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943650 943766 943996 "FSCINT" 944512 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939884 942594 942636 "FSAGG" 943006 NIL FSAGG (NIL T) -9 NIL 943265) (-394 937646 938247 939043 "FSAGG-" 939138 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936688 936831 937058 "FSAGG2" 937499 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 934347 934626 935179 "FS2UPS" 936406 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933933 933976 934129 "FS2" 934298 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932793 932964 933272 "FS2EXPXP" 933758 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 932219 932334 932486 "FRUTIL" 932673 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923640 927718 929074 "FR" 930895 NIL FR (NIL T) -8 NIL NIL) (-387 918716 921359 921400 "FRNAALG" 922796 NIL FRNAALG (NIL T) -9 NIL 923403) (-386 914395 915465 916740 "FRNAALG-" 917490 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 914033 914076 914203 "FRNAAF2" 914346 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 912398 912890 913184 "FRMOD" 913846 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 910121 910789 911105 "FRIDEAL" 912189 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 909320 909407 909694 "FRIDEAL2" 910028 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 908577 908985 909027 "FRETRCT" 909032 NIL FRETRCT (NIL T) -9 NIL 909203) (-380 907689 907920 908271 "FRETRCT-" 908276 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904898 906118 906178 "FRAMALG" 907060 NIL FRAMALG (NIL T T) -9 NIL 907352) (-378 903031 903487 904117 "FRAMALG-" 904340 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896933 902506 902782 "FRAC" 902787 NIL FRAC (NIL T) -8 NIL NIL) (-376 896569 896626 896733 "FRAC2" 896870 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 896205 896262 896369 "FR2" 896506 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890831 893744 893773 "FPS" 894892 T FPS (NIL) -9 NIL 895448) (-373 890280 890389 890553 "FPS-" 890699 NIL FPS- (NIL T) -8 NIL NIL) (-372 887681 889378 889407 "FPC" 889632 T FPC (NIL) -9 NIL 889774) (-371 887474 887514 887611 "FPC-" 887616 NIL FPC- (NIL T) -8 NIL NIL) (-370 886352 886962 887004 "FPATMAB" 887009 NIL FPATMAB (NIL T) -9 NIL 887161) (-369 884052 884528 884954 "FPARFRAC" 885989 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 879447 879944 880626 "FORTRAN" 883484 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 877163 877663 878202 "FORT" 878928 T FORT (NIL) -7 NIL NIL) (-366 874838 875400 875429 "FORTFN" 876489 T FORTFN (NIL) -9 NIL 877113) (-365 874601 874651 874680 "FORTCAT" 874739 T FORTCAT (NIL) -9 NIL 874801) (-364 872661 873144 873543 "FORMULA" 874222 T FORMULA (NIL) -8 NIL NIL) (-363 872449 872479 872548 "FORMULA1" 872625 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871972 872024 872197 "FORDER" 872391 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 871068 871232 871425 "FOP" 871799 T FOP (NIL) -7 NIL NIL) (-360 869676 870348 870522 "FNLA" 870950 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 868344 868733 868762 "FNCAT" 869334 T FNCAT (NIL) -9 NIL 869627) (-358 867910 868303 868331 "FNAME" 868336 T FNAME (NIL) -8 NIL NIL) (-357 866569 867542 867571 "FMTC" 867576 T FMTC (NIL) -9 NIL 867611) (-356 862887 864094 864722 "FMONOID" 865974 NIL FMONOID (NIL T) -8 NIL NIL) (-355 862107 862630 862778 "FM" 862783 NIL FM (NIL T T) -8 NIL NIL) (-354 859530 860176 860205 "FMFUN" 861349 T FMFUN (NIL) -9 NIL 862057) (-353 858798 858979 859008 "FMC" 859298 T FMC (NIL) -9 NIL 859480) (-352 856027 856861 856915 "FMCAT" 858097 NIL FMCAT (NIL T T) -9 NIL 858591) (-351 854922 855795 855894 "FM1" 855972 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852696 853112 853606 "FLOATRP" 854473 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 846183 850352 850982 "FLOAT" 852086 T FLOAT (NIL) -8 NIL NIL) (-348 843621 844121 844699 "FLOATCP" 845650 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 842409 843257 843298 "FLINEXP" 843303 NIL FLINEXP (NIL T) -9 NIL 843396) (-346 841564 841799 842126 "FLINEXP-" 842131 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840640 840784 841008 "FLASORT" 841416 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837858 838700 838753 "FLALG" 839980 NIL FLALG (NIL T T) -9 NIL 840447) (-343 831645 835341 835383 "FLAGG" 836645 NIL FLAGG (NIL T) -9 NIL 837297) (-342 830371 830710 831200 "FLAGG-" 831205 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 829413 829556 829783 "FLAGG2" 830224 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 826385 827403 827463 "FINRALG" 828591 NIL FINRALG (NIL T T) -9 NIL 829099) (-339 825545 825774 826113 "FINRALG-" 826118 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824951 825164 825193 "FINITE" 825389 T FINITE (NIL) -9 NIL 825496) (-337 817410 819571 819612 "FINAALG" 823279 NIL FINAALG (NIL T) -9 NIL 824732) (-336 812751 813792 814936 "FINAALG-" 816315 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 812146 812506 812609 "FILE" 812681 NIL FILE (NIL T) -8 NIL NIL) (-334 810830 811142 811197 "FILECAT" 811881 NIL FILECAT (NIL T T) -9 NIL 812097) (-333 808645 810201 810230 "FIELD" 810270 T FIELD (NIL) -9 NIL 810350) (-332 807265 807650 808161 "FIELD-" 808166 NIL FIELD- (NIL T) -8 NIL NIL) (-331 805080 805902 806248 "FGROUP" 806952 NIL FGROUP (NIL T) -8 NIL NIL) (-330 804170 804334 804554 "FGLMICPK" 804912 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799972 804095 804152 "FFX" 804157 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799573 799634 799769 "FFSLPE" 799905 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795569 796345 797141 "FFPOLY" 798809 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 795073 795109 795318 "FFPOLY2" 795527 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790895 794992 795055 "FFP" 795060 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 786263 790806 790870 "FF" 790875 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 781359 785606 785796 "FFNBX" 786117 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 776269 780494 780752 "FFNBP" 781213 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770872 775553 775764 "FFNB" 776102 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769704 769902 770217 "FFINTBAS" 770669 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765880 768120 768149 "FFIELDC" 768769 T FFIELDC (NIL) -9 NIL 769145) (-318 764543 764913 765410 "FFIELDC-" 765415 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 764113 764158 764282 "FFHOM" 764485 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761811 762295 762812 "FFF" 763628 NIL FFF (NIL T) -7 NIL NIL) (-315 757399 761553 761654 "FFCGX" 761754 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 753001 757131 757238 "FFCGP" 757342 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 748154 752728 752836 "FFCG" 752937 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729951 739074 739161 "FFCAT" 744326 NIL FFCAT (NIL T T T) -9 NIL 745813) (-311 725149 726196 727510 "FFCAT-" 728740 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724560 724603 724838 "FFCAT2" 725100 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713760 717550 718767 "FEXPR" 723415 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712759 713194 713236 "FEVALAB" 713320 NIL FEVALAB (NIL T) -9 NIL 713581) (-307 711918 712128 712466 "FEVALAB-" 712471 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710511 711301 711504 "FDIV" 711817 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707577 708292 708408 "FDIVCAT" 709976 NIL FDIVCAT (NIL T T T T) -9 NIL 710413) (-304 707339 707366 707536 "FDIVCAT-" 707541 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706559 706646 706923 "FDIV2" 707246 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 705252 705509 705796 "FCPAK1" 706292 T FCPAK1 (NIL) -7 NIL NIL) (-301 704380 704752 704893 "FCOMP" 705143 NIL FCOMP (NIL T) -8 NIL NIL) (-300 688020 691432 694992 "FC" 700840 T FC (NIL) -8 NIL NIL) (-299 680568 684614 684655 "FAXF" 686457 NIL FAXF (NIL T) -9 NIL 687148) (-298 677847 678502 679327 "FAXF-" 679792 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672953 677223 677399 "FARRAY" 677704 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668296 670367 670420 "FAMR" 671432 NIL FAMR (NIL T T) -9 NIL 671892) (-295 667187 667489 667923 "FAMR-" 667928 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666383 667109 667162 "FAMONOID" 667167 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 664215 664899 664953 "FAMONC" 665894 NIL FAMONC (NIL T T) -9 NIL 666279) (-292 662907 663969 664106 "FAGROUP" 664111 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660710 661029 661431 "FACUTIL" 662588 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659809 659994 660216 "FACTFUNC" 660520 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 652132 659060 659272 "EXPUPXS" 659665 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649631 650167 650749 "EXPRTUBE" 651570 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645825 646417 647154 "EXPRODE" 648970 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630987 644484 644910 "EXPR" 645431 NIL EXPR (NIL T) -8 NIL NIL) (-285 625415 626002 626814 "EXPR2UPS" 630285 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 625051 625108 625215 "EXPR2" 625352 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616405 624188 624483 "EXPEXPAN" 624889 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 616232 616362 616391 "EXIT" 616396 T EXIT (NIL) -8 NIL NIL) (-281 615859 615921 616034 "EVALCYC" 616164 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615399 615517 615559 "EVALAB" 615729 NIL EVALAB (NIL T) -9 NIL 615833) (-279 614880 615002 615223 "EVALAB-" 615228 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612342 613654 613683 "EUCDOM" 614238 T EUCDOM (NIL) -9 NIL 614588) (-277 610747 611189 611779 "EUCDOM-" 611784 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598360 601099 603830 "ESTOOLS" 608036 T ESTOOLS (NIL) -7 NIL NIL) (-275 597996 598053 598160 "ESTOOLS2" 598297 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597747 597789 597869 "ESTOOLS1" 597948 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591684 593408 593437 "ES" 596201 T ES (NIL) -9 NIL 597607) (-272 586632 587918 589735 "ES-" 589899 NIL ES- (NIL T) -8 NIL NIL) (-271 583039 583791 584563 "ESCONT" 585880 T ESCONT (NIL) -7 NIL NIL) (-270 582784 582816 582898 "ESCONT1" 583001 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582459 582509 582609 "ES2" 582728 NIL ES2 (NIL T T) -7 NIL NIL) (-268 582089 582147 582256 "ES1" 582395 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581305 581434 581610 "ERROR" 581933 T ERROR (NIL) -7 NIL NIL) (-266 574820 581164 581255 "EQTBL" 581260 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 567257 570138 571585 "EQ" 573406 NIL -3126 (NIL T) -8 NIL NIL) (-264 566889 566946 567055 "EQ2" 567194 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 562181 563227 564320 "EP" 565828 NIL EP (NIL T) -7 NIL NIL) (-262 561340 561904 561933 "ENTIRER" 561938 T ENTIRER (NIL) -9 NIL 561983) (-261 557796 559295 559665 "EMR" 561139 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556939 557124 557179 "ELTAGG" 557559 NIL ELTAGG (NIL T T) -9 NIL 557770) (-259 556658 556720 556861 "ELTAGG-" 556866 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556446 556475 556530 "ELTAB" 556614 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555572 555718 555917 "ELFUTS" 556297 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555313 555369 555398 "ELEMFUN" 555503 T ELEMFUN (NIL) -9 NIL NIL) (-255 555183 555204 555272 "ELEMFUN-" 555277 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 550077 553280 553322 "ELAGG" 554262 NIL ELAGG (NIL T) -9 NIL 554725) (-253 548362 548796 549459 "ELAGG-" 549464 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 541230 543029 543856 "EFUPXS" 547638 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534680 536481 537291 "EFULS" 540506 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 532111 532469 532947 "EFSTRUC" 534312 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 521183 522748 524308 "EF" 530626 NIL EF (NIL T T) -7 NIL NIL) (-248 520284 520668 520817 "EAB" 521054 T EAB (NIL) -8 NIL NIL) (-247 519497 520243 520271 "E04UCFA" 520276 T E04UCFA (NIL) -8 NIL NIL) (-246 518710 519456 519484 "E04NAFA" 519489 T E04NAFA (NIL) -8 NIL NIL) (-245 517923 518669 518697 "E04MBFA" 518702 T E04MBFA (NIL) -8 NIL NIL) (-244 517136 517882 517910 "E04JAFA" 517915 T E04JAFA (NIL) -8 NIL NIL) (-243 516351 517095 517123 "E04GCFA" 517128 T E04GCFA (NIL) -8 NIL NIL) (-242 515566 516310 516338 "E04FDFA" 516343 T E04FDFA (NIL) -8 NIL NIL) (-241 514779 515525 515553 "E04DGFA" 515558 T E04DGFA (NIL) -8 NIL NIL) (-240 508965 510309 511671 "E04AGNT" 513437 T E04AGNT (NIL) -7 NIL NIL) (-239 507691 508171 508212 "DVARCAT" 508687 NIL DVARCAT (NIL T) -9 NIL 508885) (-238 506895 507107 507421 "DVARCAT-" 507426 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499757 506697 506824 "DSMP" 506829 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494583 495714 496778 "DROPT" 498713 T DROPT (NIL) -8 NIL NIL) (-235 494248 494307 494405 "DROPT1" 494518 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489370 490494 491629 "DROPT0" 493133 T DROPT0 (NIL) -7 NIL NIL) (-233 487715 488040 488426 "DRAWPT" 489004 T DRAWPT (NIL) -7 NIL NIL) (-232 482390 483289 484344 "DRAW" 486713 NIL DRAW (NIL T) -7 NIL NIL) (-231 482031 482082 482198 "DRAWHACK" 482333 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480776 481041 481328 "DRAWCX" 481764 T DRAWCX (NIL) -7 NIL NIL) (-229 480294 480362 480512 "DRAWCURV" 480702 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470898 472820 474899 "DRAWCFUN" 478235 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467717 469593 469635 "DQAGG" 470264 NIL DQAGG (NIL T) -9 NIL 470537) (-226 456176 462914 462997 "DPOLCAT" 464835 NIL DPOLCAT (NIL T T T T) -9 NIL 465379) (-225 451016 452362 454319 "DPOLCAT-" 454324 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 445100 450878 450975 "DPMO" 450980 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 439087 444881 445047 "DPMM" 445052 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438849 438900 438974 "DOMAIN" 439033 T DOMAIN (NIL) -8 NIL NIL) (-221 432561 438486 438637 "DMP" 438750 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 432161 432217 432361 "DLP" 432499 NIL DLP (NIL T) -7 NIL NIL) (-219 425811 431262 431489 "DLIST" 431966 NIL DLIST (NIL T) -8 NIL NIL) (-218 422663 424666 424708 "DLAGG" 425258 NIL DLAGG (NIL T) -9 NIL 425487) (-217 421325 422017 422046 "DIVRING" 422196 T DIVRING (NIL) -9 NIL 422304) (-216 420313 420566 420959 "DIVRING-" 420964 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 418415 418772 419178 "DISPLAY" 419927 T DISPLAY (NIL) -7 NIL NIL) (-214 412310 418329 418392 "DIRPROD" 418397 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 411158 411361 411626 "DIRPROD2" 412103 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400791 406790 406844 "DIRPCAT" 407252 NIL DIRPCAT (NIL NIL T) -9 NIL 408079) (-211 398117 398759 399640 "DIRPCAT-" 399977 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 397404 397564 397750 "DIOSP" 397951 T DIOSP (NIL) -7 NIL NIL) (-209 394112 396316 396358 "DIOPS" 396792 NIL DIOPS (NIL T) -9 NIL 397021) (-208 393661 393775 393966 "DIOPS-" 393971 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392532 393170 393199 "DIFRING" 393386 T DIFRING (NIL) -9 NIL 393495) (-206 392178 392255 392407 "DIFRING-" 392412 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389967 391249 391290 "DIFEXT" 391649 NIL DIFEXT (NIL T) -9 NIL 391942) (-204 388253 388681 389346 "DIFEXT-" 389351 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385581 387785 387827 "DIAGG" 387832 NIL DIAGG (NIL T) -9 NIL 387852) (-202 384965 385122 385374 "DIAGG-" 385379 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 380436 383924 384201 "DHMATRIX" 384734 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 376048 376957 377967 "DFSFUN" 379446 T DFSFUN (NIL) -7 NIL NIL) (-199 370834 374762 375127 "DFLOAT" 375703 T DFLOAT (NIL) -8 NIL NIL) (-198 369067 369348 369743 "DFINTTLS" 370542 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 366100 367102 367500 "DERHAM" 368734 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363955 365875 365964 "DEQUEUE" 366044 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 363173 363306 363501 "DEGRED" 363817 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359589 360330 361178 "DEFINTRF" 362405 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 357128 357595 358191 "DEFINTEF" 359110 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350959 356569 356735 "DECIMAL" 356982 T DECIMAL (NIL) -8 NIL NIL) (-191 348471 348929 349435 "DDFACT" 350503 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 348067 348110 348261 "DBLRESP" 348422 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345777 346111 346480 "DBASE" 347825 NIL DBASE (NIL T) -8 NIL NIL) (-188 344912 345736 345764 "D03FAFA" 345769 T D03FAFA (NIL) -8 NIL NIL) (-187 344048 344871 344899 "D03EEFA" 344904 T D03EEFA (NIL) -8 NIL NIL) (-186 341998 342464 342953 "D03AGNT" 343579 T D03AGNT (NIL) -7 NIL NIL) (-185 341316 341957 341985 "D02EJFA" 341990 T D02EJFA (NIL) -8 NIL NIL) (-184 340634 341275 341303 "D02CJFA" 341308 T D02CJFA (NIL) -8 NIL NIL) (-183 339952 340593 340621 "D02BHFA" 340626 T D02BHFA (NIL) -8 NIL NIL) (-182 339270 339911 339939 "D02BBFA" 339944 T D02BBFA (NIL) -8 NIL NIL) (-181 332469 334056 335662 "D02AGNT" 337684 T D02AGNT (NIL) -7 NIL NIL) (-180 330250 330769 331312 "D01WGTS" 331946 T D01WGTS (NIL) -7 NIL NIL) (-179 329357 330209 330237 "D01TRNS" 330242 T D01TRNS (NIL) -8 NIL NIL) (-178 328464 329316 329344 "D01GBFA" 329349 T D01GBFA (NIL) -8 NIL NIL) (-177 327571 328423 328451 "D01FCFA" 328456 T D01FCFA (NIL) -8 NIL NIL) (-176 326678 327530 327558 "D01ASFA" 327563 T D01ASFA (NIL) -8 NIL NIL) (-175 325785 326637 326665 "D01AQFA" 326670 T D01AQFA (NIL) -8 NIL NIL) (-174 324892 325744 325772 "D01APFA" 325777 T D01APFA (NIL) -8 NIL NIL) (-173 323999 324851 324879 "D01ANFA" 324884 T D01ANFA (NIL) -8 NIL NIL) (-172 323106 323958 323986 "D01AMFA" 323991 T D01AMFA (NIL) -8 NIL NIL) (-171 322213 323065 323093 "D01ALFA" 323098 T D01ALFA (NIL) -8 NIL NIL) (-170 321320 322172 322200 "D01AKFA" 322205 T D01AKFA (NIL) -8 NIL NIL) (-169 320427 321279 321307 "D01AJFA" 321312 T D01AJFA (NIL) -8 NIL NIL) (-168 313759 315301 316853 "D01AGNT" 318895 T D01AGNT (NIL) -7 NIL NIL) (-167 313096 313224 313376 "CYCLOTOM" 313627 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309831 310544 311271 "CYCLES" 312389 T CYCLES (NIL) -7 NIL NIL) (-165 309143 309277 309448 "CVMP" 309692 NIL CVMP (NIL T) -7 NIL NIL) (-164 306925 307182 307557 "CTRIGMNP" 308871 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 306299 306398 306551 "CSTTOOLS" 306822 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 302098 302755 303513 "CRFP" 305611 NIL CRFP (NIL T T) -7 NIL NIL) (-161 301145 301330 301558 "CRAPACK" 301902 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 300529 300630 300834 "CPMATCH" 301021 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 300254 300282 300388 "CPIMA" 300495 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 296618 297290 298008 "COORDSYS" 299589 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 292479 294621 295113 "CONTFRAC" 296158 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291632 292196 292225 "COMRING" 292230 T COMRING (NIL) -9 NIL 292281) (-155 290713 290990 291174 "COMPPROP" 291468 T COMPPROP (NIL) -8 NIL NIL) (-154 290374 290409 290537 "COMPLPAT" 290672 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 280355 290183 290292 "COMPLEX" 290297 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279991 280048 280155 "COMPLEX2" 280292 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279709 279744 279842 "COMPFACT" 279950 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263972 274266 274307 "COMPCAT" 275309 NIL COMPCAT (NIL T) -9 NIL 276702) (-149 253488 256411 260038 "COMPCAT-" 260394 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 253219 253247 253349 "COMMUPC" 253454 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 253014 253047 253106 "COMMONOP" 253180 T COMMONOP (NIL) -7 NIL NIL) (-146 252597 252765 252852 "COMM" 252947 T COMM (NIL) -8 NIL NIL) (-145 251851 252043 252072 "COMBOPC" 252408 T COMBOPC (NIL) -9 NIL 252581) (-144 250747 250957 251199 "COMBINAT" 251641 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246953 247524 248162 "COMBF" 250171 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245739 246069 246304 "COLOR" 246738 T COLOR (NIL) -8 NIL NIL) (-141 245379 245426 245551 "CMPLXRT" 245686 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240937 241951 243017 "CLIP" 244333 T CLIP (NIL) -7 NIL NIL) (-139 239275 240045 240283 "CLIF" 240765 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 235503 237421 237463 "CLAGG" 238392 NIL CLAGG (NIL T) -9 NIL 238928) (-137 233925 234382 234965 "CLAGG-" 234970 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 233469 233554 233694 "CINTSLPE" 233834 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230970 231441 231989 "CHVAR" 232997 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 230192 230756 230785 "CHARZ" 230790 T CHARZ (NIL) -9 NIL 230804) (-133 229946 229986 230064 "CHARPOL" 230146 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 229052 229649 229678 "CHARNZ" 229725 T CHARNZ (NIL) -9 NIL 229780) (-131 227075 227742 228077 "CHAR" 228737 T CHAR (NIL) -8 NIL NIL) (-130 226800 226861 226890 "CFCAT" 227001 T CFCAT (NIL) -9 NIL NIL) (-129 226045 226156 226338 "CDEN" 226684 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 222037 225198 225478 "CCLASS" 225785 T CCLASS (NIL) -8 NIL NIL) (-127 217090 218066 218819 "CARTEN" 221340 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 216198 216346 216567 "CARTEN2" 216937 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 214495 215350 215606 "CARD" 215962 T CARD (NIL) -8 NIL NIL) (-124 213867 214195 214224 "CACHSET" 214356 T CACHSET (NIL) -9 NIL 214433) (-123 213363 213659 213688 "CABMON" 213738 T CABMON (NIL) -9 NIL 213794) (-122 210926 213055 213162 "BTREE" 213289 NIL BTREE (NIL T) -8 NIL NIL) (-121 208430 210574 210696 "BTOURN" 210836 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205854 207901 207943 "BTCAT" 208011 NIL BTCAT (NIL T) -9 NIL 208088) (-119 205521 205601 205750 "BTCAT-" 205755 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200711 204582 204611 "BTAGG" 204867 T BTAGG (NIL) -9 NIL 205046) (-117 200134 200278 200508 "BTAGG-" 200513 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 197184 199412 199627 "BSTREE" 199951 NIL BSTREE (NIL T) -8 NIL NIL) (-115 196322 196448 196632 "BRILL" 197040 NIL BRILL (NIL T) -7 NIL NIL) (-114 193029 195050 195092 "BRAGG" 195741 NIL BRAGG (NIL T) -9 NIL 195998) (-113 191558 191964 192519 "BRAGG-" 192524 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184766 190904 191088 "BPADICRT" 191406 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 183070 184703 184748 "BPADIC" 184753 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182770 182800 182913 "BOUNDZRO" 183034 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 178285 179376 180243 "BOP" 181923 T BOP (NIL) -8 NIL NIL) (-108 175906 176350 176870 "BOP1" 177798 NIL BOP1 (NIL T) -7 NIL NIL) (-107 174259 174949 175243 "BOOLEAN" 175632 T BOOLEAN (NIL) -8 NIL NIL) (-106 173625 174003 174056 "BMODULE" 174061 NIL BMODULE (NIL T T) -9 NIL 174125) (-105 169435 173423 173496 "BITS" 173572 T BITS (NIL) -8 NIL NIL) (-104 168532 168967 169119 "BINFILE" 169303 T BINFILE (NIL) -8 NIL NIL) (-103 162367 167976 168141 "BINARY" 168387 T BINARY (NIL) -8 NIL NIL) (-102 160200 161622 161664 "BGAGG" 161924 NIL BGAGG (NIL T) -9 NIL 162061) (-101 160031 160063 160154 "BGAGG-" 160159 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 159129 159415 159620 "BFUNCT" 159846 T BFUNCT (NIL) -8 NIL NIL) (-99 157830 158008 158293 "BEZOUT" 158953 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154361 156690 157018 "BBTREE" 157533 NIL BBTREE (NIL T) -8 NIL NIL) (-97 154098 154151 154178 "BASTYPE" 154295 T BASTYPE (NIL) -9 NIL NIL) (-96 153954 153982 154052 "BASTYPE-" 154057 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153392 153468 153618 "BALFACT" 153865 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 152214 152811 152996 "AUTOMOR" 153237 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151939 151944 151971 "ATTREG" 151976 T ATTREG (NIL) -9 NIL NIL) (-92 150218 150636 150988 "ATTRBUT" 151605 T ATTRBUT (NIL) -8 NIL NIL) (-91 149753 149866 149893 "ATRIG" 150094 T ATRIG (NIL) -9 NIL NIL) (-90 149562 149603 149690 "ATRIG-" 149695 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147765 149338 149426 "ASTACK" 149505 NIL ASTACK (NIL T) -8 NIL NIL) (-88 146270 146567 146932 "ASSOCEQ" 147447 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 145302 145929 146053 "ASP9" 146177 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 145066 145250 145289 "ASP8" 145294 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143936 144671 144813 "ASP80" 144955 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142835 143571 143703 "ASP7" 143835 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141791 142512 142630 "ASP78" 142748 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140762 141471 141588 "ASP77" 141705 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139677 140400 140531 "ASP74" 140662 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138578 139312 139444 "ASP73" 139576 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137533 138255 138373 "ASP6" 138491 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136482 137210 137328 "ASP55" 137446 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135432 136156 136275 "ASP50" 136394 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134520 135133 135243 "ASP4" 135353 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133608 134221 134331 "ASP49" 134441 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132393 133147 133315 "ASP42" 133497 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 131171 131926 132096 "ASP41" 132280 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 130123 130848 130966 "ASP35" 131084 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129888 130071 130110 "ASP34" 130115 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129625 129692 129768 "ASP33" 129843 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128521 129260 129392 "ASP31" 129524 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 128286 128469 128508 "ASP30" 128513 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 128021 128090 128166 "ASP29" 128241 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127786 127969 128008 "ASP28" 128013 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127551 127734 127773 "ASP27" 127778 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126635 127249 127360 "ASP24" 127471 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125552 126276 126406 "ASP20" 126536 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124640 125253 125363 "ASP1" 125473 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123584 124314 124433 "ASP19" 124552 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 123321 123388 123464 "ASP12" 123539 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 122174 122920 123064 "ASP10" 123208 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 120079 122018 122109 "ARRAY2" 122114 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115901 119727 119841 "ARRAY1" 119996 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114933 115106 115327 "ARRAY12" 115724 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 109298 111163 111239 "ARR2CAT" 113869 NIL ARR2CAT (NIL T T T) -9 NIL 114627) (-54 106732 107476 108430 "ARR2CAT-" 108435 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105492 105642 105945 "APPRULE" 106570 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 105145 105193 105311 "APPLYORE" 105438 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 104119 104410 104605 "ANY" 104968 T ANY (NIL) -8 NIL NIL) (-50 103397 103520 103677 "ANY1" 103993 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100929 101847 102172 "ANTISYM" 103122 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100756 100888 100915 "ANON" 100920 T ANON (NIL) -8 NIL NIL) (-47 94833 99301 99752 "AN" 100323 T AN (NIL) -8 NIL NIL) (-46 91139 92537 92588 "AMR" 93327 NIL AMR (NIL T T) -9 NIL 93926) (-45 90252 90473 90835 "AMR-" 90840 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74814 90169 90230 "ALIST" 90235 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71651 74408 74577 "ALGSC" 74732 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 68207 68761 69368 "ALGPKG" 71091 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 67484 67585 67769 "ALGMFACT" 68093 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 63233 63914 64568 "ALGMANIP" 67008 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 54552 62859 63009 "ALGFF" 63166 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52738 53348 53387 "ALGEBRA" 53447 NIL ALGEBRA (NIL T) -9 NIL 53505) (-36 52456 52515 52647 "ALGEBRA-" 52652 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34177 49902 49955 "ALAGG" 50091 NIL ALAGG (NIL T T) -9 NIL 50252) (-34 33712 33825 33852 "AHYP" 34053 T AHYP (NIL) -9 NIL NIL) (-33 32642 32890 32917 "AGG" 33416 T AGG (NIL) -9 NIL 33695) (-32 32076 32238 32452 "AGG-" 32457 NIL AGG- (NIL T) -8 NIL NIL) (-31 29763 30181 30598 "AF" 31719 NIL AF (NIL T T) -7 NIL NIL) (-30 29041 29295 29449 "ACPLOT" 29627 T ACPLOT (NIL) -8 NIL NIL) (-29 18460 26406 26458 "ACFS" 27169 NIL ACFS (NIL T) -9 NIL 27408) (-28 16474 16964 17739 "ACFS-" 17744 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12694 14650 14677 "ACF" 15556 T ACF (NIL) -9 NIL 15968) (-26 11398 11732 12225 "ACF-" 12230 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11192 "ABELSG" 11284 T ABELSG (NIL) -9 NIL 11349) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10232 10493 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9896 9980 10118 "ABELMON-" 10123 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9230 9576 9603 "ABELGRP" 9728 T ABELGRP (NIL) -9 NIL 9810) (-20 8693 8822 9038 "ABELGRP-" 9043 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8029 8069 "A1AGG" 8074 NIL A1AGG (NIL T) -9 NIL 8114) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
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