diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 756 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1126 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1285 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8264 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27690 |
5 files changed, 19560 insertions, 19561 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 7da8d7f8..60de9c5b 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2234201 . 3409939477) +(2234201 . 3410359537) (-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."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4235 . T) (-4233 . T) (-4232 . T) ((-4240 "*") . T) (-4231 . T) (-4236 . T) (-4230 . T) (-2047 . T)) +((-4235 . T) (-4233 . T) (-4232 . T) ((-4240 "*") . T) (-4231 . T) (-4236 . T) (-4230 . T) (-2088 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -4055) +(-31 R -4102) ((|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 -962) (QUOTE (-522))))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4238))) (-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2047 . T)) +((-2088 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#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 -4055 UP UPUP -3010) +(-39 -4102 UP UPUP -1246) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4231 |has| (-382 |#2|) (-338)) (-4236 |has| (-382 |#2|) (-338)) (-4230 |has| (-382 |#2|) (-338)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-382 |#2|) (QUOTE (-133))) (|HasCategory| (-382 |#2|) (QUOTE (-135))) (|HasCategory| (-382 |#2|) (QUOTE (-324))) (|HasCategory| (-382 |#2|) (QUOTE (-338))) (-3708 (|HasCategory| (-382 |#2|) (QUOTE (-338))) (|HasCategory| (-382 |#2|) (QUOTE (-324)))) (|HasCategory| (-382 |#2|) (QUOTE (-343))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-343))) (-3708 (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3708 (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3708 (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) -(-40 R -4055) +((|HasCategory| (-382 |#2|) (QUOTE (-133))) (|HasCategory| (-382 |#2|) (QUOTE (-135))) (|HasCategory| (-382 |#2|) (QUOTE (-324))) (|HasCategory| (-382 |#2|) (QUOTE (-338))) (-3844 (|HasCategory| (-382 |#2|) (QUOTE (-338))) (|HasCategory| (-382 |#2|) (QUOTE (-324)))) (|HasCategory| (-382 |#2|) (QUOTE (-343))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-343))) (-3844 (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3844 (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3844 (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) +(-40 R -4102) ((|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 (-426))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -405) (|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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (-3708 (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (-3844 (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -140,7 +140,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -4055) +(-53 |Base| R -4102) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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"))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . 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}"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-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}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) -(-59 -2888) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +(-59 -3015) ((|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 -2888) +(-60 -3015) ((|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 -2888) +(-61 -3015) ((|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 -2888) +(-62 -3015) ((|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 -2888) +(-63 -3015) ((|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 -2888) +(-64 -3015) ((|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 -2888) +(-65 -3015) ((|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 -2888) +(-66 -3015) ((|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 -2888) +(-67 -3015) ((|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 -2888) +(-68 -3015) ((|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 -2888) +(-69 -3015) ((|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 -2888) +(-70 -3015) ((|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 -2888) +(-71 -3015) ((|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 -2888) +(-72 -3015) ((|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 -2888) +(-75 -3015) ((|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 -2888) +(-76 -3015) ((|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 -2888) +(-77 -3015) ((|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 -2888) +(-78 -3015) ((|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 -2888) +(-79 -3015) ((|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 -2888) +(-80 -3015) ((|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 -2888) +(-81 -3015) ((|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 -2888) +(-82 -3015) ((|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 -2888) +(-83 -3015) ((|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 -2888) +(-84 -3015) ((|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 -2888) +(-85 -3015) ((|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 -2888) +(-86 -3015) ((|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 -2888) +(-87 -3015) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -287,7 +287,7 @@ NIL (-89 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -323,7 +323,7 @@ NIL (-98 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-99 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -338,12 +338,12 @@ NIL NIL (-102 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3708 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) +((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3844 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) (-104) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -372,7 +372,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-111 -4055 UP) +(-111 -4102 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -383,14 +383,14 @@ NIL (-113 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-838))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-135))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-112 |#1|) (QUOTE (-947))) (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (QUOTE (-1061))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (QUOTE (-210))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -262) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-283))) (|HasCategory| (-112 |#1|) (QUOTE (-507))) (|HasCategory| (-112 |#1|) (QUOTE (-784))) (-3708 (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))))) +((|HasCategory| (-112 |#1|) (QUOTE (-838))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-135))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-112 |#1|) (QUOTE (-947))) (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (QUOTE (-1061))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-112 |#1|) (QUOTE (-210))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -262) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-283))) (|HasCategory| (-112 |#1|) (QUOTE (-507))) (|HasCategory| (-112 |#1|) (QUOTE (-784))) (-3844 (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))))) (-114 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4239))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2047 . T)) +((-2088 . T)) NIL (-116 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -399,14 +399,14 @@ NIL (-117 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,16 +414,16 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-123 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-124) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -436,18 +436,18 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4240 "*") . T)) NIL -(-127 |minix| -2617 S T$) +(-127 |minix| -2787 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-128 |minix| -2617 R) +(-128 |minix| -2787 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 (-129) ((|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}."))) ((-4238 . T) (-4228 . T) (-4239 . T)) -((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-343))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3708 (-12 (|HasCategory| (-132) (QUOTE (-343))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792))))) +((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-343))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3844 (-12 (|HasCategory| (-132) (QUOTE (-343))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792))))) (-130 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 @@ -472,7 +472,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4235 . T)) NIL -(-136 -4055 UP UPUP) +(-136 -4102 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 @@ -486,7 +486,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -4238))) (-139 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."))) -((-2047 . T)) +((-2088 . T)) NIL (-140 |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."))) @@ -504,7 +504,7 @@ 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 -(-144 R -4055) +(-144 R -4102) ((|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 @@ -534,7 +534,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-507))) (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-980))) (|HasCategory| |#2| (QUOTE (-947))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-338))) (|HasAttribute| |#2| (QUOTE -4234)) (|HasAttribute| |#2| (QUOTE -4237)) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-784)))) (-151 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})"))) -((-4231 -3708 (|has| |#1| (-514)) (-12 (|has| |#1| (-283)) (|has| |#1| (-838)))) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4234 |has| |#1| (-6 -4234)) (-4237 |has| |#1| (-6 -4237)) (-3911 . T) (-2047 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-4231 -3844 (|has| |#1| (-514)) (-12 (|has| |#1| (-283)) (|has| |#1| (-838)))) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4234 |has| |#1| (-6 -4234)) (-4237 |has| |#1| (-6 -4237)) (-4005 . T) (-2088 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-152 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."))) @@ -546,8 +546,8 @@ NIL NIL (-154 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}."))) -((-4231 -3708 (|has| |#1| (-514)) (-12 (|has| |#1| (-283)) (|has| |#1| (-838)))) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4234 |has| |#1| (-6 -4234)) (-4237 |has| |#1| (-6 -4237)) (-3911 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-324)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-1106))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE 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T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-324)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-1106))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE 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(|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-338))) (-12 (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-838))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-838))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-338)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasAttribute| |#1| (QUOTE -4234)) (|HasAttribute| |#1| (QUOTE -4237)) (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085))))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-324))))) (-155 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 @@ -596,7 +596,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-167 R -4055) +(-167 R -4102) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -700,19 +700,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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 -(-193 -4055 UP UPUP R) +(-193 -4102 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 -(-194 -4055 FP) +(-194 -4102 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 (-195) ((|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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3708 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) -(-196 R -4055) +((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3844 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) +(-196 R -4102) ((|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 @@ -727,18 +727,18 @@ NIL (-199 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-200 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4235 . T)) NIL -(-201 R -4055) +(-201 R -4102) ((|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 (-202) ((|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}."))) -((-3898 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-3996 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-203) ((|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)}.}"))) @@ -747,14 +747,14 @@ NIL (-204 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-205 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-206 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."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-207 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}."))) @@ -778,28 +778,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4238))) (-212 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}."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-213) ((|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 -(-214 S -2617 R) +(-214 S -2787 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 (-338))) (|HasCategory| |#3| (QUOTE (-730))) (|HasCategory| |#3| (QUOTE (-782))) (|HasAttribute| |#3| (QUOTE -4235)) (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-343))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-971))) (|HasCategory| |#3| (QUOTE (-1014)))) -(-215 -2617 R) +(-215 -2787 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"))) -((-4232 |has| |#2| (-971)) (-4233 |has| |#2| (-971)) (-4235 |has| |#2| (-6 -4235)) ((-4240 "*") |has| |#2| (-157)) (-4238 . T) (-2047 . T)) +((-4232 |has| |#2| (-971)) (-4233 |has| |#2| (-971)) (-4235 |has| |#2| (-6 -4235)) ((-4240 "*") |has| |#2| (-157)) (-4238 . T) (-2088 . T)) NIL -(-216 -2617 A B) +(-216 -2787 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) 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((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -814,12 +814,12 @@ NIL NIL (-221 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."))) -((-2047 . T)) +((-2088 . T)) NIL (-222 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}"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-223 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -827,19 +827,19 @@ NIL (-224 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -850,7 +850,7 @@ NIL NIL (-230 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}."))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-231) ((|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."))) @@ -891,7 +891,7 @@ NIL (-240 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"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#3| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#3| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#3| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#3| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-241 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 @@ -936,11 +936,11 @@ 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 -(-252 R -4055) +(-252 R -4102) ((|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 -(-253 R -4055) +(-253 R -4102) ((|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 @@ -962,7 +962,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014)))) (-258 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}."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-259 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}."))) @@ -988,7 +988,7 @@ 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 -(-265 S R |Mod| -4048 -2160 |exactQuo|) +(-265 S R |Mod| -3004 -3164 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL @@ -1010,21 +1010,21 @@ NIL NIL (-270 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) -((-4235 -3708 (|has| |#1| (-971)) (|has| |#1| (-447))) (-4232 |has| |#1| (-971)) (-4233 |has| |#1| (-971))) -((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-971)))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-278))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-447)))) (-3708 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-971)))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-664))) (-3708 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-1026))) (-3708 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-21))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3708 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-25))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014))))) +((-4235 -3844 (|has| |#1| (-971)) (|has| |#1| (-447))) (-4232 |has| |#1| (-971)) (-4233 |has| |#1| (-971))) +((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-971)))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-278))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-447)))) (-3844 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-971)))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-664))) (-3844 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-1026))) (-3844 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-21))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3844 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-25))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-971)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014))))) (-271 |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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-272) ((|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 -(-273 -4055 S) +(-273 -4102 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 -(-274 E -4055) +(-274 E -4102) ((|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 @@ -1072,7 +1072,7 @@ 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 -(-286 -4055) +(-286 -4102) ((|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 @@ -1083,7 +1083,7 @@ NIL (-288 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))}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-947))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-1061))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-210))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -262) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-283))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-507))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-784))) (-3708 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-784)))) (-12 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))) (-3708 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (-12 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))))) +((|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-947))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-1061))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-210))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (LIST (QUOTE -262) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1152) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-283))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-507))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-784))) (-3844 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-784)))) (-12 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))) (-3844 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (-12 (|HasCategory| (-1152 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))))) (-289 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 @@ -1094,9 +1094,9 @@ NIL NIL (-291 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."))) -((-4235 -3708 (-4015 (|has| |#1| (-971)) (|has| |#1| (-584 (-522)))) (-12 (|has| |#1| (-514)) (-3708 (-4015 (|has| |#1| (-971)) (|has| |#1| (-584 (-522)))) (|has| |#1| (-971)) (|has| |#1| (-447)))) (|has| |#1| (-971)) (|has| |#1| (-447))) (-4233 |has| |#1| (-157)) (-4232 |has| |#1| (-157)) ((-4240 "*") |has| |#1| (-514)) (-4231 |has| |#1| (-514)) (-4236 |has| 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-382) (QUOTE (-522))))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) (|HasCategory| $ (QUOTE (-971))) (|HasCategory| $ (LIST (QUOTE -962) (QUOTE (-522))))) +(-292 R -4102) ((|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 @@ -1107,7 +1107,7 @@ NIL (-294 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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-295 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 @@ -1139,12 +1139,12 @@ NIL (-302 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."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) -(-303 S -4055) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +(-303 S -4102) ((|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 (-343)))) -(-304 -4055) +(-304 -4102) ((|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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL @@ -1164,15 +1164,15 @@ 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 -(-309 S -4055 UP UPUP R) +(-309 S -4102 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 -(-310 -4055 UP UPUP R) +(-310 -4102 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 -(-311 -4055 UP UPUP R) +(-311 -4102 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 @@ -1192,26 +1192,26 @@ 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 -(-316 S -4055 UP UPUP) +(-316 S -4102 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 (-343))) (|HasCategory| |#2| (QUOTE (-338)))) -(-317 -4055 UP UPUP) +(-317 -4102 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."))) ((-4231 |has| (-382 |#2|) (-338)) (-4236 |has| (-382 |#2|) (-338)) (-4230 |has| (-382 |#2|) (-338)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-318 |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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3708 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) +((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3844 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) (-319 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) (-320 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) (-321 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 @@ -1228,31 +1228,31 @@ 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL -(-325 R UP -4055) +(-325 R UP -4102) ((|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 (-326 |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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3708 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) +((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3844 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) (-327 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) (-328 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) (-329 |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}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3708 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) +((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-343))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3844 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-343))))) (-330 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) -(-331 -4055 GF) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +(-331 -4102 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 @@ -1260,14 +1260,14 @@ 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 -(-333 -4055 FP FPP) +(-333 -4102 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 (-334 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}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3708 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) +((|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-133))) (-3844 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-343))))) (-335 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 @@ -1322,7 +1322,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4239)) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014)))) (-348 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4238 . T) (-2047 . T)) +((-4238 . T) (-2088 . T)) NIL (-349 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1346,7 +1346,7 @@ NIL NIL (-354) ((|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}."))) -((-4221 . T) (-4229 . T) (-3898 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-4221 . T) (-4229 . T) (-3996 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-355 |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}."))) @@ -1362,11 +1362,11 @@ NIL NIL (-358) ((|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}."))) -((-2047 . T)) +((-2088 . T)) NIL (-359) ((|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.}"))) -((-2047 . T)) +((-2088 . T)) NIL (-360 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."))) @@ -1396,7 +1396,7 @@ 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 -(-367 -4055 UP UPUP R) +(-367 -4102 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 @@ -1410,27 +1410,27 @@ NIL NIL (-370) ((|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."))) -((-2047 . T)) +((-2088 . T)) NIL (-371) ((|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.}"))) -((-2047 . T)) +((-2088 . T)) NIL (-372) ((|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 -(-373 -2888 |returnType| -3890 |symbols|) +(-373 -3015 |returnType| -2174 |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 -(-374 -4055 UP) +(-374 -4102 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-375 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2047 . T)) +((-2088 . T)) NIL (-376 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1446,7 +1446,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4221)) (|HasAttribute| |#1| (QUOTE -4229))) (-379) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3898 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-3996 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-380 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."))) @@ -1459,7 +1459,7 @@ NIL (-382 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."))) ((-4225 -12 (|has| |#1| (-6 -4236)) (|has| |#1| (-426)) (|has| |#1| (-6 -4225))) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-507))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (-12 (|HasAttribute| |#1| (QUOTE -4236)) (|HasAttribute| |#1| (QUOTE -4225)) (|HasCategory| |#1| (QUOTE (-426)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (-3708 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765))))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765))))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-507))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (-12 (|HasAttribute| |#1| (QUOTE -4236)) (|HasAttribute| |#1| (QUOTE -4225)) (|HasCategory| |#1| (QUOTE (-426)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (-3844 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765))))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-765))))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-383 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1480,11 +1480,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-388 R -4055 UP A) +(-388 R -4102 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4235 . T)) NIL -(-389 R -4055 UP A |ibasis|) +(-389 R -4102 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 -962) (|devaluate| |#2|)))) @@ -1503,7 +1503,7 @@ NIL (-393 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."))) ((-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -262) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-1124))))) +((|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -262) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-1124))) (|HasCategory| |#1| (QUOTE (-947))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-1124))))) (-394 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 @@ -1530,9 +1530,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-343)))) (-400 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4238 . T) (-4228 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4228 . T) (-4239 . T) (-2088 . T)) NIL -(-401 R -4055) +(-401 R -4102) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1540,7 +1540,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4225 -12 (|has| |#1| (-6 -4225)) (|has| |#2| (-6 -4225))) (-4232 . T) (-4233 . T) (-4235 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4225)) (|HasAttribute| |#2| (QUOTE -4225)))) -(-403 R -4055) +(-403 R -4102) ((|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 @@ -1550,17 +1550,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (-405 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}."))) -((-4235 -3708 (|has| |#1| (-971)) (|has| |#1| (-447))) (-4233 |has| |#1| (-157)) (-4232 |has| |#1| (-157)) ((-4240 "*") |has| |#1| (-514)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-514)) (-4230 |has| |#1| (-514)) (-2047 . T)) +((-4235 -3844 (|has| |#1| (-971)) (|has| |#1| (-447))) (-4233 |has| |#1| (-157)) (-4232 |has| |#1| (-157)) ((-4240 "*") |has| |#1| (-514)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-514)) (-4230 |has| |#1| (-514)) (-2088 . T)) NIL -(-406 R -4055) +(-406 R -4102) ((|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 -(-407 R -4055) +(-407 R -4102) ((|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)))) -(-408 R -4055) +(-408 R -4102) ((|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 @@ -1568,7 +1568,7 @@ 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 -(-410 R -4055 UP) +(-410 R -4102 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 -962) (QUOTE (-47))))) @@ -1586,17 +1586,17 @@ NIL NIL (-414) ((|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}."))) -((-2047 . T)) +((-2088 . T)) NIL (-415) ((|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.}"))) -((-2047 . T)) +((-2088 . T)) NIL (-416 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 -(-417 R UP -4055) +(-417 R UP -4102) ((|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 @@ -1643,7 +1643,7 @@ NIL (-428 |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"))) (((-4240 "*") |has| |#2| (-157)) (-4231 |has| |#2| (-514)) (-4236 |has| |#2| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3708 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3844 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) (-429 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 @@ -1708,7 +1708,7 @@ 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 -(-445 |lv| -4055 R) +(-445 |lv| -4102 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 @@ -1723,11 +1723,11 @@ NIL (-448 |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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-449 |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."))) ((-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-450 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)}"))) ((-4239 . T) (-4238 . T)) @@ -1739,7 +1739,7 @@ NIL (-452 |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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-453) ((|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 @@ -1747,16 +1747,16 @@ NIL (-454 |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"))) (((-4240 "*") |has| |#2| (-157)) (-4231 |has| |#2| (-514)) (-4236 |has| |#2| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3708 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) -(-455 -2617 S) +((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3844 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +(-455 -2787 S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. 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((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) -(-457 -4055 UP UPUP R) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +(-457 -4102 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 @@ -1767,14 +1767,14 @@ NIL (-459) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3708 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) +((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3844 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) (-460 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL ((|HasAttribute| |#1| (QUOTE -4238)) (|HasAttribute| |#1| (QUOTE -4239)) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-461 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2047 . T)) +((-2088 . T)) NIL (-462 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1784,7 +1784,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-464 -4055 UP |AlExt| |AlPol|) +(-464 -4102 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 @@ -1795,16 +1795,16 @@ NIL (-466 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-467 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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-468 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-469 R UP -4055) +(-469 R UP -4102) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1824,7 +1824,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-474 -4055 |Expon| |VarSet| |DPoly|) +(-474 -4102 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-1085))))) @@ -1871,19 +1871,19 @@ NIL (-485 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-486 |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}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-535 |#1|) (QUOTE (-135))) (|HasCategory| (-535 |#1|) (QUOTE (-343))) (|HasCategory| (-535 |#1|) (QUOTE (-133))) (-3708 (|HasCategory| (-535 |#1|) (QUOTE (-133))) (|HasCategory| (-535 |#1|) (QUOTE (-343))))) +((|HasCategory| (-535 |#1|) (QUOTE (-135))) (|HasCategory| (-535 |#1|) (QUOTE (-343))) (|HasCategory| (-535 |#1|) (QUOTE (-133))) (-3844 (|HasCategory| (-535 |#1|) (QUOTE (-133))) (|HasCategory| (-535 |#1|) (QUOTE (-343))))) (-487 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}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-488 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."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-489 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 @@ -1895,7 +1895,7 @@ NIL (-491 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-492 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1908,7 +1908,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-495 K -4055 |Par|) +(-495 K -4102 |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 @@ -1928,7 +1928,7 @@ 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 -(-500 K -4055 |Par|) +(-500 K -4102 |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 @@ -1963,12 +1963,12 @@ NIL (-508 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) -(-509 R -4055) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +(-509 R -4102) ((|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 -(-510 R0 -4055 UP UPUP R) +(-510 R0 -4102 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 @@ -1978,7 +1978,7 @@ NIL NIL (-512 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."))) -((-3898 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-3996 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-513 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."))) @@ -1988,7 +1988,7 @@ 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."))) ((-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL -(-515 R -4055) +(-515 R -4102) ((|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 @@ -2000,7 +2000,7 @@ 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 -(-518 R -4055 L) +(-518 R -4102 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 -598) (|devaluate| |#2|)))) @@ -2008,11 +2008,11 @@ 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 -(-520 -4055 UP UPUP R) +(-520 -4102 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 -(-521 -4055 UP) +(-521 -4102 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 @@ -2024,15 +2024,15 @@ 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 -(-524 R -4055 L) +(-524 R -4102 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 -598) (|devaluate| |#2|)))) -(-525 R -4055) +(-525 R -4102) ((|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 -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-574))))) -(-526 -4055 UP) +(-526 -4102 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 @@ -2040,27 +2040,27 @@ 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 -(-528 -4055) +(-528 -4102) ((|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 (-529 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."))) -((-3898 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-3996 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-530) ((|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 -(-531 R -4055) +(-531 R -4102) ((|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 -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-574))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085))))) (-12 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-260)))) (|HasCategory| |#1| (QUOTE (-514)))) -(-532 -4055 UP) +(-532 -4102 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 -(-533 R -4055) +(-533 R -4102) ((|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 @@ -2076,15 +2076,15 @@ 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 -(-537 R -4055) +(-537 R -4102) ((|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 -(-538 E -4055) +(-538 E -4102) ((|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 -(-539 -4055) +(-539 -4102) ((|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}."))) ((-4233 . T) (-4232 . T)) ((|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-1085))))) @@ -2111,7 +2111,7 @@ NIL (-545 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-3708 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014)))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3708 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))))) +((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-3844 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014)))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3844 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))))) (-546 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 @@ -2119,7 +2119,7 @@ NIL (-547 |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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|))))) (|HasCategory| (-522) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-522))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|))))) (|HasCategory| (-522) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-522))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085))))))) (-548 |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.}"))) ((-4233 |has| |#1| (-514)) (-4232 |has| |#1| (-514)) ((-4240 "*") |has| |#1| (-514)) (-4231 |has| |#1| (-514)) (-4235 . T)) @@ -2132,7 +2132,7 @@ 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 -(-551 R -4055 FG) +(-551 R -4102 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 @@ -2143,30 +2143,30 @@ NIL (-553 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-554 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 -4239)) (|HasCategory| |#2| (QUOTE (-784))) (|HasAttribute| |#1| (QUOTE -4238)) (|HasCategory| |#3| (QUOTE (-1014)))) (-555 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2047 . T)) +((-2088 . T)) NIL (-556 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4235 -3708 (-4015 (|has| |#2| (-342 |#1|)) (|has| |#1| (-514))) (-12 (|has| |#2| (-392 |#1|)) (|has| |#1| (-514)))) (-4233 . T) (-4232 . T)) -((|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (-3708 (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))))) +((-4235 -3844 (-4079 (|has| |#2| (-342 |#1|)) (|has| |#1| (-514))) (-12 (|has| |#2| (-392 |#1|)) (|has| |#1| (-514)))) (-4233 . T) (-4232 . T)) +((|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (-3844 (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))))) (-557 |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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -562) (QUOTE (-792))))) +((|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -562) (QUOTE (-792))))) (-558 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 (-559 |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}."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-560 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"))) @@ -2184,7 +2184,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-564 -4055 UP) +(-564 -4102 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2200,7 +2200,7 @@ 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}."))) ((-4232 . T) (-4233 . T) (-4235 . T)) ((|HasCategory| |#1| (QUOTE (-782)))) -(-568 R -4055) +(-568 R -4102) ((|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 @@ -2228,18 +2228,18 @@ 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 -(-575 R -4055) +(-575 R -4102) ((|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 -(-576 |lv| -4055) +(-576 |lv| -4102) ((|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 (-577) ((|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."))) ((-4239 . T)) -((|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3048) (QUOTE (-51))))))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3149) (QUOTE (-51))))))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) (-578 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2250,8 +2250,8 @@ NIL NIL (-580 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4235 -3708 (-4015 (|has| |#2| (-342 |#1|)) (|has| |#1| (-514))) (-12 (|has| |#2| (-392 |#1|)) (|has| |#1| (-514)))) (-4233 . T) (-4232 . T)) -((|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (-3708 (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))))) +((-4235 -3844 (-4079 (|has| |#2| (-342 |#1|)) (|has| |#1| (-514))) (-12 (|has| |#2| (-392 |#1|)) (|has| |#1| (-514)))) (-4233 . T) (-4232 . T)) +((|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (-3844 (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -342) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (LIST (QUOTE -392) (|devaluate| |#1|)))))) (-581 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 @@ -2263,7 +2263,7 @@ NIL (-583 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 (-338))) (-2401 (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-338))) (-2473 (|HasCategory| |#1| (QUOTE (-338))))) (-584 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4235 . T)) @@ -2283,11 +2283,11 @@ NIL (-588 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-765))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-765))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-589 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-590 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2302,9 +2302,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4239))) (-593 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})}."))) -((-2047 . T)) +((-2088 . T)) NIL -(-594 R -4055 L) +(-594 R -4102 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 @@ -2324,11 +2324,11 @@ 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}."))) ((-4232 . T) (-4233 . T) (-4235 . T)) NIL -(-599 -4055 UP) +(-599 -4102 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)))) -(-600 A -3383) +(-600 A -3596) ((|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}}"))) ((-4232 . T) (-4233 . T) (-4235 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-338)))) @@ -2362,13 +2362,13 @@ NIL NIL (-608 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}."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL -(-609 -4055) +(-609 -4102) ((|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 -(-610 -4055 |Row| |Col| M) +(-610 -4102 |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 @@ -2379,7 +2379,7 @@ NIL (-612 |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."))) ((-4235 . T) (-4238 . T) (-4232 . T) (-4233 . T)) -((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-514))) (-3708 (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-3708 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) +((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-514))) (-3844 (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-3844 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) (-613 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2390,12 +2390,12 @@ NIL NIL (-615 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-2047 . T)) +((-2088 . T)) NIL (-616 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 (-1014))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-617 |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 @@ -2434,7 +2434,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-514)))) (-626 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"))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-627 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."))) @@ -2443,12 +2443,12 @@ NIL (-628 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."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-514))) (|HasAttribute| |#1| (QUOTE (-4240 "*"))) (|HasCategory| |#1| (QUOTE (-338))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-629 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 -(-630 S -4055 FLAF FLAS) +(-630 S -4102 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 @@ -2458,11 +2458,11 @@ NIL NIL (-632) ((|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"))) -((-4231 . T) (-4236 |has| (-637) (-338)) (-4230 |has| (-637) (-338)) (-3911 . T) (-4237 |has| (-637) (-6 -4237)) (-4234 |has| (-637) (-6 -4234)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-637) (QUOTE (-135))) (|HasCategory| (-637) (QUOTE (-133))) (|HasCategory| (-637) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-637) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-637) (QUOTE (-343))) (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-637) (QUOTE (-210))) (|HasCategory| (-637) (QUOTE (-324))) (-3708 (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-324)))) (|HasCategory| (-637) (LIST (QUOTE -262) (QUOTE (-637)) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -285) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-637) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-637) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-637) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-637) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-637) (QUOTE (-947))) (|HasCategory| (-637) (QUOTE (-1106))) (-12 (|HasCategory| (-637) (QUOTE (-928))) (|HasCategory| (-637) (QUOTE (-1106)))) (|HasCategory| (-637) (QUOTE (-507))) (|HasCategory| (-637) (QUOTE (-980))) (-12 (|HasCategory| (-637) (QUOTE (-980))) (|HasCategory| (-637) (QUOTE (-1106)))) (-3708 (|HasCategory| (-637) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-637) (QUOTE (-338)))) (|HasCategory| (-637) (QUOTE (-283))) (-3708 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-324)))) (|HasCategory| (-637) (QUOTE (-838))) (-12 (|HasCategory| (-637) (QUOTE (-210))) (|HasCategory| (-637) (QUOTE (-338)))) (-12 (|HasCategory| (-637) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-637) (QUOTE (-338)))) (|HasCategory| (-637) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-637) (QUOTE (-784))) (|HasCategory| (-637) (QUOTE (-514))) (|HasAttribute| (-637) (QUOTE -4237)) (|HasAttribute| (-637) (QUOTE -4234)) (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-338))) (-12 (|HasCategory| (-637) (QUOTE (-324))) (|HasCategory| (-637) (QUOTE (-838))))) (-3708 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (-12 (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-838)))) (-12 (|HasCategory| (-637) (QUOTE (-324))) (|HasCategory| (-637) (QUOTE (-838))))) (-3708 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-338)))) (-3708 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-514)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-133)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-324))))) +((-4231 . T) (-4236 |has| (-637) (-338)) (-4230 |has| (-637) (-338)) (-4005 . T) (-4237 |has| (-637) (-6 -4237)) (-4234 |has| (-637) (-6 -4234)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((|HasCategory| (-637) (QUOTE (-135))) (|HasCategory| (-637) (QUOTE (-133))) (|HasCategory| (-637) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-637) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-637) (QUOTE (-343))) (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-637) (QUOTE (-210))) (|HasCategory| (-637) (QUOTE (-324))) (-3844 (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-324)))) (|HasCategory| (-637) (LIST (QUOTE -262) (QUOTE (-637)) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -285) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-637)))) (|HasCategory| (-637) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-637) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-637) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-637) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-637) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-637) (QUOTE (-947))) (|HasCategory| (-637) (QUOTE (-1106))) (-12 (|HasCategory| (-637) (QUOTE (-928))) (|HasCategory| (-637) (QUOTE (-1106)))) (|HasCategory| (-637) (QUOTE (-507))) (|HasCategory| (-637) (QUOTE (-980))) (-12 (|HasCategory| (-637) (QUOTE (-980))) (|HasCategory| (-637) (QUOTE (-1106)))) (-3844 (|HasCategory| (-637) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-637) (QUOTE (-338)))) (|HasCategory| (-637) (QUOTE (-283))) (-3844 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-324)))) (|HasCategory| (-637) (QUOTE (-838))) (-12 (|HasCategory| (-637) (QUOTE (-210))) (|HasCategory| (-637) (QUOTE (-338)))) (-12 (|HasCategory| (-637) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-637) (QUOTE (-338)))) (|HasCategory| (-637) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-637) (QUOTE (-784))) (|HasCategory| (-637) (QUOTE (-514))) (|HasAttribute| (-637) (QUOTE -4237)) (|HasAttribute| (-637) (QUOTE -4234)) (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-338))) (-12 (|HasCategory| (-637) (QUOTE (-324))) (|HasCategory| (-637) (QUOTE (-838))))) (-3844 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (-12 (|HasCategory| (-637) (QUOTE (-338))) (|HasCategory| (-637) (QUOTE (-838)))) (-12 (|HasCategory| (-637) (QUOTE (-324))) (|HasCategory| (-637) (QUOTE (-838))))) (-3844 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-338)))) (-3844 (-12 (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-514)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-133)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-637) (QUOTE (-283))) (|HasCategory| (-637) (QUOTE (-838)))) (|HasCategory| (-637) (QUOTE (-324))))) (-633 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}."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-634 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}."))) @@ -2472,13 +2472,13 @@ 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 -(-636 OV E -4055 PG) +(-636 OV E -4102 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 (-637) ((|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}"))) -((-3898 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-3996 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-638 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."))) @@ -2508,7 +2508,7 @@ 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 -(-645 S -2213 I) +(-645 S -2252 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 @@ -2524,14 +2524,14 @@ 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 -(-649 R |Mod| -4048 -2160 |exactQuo|) +(-649 R |Mod| -3004 -3164 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-650 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4234 |has| |#1| (-338)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-324))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-324))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-651 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2540,7 +2540,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4233 |has| |#1| (-157)) (-4232 |has| |#1| (-157)) (-4235 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135)))) -(-653 R |Mod| -4048 -2160 |exactQuo|) +(-653 R |Mod| -3004 -3164 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4235 . T)) NIL @@ -2552,7 +2552,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4233 . T) (-4232 . T)) NIL -(-656 -4055) +(-656 -4102) ((|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]]}."))) ((-4235 . T)) NIL @@ -2588,7 +2588,7 @@ 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 -(-665 -4055 UP) +(-665 -4102 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 @@ -2607,7 +2607,7 @@ NIL (-669 |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."))) (((-4240 "*") |has| |#2| (-157)) (-4231 |has| |#2| (-514)) (-4236 |has| |#2| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3708 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3708 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-157))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-514)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338))) (-3844 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#2| (QUOTE -4236)) (|HasCategory| |#2| (QUOTE (-426))) (-3844 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) (-670 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2626,7 +2626,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-784)))) (-674 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4228 . T) (-4239 . T) (-2047 . T)) +((-4228 . T) (-4239 . T) (-2088 . T)) NIL (-675 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2740,15 +2740,15 @@ 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 -(-703 -4055) +(-703 -4102) ((|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 -(-704 P -4055) +(-704 P -4102) ((|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 -(-705 UP -4055) +(-705 UP -4102) ((|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 @@ -2764,7 +2764,7 @@ 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."))) (((-4240 "*") . T)) NIL -(-709 R -4055) +(-709 R -4102) ((|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 @@ -2784,7 +2784,7 @@ 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 -(-714 -4055 |ExtF| |SUEx| |ExtP| |n|) +(-714 -4102 |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 @@ -2799,7 +2799,7 @@ NIL (-717 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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . 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|#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-718 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 @@ -2807,14 +2807,14 @@ NIL (-719 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)}"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4234 |has| |#1| (-338)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-999) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-720 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 -382) (QUOTE (-522)))))) (-721 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.}"))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-722 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}."))) @@ -2868,23 +2868,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4232 . T) (-4233 . T) (-4235 . T)) NIL -(-735 -3708 R OS S) +(-735 -3844 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-736 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-980))) (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (-3708 (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3708 (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-980))) (|HasCategory| |#1| (QUOTE (-507))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (-3844 (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-3844 (|HasCategory| (-925 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) (-737) ((|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 -(-738 R -4055 L) +(-738 R -4102 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 -(-739 R -4055) +(-739 R -4102) ((|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 @@ -2892,7 +2892,7 @@ 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 -(-741 R -4055) +(-741 R -4102) ((|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 @@ -2900,11 +2900,11 @@ 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 -(-743 -4055 UP UPUP R) +(-743 -4102 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 -(-744 -4055 UP L LQ) +(-744 -4102 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 @@ -2912,38 +2912,38 @@ 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 -(-746 -4055 UP L LQ) +(-746 -4102 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 -(-747 -4055 UP) +(-747 -4102 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 -(-748 -4055 L UP A LO) +(-748 -4102 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 -(-749 -4055 UP) +(-749 -4102 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)))) -(-750 -4055 LO) +(-750 -4102 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 -(-751 -4055 LODO) +(-751 -4102 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-755 (-1085)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-754 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) (((-4240 "*") |has| |#2| (-338)) (-4231 |has| |#2| (-338)) (-4236 |has| |#2| (-338)) (-4230 |has| |#2| (-338)) (-4235 . T) (-4233 . T) (-4232 . T)) @@ -2998,7 +2998,7 @@ NIL NIL (-767 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4238 . T) (-4228 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4228 . T) (-4239 . T) (-2088 . T)) NIL (-768) ((|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."))) @@ -3011,7 +3011,7 @@ NIL (-770 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."))) ((-4235 |has| |#1| (-782))) -((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-507))) (-3708 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-21))) (-3708 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) +((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-507))) (-3844 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-21))) (-3844 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) (-771 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4233 |has| |#1| (-157)) (-4232 |has| |#1| (-157)) (-4235 . T)) @@ -3039,12 +3039,12 @@ NIL (-777 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."))) ((-4235 |has| |#1| (-782))) -((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-507))) (-3708 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-21))) (-3708 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) +((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-507))) (-3844 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-21))) (-3844 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) (-778) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-779 -2617 S) +(-779 -2787 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 @@ -3080,11 +3080,11 @@ 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 (-338))) (|HasCategory| |#1| (QUOTE (-514)))) -(-788 R |sigma| -1203) +(-788 R |sigma| -2764) ((|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."))) ((-4232 . T) (-4233 . T) (-4235 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-338)))) -(-789 |x| R |sigma| -1203) +(-789 |x| R |sigma| -2764) ((|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."))) ((-4232 . T) (-4233 . T) (-4235 . T)) ((|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-426))) (|HasCategory| |#2| (QUOTE (-338)))) @@ -3131,15 +3131,15 @@ NIL (-800 |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)."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-799 |#1|) (QUOTE (-838))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-135))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-799 |#1|) (QUOTE (-947))) (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (QUOTE (-1061))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (QUOTE (-210))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -262) (LIST (QUOTE -799) (|devaluate| |#1|)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (QUOTE (-283))) (|HasCategory| (-799 |#1|) (QUOTE (-507))) (|HasCategory| (-799 |#1|) (QUOTE (-784))) (-3708 (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))))) +((|HasCategory| (-799 |#1|) (QUOTE (-838))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-135))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-799 |#1|) (QUOTE (-947))) (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (QUOTE (-1061))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-799 |#1|) (QUOTE (-210))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -483) (QUOTE (-1085)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -262) (LIST (QUOTE -799) (|devaluate| |#1|)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (QUOTE (-283))) (|HasCategory| (-799 |#1|) (QUOTE (-507))) (|HasCategory| (-799 |#1|) (QUOTE (-784))) (-3844 (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))))) (-801 |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)}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-947))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-1061))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -262) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-507))) (|HasCategory| |#2| (QUOTE (-784))) (-3708 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-947))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-1061))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -262) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-507))) (|HasCategory| |#2| (QUOTE (-784))) (-3844 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) (-802 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))))) +((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))))) (-803) ((|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 @@ -3195,7 +3195,7 @@ NIL (-816 |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 -962) (QUOTE (-1085)))) (-12 (-2401 (|HasCategory| |#2| (QUOTE (-971)))) (-2401 (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))))) (-12 (|HasCategory| |#2| (QUOTE (-971))) (-2401 (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085))))))) +((|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))) (-12 (-2473 (|HasCategory| |#2| (QUOTE (-971)))) (-2473 (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))))) (-12 (|HasCategory| |#2| (QUOTE (-971))) (-2473 (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085))))))) (-817 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 @@ -3204,7 +3204,7 @@ 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 -(-819 R -2213) +(-819 R -2252) ((|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 @@ -3228,7 +3228,7 @@ 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 -(-825 UP -4055) +(-825 UP -4102) ((|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 @@ -3251,7 +3251,7 @@ NIL (-830 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-831 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ^= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3267,7 +3267,7 @@ NIL (-834 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."))) ((-4235 . T)) -((|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-784))) (-3708 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-784))))) +((|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-784))) (-3844 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-784))))) (-835 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 @@ -3288,7 +3288,7 @@ 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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) ((|HasCategory| $ (QUOTE (-135))) (|HasCategory| $ (QUOTE (-133))) (|HasCategory| $ (QUOTE (-343)))) -(-840 R0 -4055 UP UPUP R) +(-840 R0 -4102 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 @@ -3316,7 +3316,7 @@ 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 -(-847 -4055) +(-847 -4102) ((|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 @@ -3332,11 +3332,11 @@ 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}."))) (((-4240 "*") . T)) NIL -(-851 -4055 P) +(-851 -4102 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-852 |xx| -4055) +(-852 |xx| -4102) ((|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 @@ -3360,7 +3360,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-858 R -4055) +(-858 R -4102) ((|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 @@ -3372,7 +3372,7 @@ 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 -(-861 S R -4055) +(-861 S R -4102) ((|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 @@ -3392,11 +3392,11 @@ 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 -815) (|devaluate| |#1|)))) -(-866 R -4055 -2213) +(-866 R -4102 -2252) ((|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 -(-867 -2213) +(-867 -2252) ((|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 @@ -3419,7 +3419,7 @@ NIL (-872 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-873 |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 @@ -3444,7 +3444,7 @@ 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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) NIL -(-879 E V R P -4055) +(-879 E V R P -4102) ((|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 @@ -3455,8 +3455,8 @@ NIL (-881 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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) -(-882 E V R P -4055) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-1085) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +(-882 E V R P -4102) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-426)))) @@ -3475,12 +3475,12 @@ NIL (-886 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-887) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-888 -4055) +(-888 -4102) ((|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 @@ -3495,11 +3495,11 @@ NIL (-891 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}"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-124)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (-12 (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-124)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236))) (-892 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"))) ((-4235 -12 (|has| |#2| (-447)) (|has| |#1| (-447)))) -((-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))))) +((-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-447)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730))))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-730))) (|HasCategory| |#2| (QUOTE (-730)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))))) (-893) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3514,7 +3514,7 @@ NIL NIL (-896 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-897 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}}"))) @@ -3542,7 +3542,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-514)))) (-903 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."))) -((-4238 . T) (-2047 . T)) +((-4238 . T) (-2088 . T)) NIL (-904 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."))) @@ -3558,7 +3558,7 @@ NIL NIL (-907 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}."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-908 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3576,7 +3576,7 @@ 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 -(-912 K R UP -4055) +(-912 K R UP -4102) ((|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 @@ -3606,7 +3606,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-507))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-947))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-1061)))) (-919 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}."))) -((-2047 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-2088 . T) (-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-920 |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}."))) @@ -3614,7 +3614,7 @@ NIL NIL (-921 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."))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-922 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}."))) @@ -3631,11 +3631,11 @@ NIL (-925 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.}"))) ((-4231 |has| |#1| (-266)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-266))) (-3708 (|HasCategory| |#1| (QUOTE (-266))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-980))) (|HasCategory| |#1| (QUOTE (-507))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))))) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-266))) (-3844 (|HasCategory| |#1| (QUOTE (-266))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -483) (QUOTE (-1085)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -262) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-980))) (|HasCategory| |#1| (QUOTE (-507))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))))) (-926 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}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-927 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3644,14 +3644,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-929 -4055 UP UPUP |radicnd| |n|) +(-929 -4102 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4231 |has| (-382 |#2|) (-338)) (-4236 |has| (-382 |#2|) (-338)) (-4230 |has| (-382 |#2|) (-338)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-382 |#2|) (QUOTE (-133))) (|HasCategory| (-382 |#2|) (QUOTE (-135))) (|HasCategory| (-382 |#2|) (QUOTE (-324))) (|HasCategory| (-382 |#2|) (QUOTE (-338))) (-3708 (|HasCategory| (-382 |#2|) (QUOTE (-338))) (|HasCategory| (-382 |#2|) (QUOTE (-324)))) (|HasCategory| (-382 |#2|) (QUOTE (-343))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-343))) (-3708 (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3708 (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3708 (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) +((|HasCategory| (-382 |#2|) (QUOTE (-133))) (|HasCategory| (-382 |#2|) (QUOTE (-135))) (|HasCategory| (-382 |#2|) (QUOTE (-324))) (|HasCategory| (-382 |#2|) (QUOTE (-338))) (-3844 (|HasCategory| (-382 |#2|) (QUOTE (-338))) (|HasCategory| (-382 |#2|) (QUOTE (-324)))) (|HasCategory| (-382 |#2|) (QUOTE (-343))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-343))) (-3844 (|HasCategory| (-382 |#2|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3844 (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-12 (|HasCategory| (-382 |#2|) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (-3844 (-12 (|HasCategory| (-382 |#2|) (QUOTE (-210))) (|HasCategory| (-382 |#2|) (QUOTE (-338)))) (|HasCategory| (-382 |#2|) (QUOTE (-324))))) (-930 |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."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3708 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) +((|HasCategory| (-522) (QUOTE (-838))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-1085)))) (|HasCategory| (-522) (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-135))) (|HasCategory| (-522) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-947))) (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-1061))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| (-522) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| (-522) (QUOTE (-210))) (|HasCategory| (-522) (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| (-522) (LIST (QUOTE -483) (QUOTE (-1085)) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -285) (QUOTE (-522)))) (|HasCategory| (-522) (LIST (QUOTE -262) (QUOTE (-522)) (QUOTE (-522)))) (|HasCategory| (-522) (QUOTE (-283))) (|HasCategory| (-522) (QUOTE (-507))) (|HasCategory| (-522) (QUOTE (-784))) (-3844 (|HasCategory| (-522) (QUOTE (-757))) (|HasCategory| (-522) (QUOTE (-784)))) (|HasCategory| (-522) (LIST (QUOTE -584) (QUOTE (-522)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-522) (QUOTE (-838)))) (|HasCategory| (-522) (QUOTE (-133))))) (-931) ((|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 @@ -3674,7 +3674,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4239)) (|HasCategory| |#2| (QUOTE (-1014)))) (-936 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}."))) -((-2047 . T)) +((-2088 . T)) NIL (-937 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}}"))) @@ -3684,19 +3684,19 @@ 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}}"))) ((-4231 . T) (-4236 . T) (-4230 . T) (-4233 . T) (-4232 . T) ((-4240 "*") . T) (-4235 . T)) NIL -(-939 R -4055) +(-939 R -4102) ((|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 -(-940 R -4055) +(-940 R -4102) ((|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 -(-941 -4055 UP) +(-941 -4102 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 -(-942 -4055 UP) +(-942 -4102 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 @@ -3727,8 +3727,8 @@ NIL (-949 |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"))) ((-4231 . T) (-4236 . T) (-4230 . T) (-4233 . T) (-4232 . T) ((-4240 "*") . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (QUOTE (-522)))) (-3708 (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) -(-950 -4055 L) +((|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (QUOTE (-522)))) (-3844 (|HasCategory| (-382 (-522)) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))))) +(-950 -4102 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 @@ -3764,14 +3764,14 @@ 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 -(-959 -4055 |Expon| |VarSet| |FPol| |LFPol|) +(-959 -4102 |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"))) (((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-960) ((|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.}"))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (QUOTE (-1085))) (LIST (QUOTE |:|) (QUOTE -3048) (QUOTE (-51))))))) (|HasCategory| (-1085) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (QUOTE (-1085))) (LIST (QUOTE |:|) (QUOTE -3149) (QUOTE (-51))))))) (|HasCategory| (-1085) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) (-961 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 @@ -3816,7 +3816,7 @@ 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."))) ((-4235 . T)) NIL -(-972 |xx| -4055) +(-972 |xx| -4102) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3826,12 +3826,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-283))) (|HasCategory| |#4| (QUOTE (-338))) (|HasCategory| |#4| (QUOTE (-514))) (|HasCategory| |#4| (QUOTE (-157)))) (-974 |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"))) -((-4238 . T) (-2047 . T) (-4233 . T) (-4232 . T)) +((-4238 . T) (-2088 . T) (-4233 . T) (-4232 . T)) NIL (-975 |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}."))) ((-4238 . T) (-4233 . T) (-4232 . T)) -((|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-283))) (|HasCategory| |#3| (QUOTE (-514))) (|HasCategory| |#3| (QUOTE (-157))) (-3708 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-338)))) (|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-3708 (-12 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))))) +((|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-283))) (|HasCategory| |#3| (QUOTE (-514))) (|HasCategory| |#3| (QUOTE (-157))) (-3844 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-338)))) (|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-3844 (-12 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (LIST (QUOTE -285) (|devaluate| |#3|)))))) (-976 |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 @@ -3863,7 +3863,7 @@ NIL (-983) ((|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}"))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (QUOTE (-1085))) (LIST (QUOTE |:|) (QUOTE -3048) (QUOTE (-51))))))) (|HasCategory| (-1085) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (QUOTE (-1085))) (LIST (QUOTE |:|) (QUOTE -3149) (QUOTE (-51))))))) (|HasCategory| (-1085) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-1014)))) (-12 (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -285) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -562) (QUOTE (-792)))))) (-984 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 @@ -3890,7 +3890,7 @@ NIL NIL (-990 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}."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-991 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."))) @@ -3900,11 +3900,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-993 |Base| R -4055) +(-993 |Base| R -4102) ((|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 -(-994 |Base| R -4055) +(-994 |Base| R -4102) ((|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 @@ -3919,7 +3919,7 @@ NIL (-997 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."))) ((-4231 |has| |#1| (-338)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-324)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085))))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085))))) (-12 (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-338)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-324))))) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-324)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085))))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085))))) (-12 (|HasCategory| |#1| (QUOTE (-324))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-338)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-324))))) (-998 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 @@ -3943,7 +3943,7 @@ NIL (-1003 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"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| (-1004 (-1085)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-1004 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 @@ -3962,7 +3962,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1014)))) (-1008 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."))) -((-2047 . T)) +((-2088 . T)) NIL (-1009 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3970,7 +3970,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (QUOTE (-1014)))) (-1010 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2047 . T)) +((-2088 . T)) NIL (-1011 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3978,7 +3978,7 @@ NIL NIL (-1012 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4228 . T) (-2047 . T)) +((-4228 . T) (-2088 . T)) NIL (-1013 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}."))) @@ -3995,7 +3995,7 @@ NIL (-1016 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)}}"))) ((-4238 . T) (-4228 . T) (-4239 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-784))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-784))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792))))) (-1017 |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 @@ -4022,7 +4022,7 @@ NIL NIL (-1023 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.}"))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-1024) ((|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."))) @@ -4039,12 +4039,12 @@ NIL (-1027 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-426)))) -(-1029 R -4055) +(-1029 R -4102) ((|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 @@ -4062,7 +4062,7 @@ NIL NIL (-1033 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4238 . T) (-4239 . T) (-2047 . T)) +((-4238 . T) (-4239 . T) (-2088 . T)) NIL (-1034 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4070,7 +4070,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-338))) (|HasAttribute| |#3| (QUOTE (-4240 "*"))) (|HasCategory| |#3| (QUOTE (-157)))) (-1035 |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."))) -((-2047 . T) (-4238 . T) (-4232 . T) (-4233 . T) (-4235 . T)) +((-2088 . T) (-4238 . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-1036 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}."))) @@ -4079,16 +4079,16 @@ NIL (-1037 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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3708 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-354)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-354))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-522))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-354)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236)) (|HasCategory| |#1| (QUOTE (-426))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (|HasCategory| |#1| (QUOTE (-426))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3844 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) (-1038 |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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-514))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-338)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-514))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-338)))) (-1039 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}"))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL -(-1040 UP -4055) +(-1040 UP -4102) ((|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 @@ -4135,18 +4135,18 @@ NIL (-1051 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014))) (-12 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -285) (LIST (QUOTE -1050) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -285) (LIST (QUOTE -1050) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014)))))) +((|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014))) (-12 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -285) (LIST (QUOTE -1050) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -562) (QUOTE (-792)))) (-12 (|HasCategory| (-1050 |#1| |#2|) (LIST (QUOTE -285) (LIST (QUOTE -1050) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1050 |#1| |#2|) (QUOTE (-1014)))))) (-1052 |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}."))) ((-4235 . T) (-4227 |has| |#2| (-6 (-4240 "*"))) (-4238 . T) (-4232 . T) (-4233 . T)) -((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-338))) (-3708 (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-3708 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) +((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-514))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-338))) (-3844 (|HasAttribute| |#2| (QUOTE (-4240 "*"))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-3844 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -584) (QUOTE (-522))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) (-1053 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1054) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-1055 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4159,19 +4159,19 @@ NIL (-1057 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1058 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1059 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})}."))) -((-2047 . T)) +((-2088 . T)) NIL (-1060 |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."))) ((-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1061) ((|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 @@ -4195,19 +4195,19 @@ NIL (-1066 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4239 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1067) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-1068) NIL ((-4239 . T) (-4238 . T)) -((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3708 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792))))) +((|HasCategory| (-132) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1014))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-3844 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1014))) (|HasCategory| (-132) (LIST (QUOTE -285) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-792))))) (-1069 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#1|)))))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (QUOTE (-1068))) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#1|)))))) (|HasCategory| (-1068) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-1014)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1070 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 @@ -4234,9 +4234,9 @@ NIL NIL (-1076 |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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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4255,15 +4255,15 @@ NIL (-1081 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . 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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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|))))) (|HasCategory| (-708) (QUOTE (-1026))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|))))) (|HasCategory| (-708) (QUOTE (-1026))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-1084) ((|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 @@ -4279,7 +4279,7 @@ NIL (-1087 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-6 -4236)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (-12 (|HasCategory| (-898) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-514)))) (-3708 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-426))) (-12 (|HasCategory| (-898) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasAttribute| |#1| (QUOTE -4236))) (-1088) ((|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 @@ -4307,7 +4307,7 @@ NIL (-1094 |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}"))) ((-4238 . T) (-4239 . T)) -((|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2530) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3048) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3708 (|HasCategory| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -285) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2644) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3149) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1014))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792))))) (-3844 (|HasCategory| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (LIST (QUOTE -562) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1095 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 @@ -4318,7 +4318,7 @@ NIL NIL (-1097 |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})}."))) -((-4239 . T) (-2047 . T)) +((-4239 . T) (-2088 . T)) NIL (-1098 |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."))) @@ -4359,7 +4359,7 @@ NIL (-1107 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1108 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1110 R -4055) +(-1110 R -4102) ((|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 @@ -4376,7 +4376,7 @@ 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 -(-1112 R -4055) +(-1112 R -4102) ((|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 -563) (LIST (QUOTE -821) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -815) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -563) (LIST (QUOTE -821) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -815) (|devaluate| |#1|))))) @@ -4386,12 +4386,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-343)))) (-1114 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-1115 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4233 . T) (-4232 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-514))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-338)))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-514))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-338)))) (-1116 |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 @@ -4404,13 +4404,13 @@ 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 (-1014))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792))))) -(-1119 -4055) +(-1119 -4102) ((|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 (-1120) ((|constructor| (NIL "The fundamental Type."))) -((-2047 . T)) +((-2088 . T)) NIL (-1121 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}.}"))) @@ -4442,16 +4442,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-338)))) (-1128 |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)}."))) -(((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-2047 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) +(((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-2088 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) NIL (-1129 |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)}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| (-522) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-135))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-135))))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-210)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-522)) (|devaluate| |#1|))))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -962) (QUOTE (-1085))))) (-12 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univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4487,7 +4487,7 @@ NIL (-1139 |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."))) (((-4240 "*") |has| |#2| (-157)) (-4231 |has| |#2| (-514)) (-4234 |has| |#2| (-338)) (-4236 |has| |#2| (-6 -4236)) (-4233 . T) (-4232 . T) (-4235 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4503,7 +4503,7 @@ NIL (-1143 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 -829) (QUOTE (-1085)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2190) (LIST (|devaluate| |#2|) (QUOTE (-1085)))))) +((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2217) (LIST (|devaluate| |#2|) (QUOTE (-1085)))))) (-1144 |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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) @@ -4531,22 +4531,22 @@ NIL (-1150 |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)}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-1151 |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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4236 |has| |#1| (-338)) (-4230 |has| |#1| (-338)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3708 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522))) (|devaluate| |#1|))))) (|HasCategory| (-382 (-522)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (-3844 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-1152 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))}."))) (((-4240 "*") |has| (-1151 |#2| |#3| |#4|) (-157)) (-4231 |has| (-1151 |#2| |#3| |#4|) (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-157))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-338))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-426))) (-3708 (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-514)))) +((|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-157))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (QUOTE (-522)))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-338))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-426))) (-3844 (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (LIST (QUOTE -962) (LIST (QUOTE -382) (QUOTE (-522)))))) (|HasCategory| (-1151 |#2| |#3| |#4|) (QUOTE (-514)))) (-1153 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4239))) (-1154 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2047 . T)) +((-2088 . T)) NIL (-1155 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4555,7 +4555,7 @@ NIL (-1156 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-522)))) (|HasCategory| |#2| (QUOTE (-887))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1858) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1085))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#2| (QUOTE (-887))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2611) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1085))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#2| (QUOTE (-338)))) (-1157 |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."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) @@ -4563,18 +4563,18 @@ NIL (-1158 |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}."))) (((-4240 "*") |has| |#1| (-157)) (-4231 |has| |#1| (-514)) (-4232 . T) (-4233 . T) (-4235 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3708 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|))))) (|HasCategory| (-708) (QUOTE (-1026))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (|HasSignature| |#1| (LIST (QUOTE -2190) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (QUOTE (-338))) (-3708 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -1858) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -4090) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasCategory| |#1| (QUOTE (-514))) (|HasCategory| |#1| (QUOTE (-157))) (-3844 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-514)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1085)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-708)) (|devaluate| |#1|))))) (|HasCategory| (-708) (QUOTE (-1026))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-708))))) (|HasSignature| |#1| (LIST (QUOTE -2217) (LIST (|devaluate| |#1|) (QUOTE (-1085)))))) (|HasCategory| |#1| (QUOTE (-338))) (-3844 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-522)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -382) (QUOTE (-522))))) (|HasSignature| |#1| (LIST (QUOTE -2611) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1085))))) (|HasSignature| |#1| (LIST (QUOTE -3533) (LIST (LIST (QUOTE -588) (QUOTE (-1085))) (|devaluate| |#1|))))))) (-1159 |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 -(-1160 -4055 UP L UTS) +(-1160 -4102 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 (-514)))) (-1161) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) -((-2047 . T)) +((-2088 . T)) NIL (-1162 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4586,7 +4586,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1164 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4239 . T) (-4238 . T) (-2047 . T)) +((-4239 . T) (-4238 . T) (-2088 . T)) NIL (-1165 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4595,7 +4595,7 @@ NIL (-1166 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3708 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3708 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-498)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-522) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014))) (-3844 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-971))) (-12 (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-971)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))) (-3844 (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-792)))))) (-1167) ((|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 @@ -4628,7 +4628,7 @@ 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 -(-1175 K R UP -4055) +(-1175 K R UP -4102) ((|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 @@ -4656,11 +4656,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4231 |has| |#2| (-6 -4231)) (-4233 . T) (-4232 . T) (-4235 . T)) NIL -(-1182 S -4055) +(-1182 S -4102) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-343))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135)))) -(-1183 -4055) +(-1183 -4102) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4230 . T) (-4236 . T) (-4231 . T) ((-4240 "*") . T) (-4232 . T) (-4233 . T) (-4235 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 9583d92d..d48ed6f3 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(142485 . 3409939483) -(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(142485 . 3410359543) +(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (((|#2| |#2|) . T)) ((((-522)) . T)) -((($ $) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((|#2| |#2|) . T) ((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522))))) +((($ $) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((|#2| |#2|) . T) ((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#2|) . T)) -((($) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((|#2|) . T) (((-382 (-522))) |has| |#2| (-37 (-382 (-522))))) +((($) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((|#2|) . T) (((-382 (-522))) |has| |#2| (-37 (-382 (-522))))) (|has| |#1| (-838)) ((((-792)) . T)) ((((-792)) . T)) @@ -23,28 +23,28 @@ ((((-202)) . T) (((-792)) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1|) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-782))) -((($ $) . T) ((#0=(-382 (-522)) #0#) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1| |#1|) . T)) -(-3708 (|has| |#1| (-757)) (|has| |#1| (-784))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-782))) +((($ $) . T) ((#0=(-382 (-522)) #0#) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1| |#1|) . T)) +(-3844 (|has| |#1| (-757)) (|has| |#1| (-784))) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) ((((-792)) . T)) ((((-792)) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (|has| |#1| (-782)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +((($) . T) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) ((((-792)) . T)) ((((-792)) |has| |#1| (-1014))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . T) (((-522)) |has| |#1| (-962 (-522))) (((-382 (-522))) |has| |#1| (-962 (-382 (-522))))) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) -(((|#2| (-455 (-3480 |#1|) (-708))) . T)) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(((|#2| (-455 (-3591 |#1|) (-708))) . T)) (((|#1| (-494 (-1085))) . T)) (((#0=(-799 |#1|) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (|has| |#4| (-343)) (|has| |#3| (-343)) (((|#1|) . T)) @@ -54,10 +54,10 @@ (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-514)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) ((($) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) ((($) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) . T)) ((($) . T)) @@ -66,59 +66,59 @@ ((((-792)) . T)) ((((-792)) . T)) ((((-382 (-522))) . T) (($) . T)) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) (($) . T) ((|#1|) . T)) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) (($) . T) ((|#1|) . T)) ((((-792)) . T)) ((((-792)) . T)) ((((-792)) . T)) (((|#1|) . T)) -(((|#1|) . T) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) . T)) +(((|#1|) . T) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) . T)) (((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) (($) . T)) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1| |#2|) . T)) ((((-792)) . T)) (((|#1|) . T)) -(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3708 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3844 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) (((|#1|) . 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T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) -(-3708 (|has| |#4| (-730)) (|has| |#4| (-782))) -(-3708 (|has| |#4| (-730)) (|has| |#4| (-782))) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#4| (-730)) (|has| |#4| (-782))) +(-3844 (|has| |#4| (-730)) (|has| |#4| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1014)) @@ -132,21 +132,21 @@ ((((-522)) . T)) ((((-522)) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) (((|#1| (-708)) . T)) (|has| |#2| (-730)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) (|has| |#2| (-782)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1068) |#1|) . 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T)) (((|#1|) . T)) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) (((|#1|) . T) (((-522)) |has| |#1| (-584 (-522)))) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (|has| |#1| (-514)) (|has| |#1| (-514)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1|) . T)) (|has| |#1| (-514)) (|has| |#1| (-514)) @@ -218,11 +218,11 @@ (((|#2|) . T) (($) . T) (((-382 (-522))) . T)) (-12 (|has| |#1| (-1014)) (|has| |#2| (-1014))) ((($) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) . 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T) (((-202)) . T) (((-354)) . T) (((-821 (-354))) . T)) ((((-792)) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) (((|#1|) |has| |#1| (-157))) (((|#1| $) |has| |#1| (-262 |#1| |#1|))) ((((-792)) . T)) @@ -256,13 +256,13 @@ (|has| |#1| (-784)) (|has| |#1| (-1014)) (((|#1|) . 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T)) (((|#1| (-898)) . T)) (((#0=(-799 |#1|) $) |has| #0# (-262 #0# #0#))) @@ -271,7 +271,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1061)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (|has| (-1152 |#1| |#2| |#3| |#4|) (-133)) (|has| (-1152 |#1| |#2| |#3| |#4|) (-135)) (|has| |#1| (-133)) @@ -288,20 +288,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-971))) ((((-792)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (((|#1|) . 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T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) +((($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) ((((-792)) . T)) ((((-792)) . T)) (|has| (-1151 |#2| |#3| |#4|) (-135)) @@ -312,16 +312,16 @@ ((((-792)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) (((|#1|) . T)) ((((-522) |#1|) . 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T)) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) (|has| |#3| (-730)) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) (|has| |#3| (-782)) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#2|) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) -(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514)))) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#2|) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) +(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514)))) (((|#2|) . T)) ((((-792)) . T)) ((((-792)) . T)) @@ -652,22 +652,22 @@ (|has| |#1| (-1014)) (((|#2|) . T)) ((((-498)) |has| |#2| (-563 (-498))) (((-821 (-354))) |has| |#2| (-563 (-821 (-354)))) (((-821 (-522))) |has| |#2| (-563 (-821 (-522))))) -(((|#4|) -3708 (|has| |#4| (-157)) (|has| |#4| (-338)))) -(((|#3|) -3708 (|has| |#3| (-157)) (|has| |#3| (-338)))) +(((|#4|) -3844 (|has| |#4| (-157)) (|has| |#4| (-338)))) +(((|#3|) -3844 (|has| |#3| (-157)) (|has| |#3| (-338)))) ((((-792)) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-838))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) ((($ $) . T) ((#0=(-1085) $) |has| |#1| (-210)) ((#0# |#1|) |has| |#1| (-210)) ((#1=(-755 (-1085)) |#1|) . T) ((#1# $) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-838))) ((((-522) |#2|) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -((($) -3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((|#3|) -3708 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-971)))) +((($) -3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((|#3|) -3844 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-971)))) ((((-522) |#1|) . T)) (|has| (-382 |#2|) (-135)) (|has| (-382 |#2|) (-133)) @@ -680,21 +680,21 @@ (|has| |#1| (-514)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (|has| |#1| (-37 (-382 (-522)))) -((((-363) (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-363) (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#2| (-1061)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((|#1|) . T)) ((((-363) (-1068)) . T)) (|has| |#1| (-514)) ((((-112 |#1|)) . T)) ((((-522) |#1|) . T)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (((|#2|) . T)) ((((-792)) . T)) ((((-756 |#1|)) . T)) @@ -707,7 +707,7 @@ (((|#1|) |has| |#1| (-157))) ((((-792)) . T)) ((((-498)) |has| |#1| (-563 (-498)))) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#2|) |has| |#2| (-285 |#2|))) (((#0=(-522) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -717,7 +717,7 @@ (((#0=(-522) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) ((($) . T) (((-522)) . T) (((-382 (-522))) . T)) (|has| |#2| (-343)) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) @@ -728,9 +728,9 @@ ((((-1083 |#1| |#2| |#3|) $) -12 (|has| (-1083 |#1| |#2| |#3|) (-262 (-1083 |#1| |#2| |#3|) (-1083 |#1| |#2| |#3|))) (|has| |#1| (-338))) (($ $) . T)) ((((-792)) . T)) ((((-792)) . T)) -((($) . T) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +((($) . T) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) ((($ $) . T)) ((($ $) . T)) ((((-792)) . T)) @@ -740,12 +740,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) ((((-382 (-522))) . T) (((-522)) . T)) ((((-522) (-132)) . T)) ((((-132)) . T)) (((|#1|) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) ((((-108)) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) ((((-108)) . T)) @@ -753,38 +753,38 @@ ((((-498)) |has| |#1| (-563 (-498))) (((-202)) . #0=(|has| |#1| (-947))) (((-354)) . #0#)) ((((-792)) . T)) (|has| |#1| (-757)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (|has| |#1| (-784)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-514))) (|has| |#1| (-514)) (|has| |#1| (-838)) (((|#1|) . T)) (|has| |#1| (-1014)) ((((-792)) . 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T)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) (-12 (|has| |#1| (-447)) (|has| |#2| (-447))) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) -(-3708 (-12 (|has| |#1| (-447)) (|has| |#2| (-447))) (-12 (|has| |#1| (-664)) (|has| |#2| (-664)))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (-12 (|has| |#1| (-447)) (|has| |#2| (-447))) (-12 (|has| |#1| (-664)) (|has| |#2| (-664)))) (((|#1|) . T)) (|has| |#2| (-730)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (|has| |#2| (-782)) @@ -799,7 +799,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-382 (-522))) . T) (($) . T)) -((($) . T) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) . T)) +((($) . T) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) . T)) (|has| |#1| (-765)) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) (|has| |#1| (-1014)) @@ -810,8 +810,8 @@ (((|#3|) |has| |#3| (-1014))) (|has| |#3| (-343)) (((|#1|) . T) (((-792)) . T)) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) -(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514)))) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) +(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514)))) ((((-792)) . T)) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#2|) . T)) @@ -821,30 +821,30 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-157))) ((((-382 (-522))) . T) (((-522)) . T)) -((($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-514))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-514))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-514))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-514))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) ((((-132)) . T)) (((|#1|) . T)) ((((-132)) . T)) -((($) -3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971)))) +((($) -3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971)))) ((((-132)) . T)) (((|#1| |#2| |#3|) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) (|has| $ (-135)) (|has| $ (-135)) (|has| |#1| (-1014)) ((((-792)) . T)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-447)) (|has| |#1| (-514)) (|has| |#1| (-971)) (|has| |#1| (-1026))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-447)) (|has| |#1| (-514)) (|has| |#1| (-971)) (|has| |#1| (-1026))) ((($ $) |has| |#1| (-262 $ $)) ((|#1| $) |has| |#1| (-262 |#1| |#1|))) (((|#1| (-382 (-522))) . T)) (((|#1|) . T)) ((((-1085)) . T)) (|has| |#1| (-514)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (|has| |#1| (-514)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) @@ -855,7 +855,7 @@ (|has| |#1| (-135)) (|has| |#1| (-133)) (|has| |#4| (-782)) -(((|#2| (-217 (-3480 |#1|) (-708)) (-794 |#1|)) . T)) +(((|#2| (-217 (-3591 |#1|) (-708)) (-794 |#1|)) . T)) (|has| |#3| (-782)) (((|#1| (-494 |#3|) |#3|) . T)) (|has| |#1| (-135)) @@ -869,21 +869,21 @@ (|has| |#1| (-133)) ((((-382 (-522))) |has| |#2| (-338)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-324)) (|has| |#1| (-343))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-324)) (|has| |#1| (-343))) ((((-1052 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-157)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-210)) (|has| |#2| (-971))) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) ((((-792)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-637)) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) (|has| |#1| (-514)) (((|#1|) . T)) (((|#1|) . T)) @@ -905,10 +905,10 @@ (((|#1| (-382 (-522))) . T)) (((|#3|) . T) (((-561 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) (((#0=(-1083 |#1| |#2| |#3|) #0#) -12 (|has| (-1083 |#1| |#2| |#3|) (-285 (-1083 |#1| |#2| |#3|))) (|has| |#1| (-338))) (((-1085) #0#) -12 (|has| (-1083 |#1| |#2| |#3|) (-483 (-1085) (-1083 |#1| |#2| |#3|))) (|has| |#1| (-338)))) @@ -916,8 +916,8 @@ ((((-792)) . T)) ((((-792)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) -(((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) (((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) |has| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (-285 (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))))) +(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) +(((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) (((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) |has| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (-285 (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))))) ((((-792)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -928,10 +928,10 @@ ((($ $) . T) ((#0=(-794 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-765)) (|has| |#1| (-1014)) -(((|#2| |#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($ $) |has| |#2| (-157))) -(((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)))) -((((-522) (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($) |has| |#2| (-157))) +(((|#2| |#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($ $) |has| |#2| (-157))) +(((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)))) +((((-522) (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($) |has| |#2| (-157))) ((((-708)) . T)) ((((-522)) . T)) (|has| |#1| (-514)) @@ -944,29 +944,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . 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T)) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (-12 (|has| |#3| (-210)) (|has| |#3| (-971))) (|has| |#2| (-1061)) -(((#0=(-51)) . T) (((-2 (|:| -2530 (-1085)) (|:| -3048 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2644 (-1085)) (|:| -3149 #0#))) . T)) (((|#1| |#2|) . T)) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) (((|#1| (-522) (-999)) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1| (-382 (-522)) (-999)) . T)) -((($) -3708 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324)) (|has| |#1| (-514))) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +((($) -3844 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324)) (|has| |#1| (-514))) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) ((((-522) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -974,37 +974,37 @@ (-12 (|has| |#1| (-343)) (|has| |#2| (-343))) ((((-792)) . T)) ((((-1085) |#1|) |has| |#1| (-483 (-1085) |#1|)) ((|#1| |#1|) |has| |#1| (-285 |#1|))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-285 |#1|))) (|has| |#1| (-343)) @@ -1012,31 +1012,31 @@ (|has| |#1| (-343)) ((((-1085) $) |has| |#1| (-483 (-1085) $)) (($ $) |has| |#1| (-285 $)) ((|#1| |#1|) |has| |#1| (-285 |#1|)) (((-1085) |#1|) |has| |#1| (-483 (-1085) |#1|))) ((((-1085)) |has| |#1| (-829 (-1085)))) -(-3708 (-12 (|has| |#1| (-210)) (|has| |#1| (-338))) (|has| |#1| (-324))) +(-3844 (-12 (|has| |#1| (-210)) (|has| |#1| (-338))) (|has| |#1| (-324))) ((((-363) (-1032)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-363) |#1|) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-1014)) ((((-792)) . T)) ((((-792)) . T)) ((((-839 |#1|)) . T)) -((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) -((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) |has| |#1| (-157)) (($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838)))) +((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) |has| |#1| (-157)) (($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-799 |#1|)) |has| #0# (-285 #0#))) (((|#1| |#2|) . T)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) (-12 (|has| |#1| (-730)) (|has| |#2| (-730))) (((|#1|) . T)) (-12 (|has| |#1| (-730)) (|has| |#2| (-730))) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (|has| |#1| (-1106)) (((#0=(-522) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) ((((-382 (-522))) . T) (($) . T)) @@ -1047,8 +1047,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-382 (-522)) #0#) . T)) (|has| |#1| (-338)) ((((-522)) . T) (((-382 (-522))) . T) (($) . T)) -((($ $) . T) ((#0=(-382 (-522)) #0#) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1| |#1|) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((($ $) . T) ((#0=(-382 (-522)) #0#) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1| |#1|) . T)) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#1|) . T) (($) . T) (((-382 (-522))) . T)) ((((-792)) . T)) ((((-792)) . T)) @@ -1063,14 +1063,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-782)) (|has| |#1| (-782)) -((($) . T) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-514))) -(((#0=(-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) #0#) |has| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))))) +((($) . T) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-514))) +(((#0=(-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) #0#) |has| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))))) ((($) . T)) (|has| |#2| (-784)) ((($) . T)) (((|#2|) |has| |#2| (-1014))) -((((-792)) -3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-562 (-792))) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((-1166 |#2|)) . T)) +((((-792)) -3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-562 (-792))) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((-1166 |#2|)) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) ((((-1068) (-51)) . T)) @@ -1078,10 +1078,10 @@ ((((-792)) . T)) ((((-522)) |has| #0=(-382 |#2|) (-584 (-522))) ((#0#) . T)) ((((-522) (-132)) . T)) -((((-522) (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T) ((|#1| |#2|) . T)) +((((-522) (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T) ((|#1| |#2|) . T)) ((((-382 (-522))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-792)) . T)) ((((-839 |#1|)) . T)) (|has| |#1| (-338)) @@ -1106,31 +1106,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-157))) -((((-522) (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T) ((|#1| |#2|) . T)) +((((-522) (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-157))) -((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) |has| |#1| (-157)) (($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838)))) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) |has| |#1| (-157)) (($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838)))) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#1|) . T)) (((|#1|) . T)) ((((-498)) |has| |#1| (-563 (-498))) (((-821 (-354))) |has| |#1| (-563 (-821 (-354)))) (((-821 (-522))) |has| |#1| (-563 (-821 (-522))))) ((((-792)) . T)) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (|has| |#2| (-782)) (-12 (|has| |#2| (-210)) (|has| |#2| (-971))) (|has| |#1| (-514)) (|has| |#1| (-1061)) ((((-1068) |#1|) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) -(((#0=(-382 (-522)) #0#) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#1| |#1|) . T)) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(((#0=(-382 (-522)) #0#) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#1| |#1|) . T)) ((((-382 (-522))) |has| |#1| (-962 (-522))) (((-522)) |has| |#1| (-962 (-522))) (((-1085)) |has| |#1| (-962 (-1085))) ((|#1|) . T)) ((((-522) |#2|) . T)) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) ((((-522)) |has| |#1| (-815 (-522))) (((-354)) |has| |#1| (-815 (-354)))) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#1|) . T)) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) ((|#1|) . T)) (((|#1|) . T)) ((((-588 |#4|)) . T) (((-792)) . T)) ((((-498)) |has| |#4| (-563 (-498)))) @@ -1143,17 +1143,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1085)) |has| (-382 |#2|) (-829 (-1085)))) -(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-792)) -3708 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-562 (-792))) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) (((-1166 |#3|)) . T)) +((((-792)) -3844 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-562 (-792))) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) (((-1166 |#3|)) . T)) ((((-522) |#2|) . T)) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) -(((|#2| |#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($ $) |has| |#2| (-157))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(((|#2| |#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($ $) |has| |#2| (-157))) ((((-792)) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T) ((|#2|) . T)) ((((-792)) . T)) ((((-792)) . T)) ((((-1068) (-1085) (-522) (-202) (-792)) . T)) @@ -1188,8 +1188,8 @@ (|has| |#1| (-37 (-382 (-522)))) ((((-792)) . T)) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) -(((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($) |has| |#2| (-157))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +(((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-971))) (($) |has| |#2| (-157))) (|has| $ (-135)) ((((-382 |#2|)) . T)) ((((-382 (-522))) |has| #0=(-382 |#2|) (-962 (-382 (-522)))) (((-522)) |has| #0# (-962 (-522))) ((#0#) . T)) @@ -1200,11 +1200,11 @@ (((|#3|) |has| |#3| (-157))) (|has| |#1| (-135)) (|has| |#1| (-133)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) (((|#1|) . T)) (((|#2|) . T)) @@ -1235,7 +1235,7 @@ ((((-925 |#1|)) . T) ((|#1|) . T)) ((((-792)) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-382 (-522))) . T) (((-382 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1081 |#1|)) . T)) ((((-522)) . T) (($) . T) (((-382 (-522))) . T)) @@ -1243,9 +1243,9 @@ (|has| |#1| (-784)) (((|#2|) . T)) ((((-522)) . T) (($) . T) (((-382 (-522))) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) ((((-522) |#2|) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#2|) . T)) ((((-522) |#3|) . T)) (((|#2|) . T)) @@ -1260,7 +1260,7 @@ (((|#3|) -12 (|has| |#3| (-285 |#3|)) (|has| |#3| (-1014)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-338)) (((|#2|) . T) (((-522)) |has| |#2| (-962 (-522))) (((-382 (-522))) |has| |#2| (-962 (-382 (-522))))) @@ -1290,19 +1290,19 @@ (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1| |#2|) . T)) ((((-522) (-132)) . T)) -(((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) -((($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +(((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) +((($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (|has| |#1| (-784)) (((|#2| (-708) (-999)) . T)) (((|#1| |#2|) . T)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-514))) (|has| |#1| (-728)) (((|#1|) |has| |#1| (-157))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3708 (|has| |#1| (-135)) (-12 (|has| |#1| (-338)) (|has| |#2| (-135)))) -(-3708 (|has| |#1| (-133)) (-12 (|has| |#1| (-338)) (|has| |#2| (-133)))) +(-3844 (|has| |#1| (-135)) (-12 (|has| |#1| (-338)) (|has| |#2| (-135)))) +(-3844 (|has| |#1| (-133)) (-12 (|has| |#1| (-338)) (|has| |#2| (-133)))) (((|#4|) . T)) (|has| |#1| (-133)) ((((-1068) |#1|) . T)) @@ -1315,10 +1315,10 @@ (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#3|) . T)) ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1|) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014))) (((-886 |#1|)) . T)) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014))) (((-886 |#1|)) . T)) (|has| |#1| (-782)) (|has| |#1| (-782)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) @@ -1331,8 +1331,8 @@ ((($) . T)) ((((-363) (-1068)) . T)) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) -((((-792)) -3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-562 (-792))) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((-1166 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2530 (-1068)) (|:| -3048 #0#))) . T)) +((((-792)) -3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-562 (-792))) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((-1166 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2644 (-1068)) (|:| -3149 #0#))) . T)) (((|#1|) . T)) ((((-792)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) @@ -1340,7 +1340,7 @@ (|has| |#2| (-133)) (|has| |#2| (-135)) (|has| |#1| (-447)) -(-3708 (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) (|has| |#1| (-338)) ((((-792)) . T)) (|has| |#1| (-37 (-382 (-522)))) @@ -1349,8 +1349,8 @@ (|has| |#1| (-782)) (|has| |#1| (-782)) ((((-792)) . T)) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) -(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514)))) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1158 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) +(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514)))) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#1| |#2|) . T)) ((((-1085)) |has| |#1| (-829 (-1085)))) @@ -1358,7 +1358,7 @@ ((((-792)) . T)) ((((-792)) . T)) (|has| |#1| (-1014)) -(((|#2| (-455 (-3480 |#1|) (-708)) (-794 |#1|)) . T)) +(((|#2| (-455 (-3591 |#1|) (-708)) (-794 |#1|)) . T)) ((((-382 (-522))) . #0=(|has| |#2| (-338))) (($) . #0#)) (((|#1| (-494 (-1085)) (-1085)) . T)) (((|#1|) . T)) @@ -1378,16 +1378,16 @@ (|has| |#1| (-135)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) ((((-1083 |#1| |#2| |#3|)) |has| |#1| (-338))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-1085) (-51)) . T)) ((($ $) . T)) (((|#1| (-522)) . T)) ((((-839 |#1|)) . T)) -(((|#1|) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971))) (($) -3708 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)))) +(((|#1|) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971))) (($) -3844 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)))) (((|#1|) . T) (((-522)) |has| |#1| (-962 (-522))) (((-382 (-522))) |has| |#1| (-962 (-382 (-522))))) (|has| |#1| (-784)) (|has| |#1| (-784)) @@ -1402,13 +1402,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) (((|#1|) |has| |#1| (-157))) (((|#4| |#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) -(((|#3|) -3708 (|has| |#3| (-157)) (|has| |#3| (-338)))) +(((|#3|) -3844 (|has| |#3| (-157)) (|has| |#3| (-338)))) (|has| |#2| (-784)) (|has| |#1| (-784)) -(-3708 (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-838))) +(-3844 (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-838))) ((($ $) . T) ((#0=(-382 (-522)) #0#) . T)) ((((-522) |#2|) . T)) -(((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)))) +(((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)))) (|has| |#1| (-324)) (((|#3| |#3|) -12 (|has| |#3| (-285 |#3|)) (|has| |#3| (-1014)))) ((($) . T) (((-382 (-522))) . T)) @@ -1416,7 +1416,7 @@ (|has| |#1| (-757)) (|has| |#1| (-757)) (((|#1|) . T)) -(-3708 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-782)) (|has| |#1| (-782)) (|has| |#1| (-782)) @@ -1425,13 +1425,13 @@ ((((-522)) . T) (($) . T) (((-382 (-522))) . T)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-37 (-382 (-522)))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-1085)) |has| |#1| (-829 (-1085))) (((-999)) . T)) (((|#1|) . T)) (|has| |#1| (-782)) -(((#0=(-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) #0#) |has| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))))) +(((#0=(-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) #0#) |has| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (|has| |#1| (-1014)) (((|#1|) . T)) @@ -1449,7 +1449,7 @@ (((|#1|) . T)) ((((-132)) . T)) (((|#2|) |has| |#2| (-157))) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((|#1|) . T)) (|has| |#1| (-133)) (|has| |#1| (-135)) @@ -1471,32 +1471,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) ((#0=(-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) #0#) |has| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (-285 (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))))) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-838))) +(((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) ((#0=(-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) #0#) |has| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (-285 (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-838))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3708 (|has| |#3| (-157)) (|has| |#3| (-338)))) +(((|#3|) -3844 (|has| |#3| (-157)) (|has| |#3| (-338)))) (|has| |#1| (-784)) (|has| |#1| (-514)) ((((-535 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3708 (-12 (|has| |#1| (-338)) (|has| |#2| (-757))) (-12 (|has| |#1| (-338)) (|has| |#2| (-784)))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (-12 (|has| |#1| (-338)) (|has| |#2| (-757))) (-12 (|has| |#1| (-338)) (|has| |#2| (-784)))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) ((((-839 |#1|)) . T)) (((|#1| (-466 |#1| |#3|) (-466 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-708)) . T)) ((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) |has| |#1| (-157)) (($) |has| |#1| (-514))) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1083 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) -(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514)))) +((((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-1083 |#1| |#2| |#3|)) |has| |#1| (-338)) ((|#1|) |has| |#1| (-157))) +(((|#1|) |has| |#1| (-157)) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) (($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514)))) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) ((((-382 |#2|)) . T) (((-382 (-522))) . T) (($) . T)) ((((-613 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1504,17 +1504,17 @@ ((((-792)) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) ((((-792)) . T)) -((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) ((((-792)) . T)) ((((-792)) . T)) ((((-792)) . T)) (((|#2|) . T)) -(-3708 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) (|has| |#1| (-1106)) (|has| |#1| (-1106)) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (|has| |#1| (-1106)) (|has| |#1| (-1106)) (((|#3| |#3|) . T)) @@ -1527,43 +1527,43 @@ (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) ((((-1068) (-51)) . T)) (|has| |#1| (-1014)) -(-3708 (|has| |#2| (-757)) (|has| |#2| (-784))) +(-3844 (|has| |#2| (-757)) (|has| |#2| (-784))) (((|#1|) . T)) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) (((|#1|) |has| |#1| (-157)) (($) . T)) ((($) . T)) ((((-1083 |#1| |#2| |#3|)) -12 (|has| (-1083 |#1| |#2| |#3|) (-285 (-1083 |#1| |#2| |#3|))) (|has| |#1| (-338)))) ((((-792)) . T)) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((($) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) ((((-792)) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-838))) (|has| |#2| (-838)) (|has| |#1| (-338)) (((|#2|) |has| |#2| (-1014))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((($) . T) ((|#2|) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) (|has| |#1| (-838)) (|has| |#1| (-838)) ((((-498)) . T) (((-382 (-1081 (-522)))) . T) (((-202)) . T) (((-354)) . T)) ((((-354)) . T) (((-202)) . T) (((-792)) . T)) (|has| |#1| (-838)) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) ((($ $) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((($ $) . T)) ((((-522) (-108)) . T)) ((($) . T)) (((|#1|) . T)) ((((-522)) . T)) ((((-108)) . T)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-514))) (|has| |#1| (-37 (-382 (-522)))) (((|#1| (-522)) . T)) ((($) . T)) @@ -1585,7 +1585,7 @@ (((|#1| (-1130 |#1| |#2| |#3|)) . T)) (((|#1| (-708)) . T)) (((|#1|) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-792)) . T)) (|has| |#1| (-1014)) ((((-1068) |#1|) . T)) @@ -1605,18 +1605,18 @@ (((|#1|) . T)) ((((-522)) . T)) ((((-792)) . T)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-324))) ((((-792)) . T)) (|has| |#1| (-135)) (((|#3|) . T)) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((((-792)) . T)) ((((-1151 |#2| |#3| |#4|)) . T) (((-1152 |#1| |#2| |#3| |#4|)) . T)) ((((-792)) . T)) -((((-47)) -12 (|has| |#1| (-514)) (|has| |#1| (-962 (-522)))) (((-561 $)) . T) ((|#1|) . T) (((-522)) |has| |#1| (-962 (-522))) (((-382 (-522))) -3708 (-12 (|has| |#1| (-514)) (|has| |#1| (-962 (-522)))) (|has| |#1| (-962 (-382 (-522))))) (((-382 (-881 |#1|))) |has| |#1| (-514)) (((-881 |#1|)) |has| |#1| (-971)) (((-1085)) . T)) +((((-47)) -12 (|has| |#1| (-514)) (|has| |#1| (-962 (-522)))) (((-561 $)) . T) ((|#1|) . T) (((-522)) |has| |#1| (-962 (-522))) (((-382 (-522))) -3844 (-12 (|has| |#1| (-514)) (|has| |#1| (-962 (-522)))) (|has| |#1| (-962 (-382 (-522))))) (((-382 (-881 |#1|))) |has| |#1| (-514)) (((-881 |#1|)) |has| |#1| (-971)) (((-1085)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-708)) . T)) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) |has| |#1| (-157))) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-285 |#1|))) ((((-1152 |#1| |#2| |#3| |#4|)) . T)) ((((-522)) |has| |#1| (-815 (-522))) (((-354)) |has| |#1| (-815 (-354)))) @@ -1624,14 +1624,14 @@ (|has| |#1| (-514)) (((|#1|) . T)) ((((-792)) . T)) -(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (((|#1|) |has| |#1| (-157))) ((($) |has| |#1| (-514)) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1014))) -(((|#2|) -3708 (|has| |#2| (-157)) (|has| |#2| (-338)))) +(((|#2|) -3844 (|has| |#2| (-157)) (|has| |#2| (-338)))) ((((-1151 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-757)) @@ -1641,8 +1641,8 @@ (|has| |#1| (-782)) (|has| |#1| (-782)) (((|#1| (-522) (-999)) . T)) -(-3708 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +(-3844 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1| (-382 (-522)) (-999)) . T)) (((|#1| (-708) (-999)) . T)) (|has| |#1| (-784)) @@ -1658,28 +1658,28 @@ (((|#1|) . T)) (|has| |#1| (-1014)) ((((-522)) -12 (|has| |#1| (-338)) (|has| |#2| (-584 (-522)))) ((|#2|) |has| |#1| (-338))) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((|#2|) |has| |#2| (-157))) (((|#1|) |has| |#1| (-157))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) ((((-792)) . T)) (|has| |#3| (-782)) ((((-792)) . T)) ((((-1151 |#2| |#3| |#4|) (-294 |#2| |#3| |#4|)) . T)) ((((-792)) . T)) -(((|#1| |#1|) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971)))) +(((|#1| |#1|) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971)))) (((|#1|) . T)) ((((-522)) . T)) ((((-522)) . T)) -(((|#1|) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971)))) +(((|#1|) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-971)))) (((|#2|) |has| |#2| (-338))) ((($) . T) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-338))) (|has| |#1| (-784)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) |has| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-838))) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) |has| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-838))) (((|#2|) . T) (((-522)) |has| |#2| (-584 (-522)))) ((((-792)) . T)) ((((-792)) . T)) @@ -1713,18 +1713,18 @@ (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) (((|#1|) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) (((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) . T) (($ $) . T)) ((((-792)) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (|has| |#1| (-338)) (|has| |#1| (-338)) (|has| (-382 |#2|) (-210)) (|has| |#1| (-838)) (((|#2|) |has| |#2| (-971))) -(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (|has| |#1| (-338)) (((|#1|) |has| |#1| (-157))) (((|#1| |#1|) . T)) @@ -1749,7 +1749,7 @@ (((|#1| (-382 (-522)) (-999)) . T)) (((|#1| (-708) (-999)) . T)) (((#0=(-382 |#2|) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-522)) -3708 (|has| (-382 (-522)) (-962 (-522))) (|has| |#1| (-962 (-522)))) (((-382 (-522))) . T)) +(((|#1|) . T) (((-522)) -3844 (|has| (-382 (-522)) (-962 (-522))) (|has| |#1| (-962 (-522)))) (((-382 (-522))) . T)) (((|#1| (-553 |#1| |#3|) (-553 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) @@ -1768,24 +1768,24 @@ ((((-637)) . T)) (((|#2|) |has| |#2| (-157))) (|has| |#2| (-782)) -((((-108)) |has| |#1| (-1014)) (((-792)) -3708 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014)))) +((((-108)) |has| |#1| (-1014)) (((-792)) -3844 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))) . T)) ((((-792)) . T)) ((((-522) |#1|) . T)) ((((-637)) . T) (((-382 (-522))) . T) (((-522)) . T)) (((|#1| |#1|) |has| |#1| (-157))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) ((((-354)) . T)) ((((-637)) . T)) ((((-382 (-522))) . #0=(|has| |#2| (-338))) (($) . #0#)) (((|#1|) |has| |#1| (-157))) ((((-382 (-881 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (((|#2|) . T)) (|has| |#2| (-784)) (((|#3|) |has| |#3| (-971))) @@ -1795,14 +1795,14 @@ (|has| |#1| (-784)) ((((-1085)) |has| |#2| (-829 (-1085)))) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-382 (-522))) . T) (($) . T)) (|has| |#1| (-447)) (|has| |#1| (-343)) (|has| |#1| (-343)) (|has| |#1| (-343)) (|has| |#1| (-338)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-447)) (|has| |#1| (-514)) (|has| |#1| (-971)) (|has| |#1| (-1026))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-447)) (|has| |#1| (-514)) (|has| |#1| (-971)) (|has| |#1| (-1026))) (|has| |#1| (-37 (-382 (-522)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1823,11 +1823,11 @@ (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-784)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-135)) (|has| |#1| (-133)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)))) ((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)))) ((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1845,11 +1845,11 @@ ((((-498)) |has| |#1| (-563 (-498))) (((-821 (-522))) |has| |#1| (-563 (-821 (-522)))) (((-821 (-354))) |has| |#1| (-563 (-821 (-354)))) (((-354)) . #0=(|has| |#1| (-947))) (((-202)) . #0#)) (((|#1|) |has| |#1| (-338))) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((($ $) . T) (((-561 $) $) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) ((($) . T) (((-1152 |#1| |#2| |#3| |#4|)) . T) (((-382 (-522))) . T)) -((($) -3708 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-514))) +((($) -3844 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-514))) (|has| |#1| (-338)) (|has| |#1| (-338)) (|has| |#1| (-338)) @@ -1860,11 +1860,11 @@ ((((-354)) . T)) (((|#3|) -12 (|has| |#3| (-285 |#3|)) (|has| |#3| (-1014)))) ((((-792)) . T)) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-838))) (((|#1|) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) (((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (|has| |#1| (-1014)) @@ -1873,13 +1873,13 @@ (|has| |#1| (-133)) (|has| |#1| (-135)) ((((-522)) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((#0=(-1151 |#2| |#3| |#4|)) . T) (((-382 (-522))) |has| #0# (-37 (-382 (-522)))) (($) . T)) ((((-522)) . T)) (|has| |#1| (-338)) -(-3708 (-12 (|has| (-1158 |#1| |#2| |#3|) (-135)) (|has| |#1| (-338))) (|has| |#1| (-135))) -(-3708 (-12 (|has| (-1158 |#1| |#2| |#3|) (-133)) (|has| |#1| (-338))) (|has| |#1| (-133))) +(-3844 (-12 (|has| (-1158 |#1| |#2| |#3|) (-135)) (|has| |#1| (-338))) (|has| |#1| (-135))) +(-3844 (-12 (|has| (-1158 |#1| |#2| |#3|) (-133)) (|has| |#1| (-338))) (|has| |#1| (-133))) (|has| |#1| (-338)) (|has| |#1| (-133)) (|has| |#1| (-135)) @@ -1896,18 +1896,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-522)) |has| |#1| (-584 (-522)))) (((|#3|) |has| |#3| (-157))) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) ((((-522)) . T)) (((|#1| $) |has| |#1| (-262 |#1| |#1|))) ((((-382 (-522))) . T) (($) . T) (((-382 |#1|)) . T) ((|#1|) . T)) ((((-792)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3708 (|has| |#1| (-266)) (|has| |#1| (-338))) ((#0=(-382 (-522)) #0#) |has| |#1| (-338))) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3844 (|has| |#1| (-266)) (|has| |#1| (-338))) ((#0=(-382 (-522)) #0#) |has| |#1| (-338))) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) ((($) . T)) ((((-522) |#1|) . T)) ((((-1085)) |has| (-382 |#2|) (-829 (-1085)))) -(((|#1|) . T) (($) -3708 (|has| |#1| (-266)) (|has| |#1| (-338))) (((-382 (-522))) |has| |#1| (-338))) +(((|#1|) . T) (($) -3844 (|has| |#1| (-266)) (|has| |#1| (-338))) (((-382 (-522))) |has| |#1| (-338))) ((((-498)) |has| |#2| (-563 (-498)))) ((((-628 |#2|)) . T) (((-792)) . T)) (((|#1|) . T)) @@ -1915,8 +1915,8 @@ (((|#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) ((((-799 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -(-3708 (|has| |#4| (-730)) (|has| |#4| (-782))) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#4| (-730)) (|has| |#4| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) ((((-792)) . T)) ((((-792)) . T)) (((|#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) @@ -1932,17 +1932,17 @@ ((((-382 (-522))) . T) (($) . T)) ((((-382 (-522))) . T) (($) . T)) ((((-382 (-522))) . T) (($) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-1124))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-1124))) ((($) . T)) ((((-382 (-522))) |has| #0=(-382 |#2|) (-962 (-382 (-522)))) (((-522)) |has| #0# (-962 (-522))) ((#0#) . T)) (((|#2|) . T) (((-522)) |has| |#2| (-584 (-522)))) (((|#1| (-708)) . T)) (|has| |#1| (-784)) (((|#1|) . T) (((-522)) |has| |#1| (-584 (-522)))) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) (((-382 (-522))) -3708 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (((-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((|#1|) . T)) ((((-522)) . T)) (|has| |#1| (-37 (-382 (-522)))) -((((-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))) |has| (-2 (|:| -2530 (-1068)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))))) +((((-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))) |has| (-2 (|:| -2644 (-1068)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))))) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (|has| |#1| (-782)) (|has| |#1| (-37 (-382 (-522)))) @@ -1967,24 +1967,24 @@ (((|#1| |#2|) . T)) ((((-132)) . T)) ((((-717 |#1| (-794 |#2|))) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (|has| |#1| (-1106)) (((|#1|) . T)) -(-3708 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) +(-3844 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-343)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971)) (|has| |#3| (-1014))) ((((-1085) |#1|) |has| |#1| (-483 (-1085) |#1|))) (((|#2|) . T)) -((($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) ((((-839 |#1|)) . T)) ((($) . T)) ((((-382 (-881 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) ((((-498)) |has| |#4| (-563 (-498)))) ((((-792)) . T) (((-588 |#4|)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-782)) -(((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) (((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) |has| (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|)) (-285 (-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))))) +(((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014))) (((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) |has| (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|)) (-285 (-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))))) (|has| |#1| (-1014)) (|has| |#1| (-338)) (|has| |#1| (-784)) @@ -1992,16 +1992,16 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-382 (-522))) . T)) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) |has| |#1| (-157))) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) |has| |#1| (-157))) (|has| |#1| (-133)) (|has| |#1| (-135)) -(-3708 (-12 (|has| (-1083 |#1| |#2| |#3|) (-135)) (|has| |#1| (-338))) (|has| |#1| (-135))) -(-3708 (-12 (|has| (-1083 |#1| |#2| |#3|) (-133)) (|has| |#1| (-338))) (|has| |#1| (-133))) +(-3844 (-12 (|has| (-1083 |#1| |#2| |#3|) (-135)) (|has| |#1| (-338))) (|has| |#1| (-135))) +(-3844 (-12 (|has| (-1083 |#1| |#2| |#3|) (-133)) (|has| |#1| (-338))) (|has| |#1| (-133))) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-135)) (|has| |#1| (-133)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) (|has| |#1| (-782)) (((|#1| |#2|) . T)) @@ -2024,9 +2024,9 @@ ((((-792)) . T)) ((((-792)) . T)) ((((-498)) |has| |#1| (-563 (-498)))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-1085) |#1|) |has| |#1| (-483 (-1085) |#1|)) ((|#1| |#1|) |has| |#1| (-285 |#1|))) -(((|#1|) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)))) +(((|#1|) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)))) ((((-291 |#1|)) . T)) (((|#2|) |has| |#2| (-338))) (((|#2|) . T)) @@ -2047,14 +2047,14 @@ (|has| |#1| (-133)) (|has| |#1| (-135)) ((($ $) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014))) (|has| |#1| (-514)) (((|#2|) . T)) ((((-522)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) ((((-535 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2079,12 +2079,12 @@ (((|#1| |#2|) . T)) ((((-1085) |#1|) . T)) (((|#4|) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) ((((-1085) (-51)) . T)) ((((-1151 |#2| |#3| |#4|) (-294 |#2| |#3| |#4|)) . T)) ((((-382 (-522))) |has| |#1| (-962 (-382 (-522)))) (((-522)) |has| |#1| (-962 (-522))) ((|#1|) . T)) ((((-792)) . T)) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-343)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971)) (|has| |#2| (-1014))) (((#0=(-1152 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-382 (-522)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-157)) ((#0=(-382 (-522)) #0#) |has| |#1| (-514)) (($ $) |has| |#1| (-514))) (((|#1|) . T) (($) . T) (((-382 (-522))) . T)) @@ -2103,14 +2103,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (((|#2| |#3|) . T)) -(-3708 (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#2| (-338)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) (((|#1| (-494 |#2|)) . T)) (((|#1| (-708)) . T)) (((|#1| (-494 (-1004 (-1085)))) . T)) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) (|has| |#2| (-838)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) ((((-792)) . T)) ((($ $) . T) ((#0=(-1151 |#2| |#3| |#4|) #0#) . T) ((#1=(-382 (-522)) #1#) |has| #0# (-37 (-382 (-522))))) ((((-839 |#1|)) . T)) @@ -2119,13 +2119,13 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-338)) -(-3708 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324)) (|has| |#1| (-514))) (|has| |#1| (-338)) ((($) . T) ((#0=(-1151 |#2| |#3| |#4|)) . T) (((-382 (-522))) |has| #0# (-37 (-382 (-522))))) (((|#1| |#2|) . T)) ((((-1083 |#1| |#2| |#3|)) |has| |#1| (-338))) -(-3708 (-12 (|has| |#1| (-283)) (|has| |#1| (-838))) (|has| |#1| (-338)) (|has| |#1| (-324))) -(-3708 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) +(-3844 (-12 (|has| |#1| (-283)) (|has| |#1| (-838))) (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-829 (-1085))) (|has| |#1| (-971))) ((((-522)) |has| |#1| (-584 (-522))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-792)) . T)) @@ -2157,27 +2157,27 @@ (((|#1|) |has| |#1| (-157))) ((((-792)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) -(((|#2|) -3708 (|has| |#2| (-6 (-4240 "*"))) (|has| |#2| (-157)))) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(((|#2|) -3844 (|has| |#2| (-6 (-4240 "*"))) (|has| |#2| (-157)))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (|has| |#2| (-784)) (|has| |#2| (-838)) (|has| |#1| (-838)) (((|#2|) |has| |#2| (-157))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) ((((-792)) . T)) ((((-792)) . T)) ((((-498)) . T) (((-522)) . T) (((-821 (-522))) . T) (((-354)) . T) (((-202)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))) . T)) (((|#1|) . T)) ((((-792)) . T)) (((|#1| |#2|) . T)) (((|#1| (-382 (-522))) . T)) (((|#1|) . T)) -(-3708 (|has| |#1| (-266)) (|has| |#1| (-338))) +(-3844 (|has| |#1| (-266)) (|has| |#1| (-338))) ((((-132)) . T)) ((((-382 |#2|)) . T) (((-382 (-522))) . T) (($) . T)) (|has| |#1| (-782)) @@ -2192,7 +2192,7 @@ ((((-382 (-522))) . T) (($) . T)) ((((-792)) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-792)) . T)) ((((-792)) . T)) @@ -2203,7 +2203,7 @@ (((|#1|) . T)) ((((-588 (-132))) . T) (((-1068)) . T)) ((((-792)) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) ((((-1085) |#1|) |has| |#1| (-483 (-1085) |#1|)) ((|#1| |#1|) |has| |#1| (-285 |#1|))) (|has| |#1| (-784)) ((((-792)) . T)) @@ -2215,16 +2215,16 @@ ((((-792)) . T) (((-588 |#4|)) . T)) (((|#2|) . T)) ((((-839 |#1|)) . T) (((-382 (-522))) . T) (($) . T)) -(-3708 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((((-1085) (-51)) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-782)) (|has| |#2| (-971))) (|has| |#1| (-838)) (|has| |#1| (-838)) (((|#2|) . T)) @@ -2239,12 +2239,12 @@ (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (|has| |#1| (-757)) (((#0=(-839 |#1|) #0#) . T) (($ $) . T) ((#1=(-382 (-522)) #1#) . T)) ((((-382 |#2|)) . T)) (|has| |#1| (-782)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) . T) ((#1=(-522) #1#) . T) (($ $) . T)) ((((-839 |#1|)) . T) (($) . T) (((-382 (-522))) . T)) (((|#2|) |has| |#2| (-971)) (((-522)) -12 (|has| |#2| (-584 (-522))) (|has| |#2| (-971)))) @@ -2254,25 +2254,25 @@ (|has| |#1| (-133)) (((|#2|) . T)) ((((-792)) . T)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2530 (-1085)) (|:| -3048 #0#))) . T)) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2644 (-1085)) (|:| -3149 #0#))) . T)) (|has| |#1| (-324)) ((((-522)) . T)) ((((-792)) . T)) (((#0=(-1152 |#1| |#2| |#3| |#4|) $) |has| #0# (-262 #0# #0#))) (|has| |#1| (-338)) (((#0=(-999) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (((#0=(-382 (-522)) #0#) . T) ((#1=(-637) #1#) . T) (($ $) . T)) ((((-291 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-382 (-522))) |has| |#1| (-338))) (|has| |#1| (-1014)) (((|#1|) . T)) -(((|#1|) -3708 (|has| |#2| (-342 |#1|)) (|has| |#2| (-392 |#1|)))) -(((|#1|) -3708 (|has| |#2| (-342 |#1|)) (|has| |#2| (-392 |#1|)))) +(((|#1|) -3844 (|has| |#2| (-342 |#1|)) (|has| |#2| (-392 |#1|)))) +(((|#1|) -3844 (|has| |#2| (-342 |#1|)) (|has| |#2| (-392 |#1|)))) (((|#2|) . T)) ((((-382 (-522))) . T) (((-637)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2291,7 +2291,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-522)) . T)) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) (((|#2|) . T) (((-522)) |has| |#2| (-584 (-522)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2328,7 +2328,7 @@ (|has| |#2| (-947)) ((($) . T)) (|has| |#1| (-838)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2336,24 +2336,24 @@ ((($) . T)) (|has| |#1| (-338)) ((((-839 |#1|)) . T)) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) ((($ $) . T) ((#0=(-382 (-522)) #0#) . T)) -(-3708 (|has| |#1| (-343)) (|has| |#1| (-784))) +(-3844 (|has| |#1| (-343)) (|has| |#1| (-784))) (((|#1|) . T)) ((((-792)) . T)) ((((-1085)) -12 (|has| |#1| (-15 * (|#1| (-382 (-522)) |#1|))) (|has| |#1| (-829 (-1085))))) ((((-382 |#2|) |#3|) . T)) ((($) . T) (((-382 (-522))) . T)) ((((-708) |#1|) . T)) -(((|#2| (-217 (-3480 |#1|) (-708))) . T)) +(((|#2| (-217 (-3591 |#1|) (-708))) . T)) (((|#1| (-494 |#3|)) . T)) ((((-382 (-522))) . T)) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((((-792)) . T)) -(((#0=(-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) #0#) |has| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))))) +(((#0=(-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) #0#) |has| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))))) (|has| |#1| (-838)) (|has| |#2| (-338)) -(-3708 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((((-154 (-354))) . T) (((-202)) . T) (((-354)) . T)) ((((-792)) . T)) (((|#1|) . T)) @@ -2370,11 +2370,11 @@ (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-37 (-382 (-522)))) (-12 (|has| |#1| (-507)) (|has| |#1| (-765))) ((((-792)) . T)) -((((-1085)) -3708 (-12 (|has| |#1| (-15 * (|#1| (-522) |#1|))) (|has| |#1| (-829 (-1085)))) (-12 (|has| |#1| (-338)) (|has| |#2| (-829 (-1085)))))) +((((-1085)) -3844 (-12 (|has| |#1| (-15 * (|#1| (-522) |#1|))) (|has| |#1| (-829 (-1085)))) (-12 (|has| |#1| (-338)) (|has| |#2| (-829 (-1085)))))) (|has| |#1| (-338)) ((((-1085)) -12 (|has| |#1| (-15 * (|#1| (-382 (-522)) |#1|))) (|has| |#1| (-829 (-1085))))) (|has| |#1| (-338)) @@ -2384,7 +2384,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-338))) (((|#2|) |has| |#1| (-338))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) @@ -2407,31 +2407,31 @@ (((|#2|) |has| |#1| (-338))) ((((-354)) -12 (|has| |#1| (-338)) (|has| |#2| (-815 (-354)))) (((-522)) -12 (|has| |#1| (-338)) (|has| |#2| (-815 (-522))))) (|has| |#1| (-338)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (|has| |#1| (-338)) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) (|has| |#1| (-338)) (|has| |#1| (-514)) (((|#4| |#4|) -12 (|has| |#4| (-285 |#4|)) (|has| |#4| (-1014)))) (((|#3|) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) (((|#2|) . T)) (((|#2|) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (|has| |#1| (-37 (-382 (-522)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) ((((-1068) |#1|) . T)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-343))) (|has| |#1| (-135)) ((((-535 |#1|)) . T)) ((($) . T)) @@ -2439,7 +2439,7 @@ (|has| |#1| (-514)) (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-37 (-382 (-522)))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-324))) (|has| |#1| (-135)) ((((-792)) . T)) ((($) . T)) @@ -2464,7 +2464,7 @@ (|has| |#1| (-728)) (|has| |#1| (-728)) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2484,7 +2484,7 @@ ((((-522)) . T)) ((((-792)) . T)) ((((-522)) . T)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) ((((-154 (-354))) . T) (((-202)) . T) (((-354)) . T)) ((((-792)) . T)) ((((-792)) . T)) @@ -2496,9 +2496,9 @@ (((|#1|) . T) (($) . T) (((-382 (-522))) . T)) (|has| |#1| (-338)) (|has| |#1| (-338)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-447)) (|has| |#1| (-664)) (|has| |#1| (-829 (-1085))) (|has| |#1| (-971)) (|has| |#1| (-1026)) (|has| |#1| (-1014))) (|has| |#1| (-1061)) ((((-522) |#1|) . T)) (((|#1|) . T)) @@ -2516,8 +2516,8 @@ (((|#1|) . T)) (|has| |#1| (-514)) ((((-382 |#2|)) . T) (((-382 (-522))) . T) (($) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) ((((-354)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2526,7 +2526,7 @@ (|has| |#1| (-514)) (|has| |#1| (-1014)) ((((-717 |#1| (-794 |#2|))) |has| (-717 |#1| (-794 |#2|)) (-285 (-717 |#1| (-794 |#2|))))) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-838)) @@ -2536,12 +2536,12 @@ (|has| |#1| (-210)) (((|#1| (-494 (-1004 (-1085)))) . T)) (|has| |#2| (-338)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) ((((-792)) . T)) ((((-792)) . T)) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) ((((-792)) . T)) ((((-792)) . T)) (((|#1|) . T)) @@ -2550,8 +2550,8 @@ ((((-522)) . T)) (((|#3|) . T)) ((((-792)) . T)) -(-3708 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) -(-3708 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) +(-3844 (|has| |#1| (-283)) (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-514)) (|has| |#1| (-971))) (((#0=(-535 |#1|) #0#) . T) (($ $) . T) ((#1=(-382 (-522)) #1#) . T)) ((($ $) . T) ((#0=(-382 (-522)) #0#) . T)) (((|#1|) |has| |#1| (-157))) @@ -2564,7 +2564,7 @@ (((|#1|) . T)) ((((-792)) |has| |#1| (-562 (-792)))) ((((-270 |#3|)) . T)) -(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3708 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3844 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) . T)) @@ -2572,20 +2572,20 @@ (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) (((|#1|) . T) (((-382 (-522))) . T) (($) . T)) -((($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) -((($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . 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T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) +((($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) ((((-792)) . T)) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (|has| |#2| (-838)) (|has| |#1| (-838)) -((($) -3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#1|) . T)) -((((-2 (|:| -2530 (-1068)) (|:| -3048 |#1|))) . T)) +((((-2 (|:| -2644 (-1068)) (|:| -3149 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2599,10 +2599,10 @@ (((|#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014)))) (((#0=(-382 (-522)) #0#) . T)) ((((-382 (-522))) . 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T) (($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-514)))) +((($) . T) (((-382 (-522))) -3844 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#1|) . T)) +(((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522)))) ((|#1| |#1|) . T) (($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-514)))) ((($) . T) (((-382 (-522))) . T)) (((|#1|) . T) (((-382 (-522))) . T) (((-522)) . T) (($) . T)) (((|#2|) |has| |#2| (-971)) (((-522)) -12 (|has| |#2| (-584 (-522))) (|has| |#2| (-971)))) -((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) . T) (($) -3708 (|has| |#1| (-157)) (|has| |#1| (-514)))) +((((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) . T) (($) -3844 (|has| |#1| (-157)) (|has| |#1| (-514)))) (|has| |#1| (-514)) (((|#1|) |has| |#1| (-338))) ((((-522)) . T)) @@ -2640,8 +2640,8 @@ ((((-792)) . T)) (|has| |#2| (-757)) (|has| |#2| (-757)) -((((-382 (-522))) -3708 (|has| |#1| (-37 (-382 (-522)))) (|has| |#1| (-338))) ((|#2|) |has| |#1| (-338)) (($) . T) ((|#1|) . T)) -(((|#1|) . 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T)) -(-3708 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971))) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-730)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((((-792)) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-730)) (|has| |#2| (-782))) -(-3708 (-12 (|has| |#1| (-730)) (|has| |#2| (-730))) (-12 (|has| |#1| (-784)) (|has| |#2| (-784)))) +(-3844 (|has| |#2| (-730)) (|has| |#2| (-782))) +(-3844 (-12 (|has| |#1| (-730)) (|has| |#2| (-730))) (-12 (|has| |#1| (-784)) (|has| |#2| (-784)))) ((((-799 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-343)) @@ -2698,7 +2698,7 @@ (((|#1|) . T)) ((((-792)) . T)) (|has| |#2| (-838)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) ((((-498)) |has| |#2| (-563 (-498))) (((-821 (-354))) |has| |#2| (-563 (-821 (-354)))) (((-821 (-522))) |has| |#2| (-563 (-821 (-522))))) ((((-792)) . T)) ((((-792)) . T)) @@ -2731,11 +2731,11 @@ ((((-382 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1014)) -(((|#2| (-455 (-3480 |#1|) (-708))) . T)) +(((|#2| (-455 (-3591 |#1|) (-708))) . T)) ((((-522) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-494 (-1085))) . T)) -(-3708 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((((-522)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2745,9 +2745,9 @@ ((($) . T) (((-382 (-522))) . T)) ((($) . T)) ((($) . T)) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) (((|#1|) . 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T) (((-382 (-522))) . T) (($) . T)) ((($ $) . T) ((#0=(-382 (-522)) #0#) . T)) @@ -2820,14 +2820,14 @@ (((|#2|) |has| |#2| (-971)) (((-522)) -12 (|has| |#2| (-584 (-522))) (|has| |#2| (-971)))) (((|#1|) . T)) (|has| |#2| (-338)) -(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3708 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) -((($ $) -3708 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) +(((#0=(-382 (-522)) #0#) |has| |#2| (-37 (-382 (-522)))) ((|#2| |#2|) . T) (($ $) -3844 (|has| |#2| (-157)) (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +((($ $) -3844 (|has| |#1| (-157)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-382 (-522)) #0#) |has| |#1| (-37 (-382 (-522))))) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-382 (-522)) #0#) . T)) (((|#1| |#1|) . 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T)) @@ -2846,25 +2846,25 @@ (((|#1|) |has| |#2| (-392 |#1|))) (((|#1|) |has| |#2| (-392 |#1|))) ((((-839 |#1|)) . T) (((-382 (-522))) . T) (($) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) ((((-792)) . T)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) |has| (-2 (|:| -2530 (-1085)) (|:| -3048 (-51))) (-285 (-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))))) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) |has| (-2 (|:| -2644 (-1085)) (|:| -3149 (-51))) (-285 (-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) ((((-522) |#1|) . T)) ((((-522) |#1|) . T)) ((((-522) |#1|) . 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T)) -(-3708 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) -(-3708 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-730)) (|has| |#2| (-730)))) +(-3844 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-730)) (|has| |#2| (-730)))) ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) ((($) . T) (((-799 |#1|)) . T) (((-382 (-522))) . T)) ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) @@ -2939,15 +2939,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-382 |#2|)) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-382 (-522)) #0#) . T) (($ $) . T)) ((((-522)) . T)) @@ -2976,32 +2976,32 @@ ((((-1158 |#1| |#2| |#3|)) |has| |#1| (-338))) ((((-1085)) . T) (((-792)) . T)) (|has| |#1| (-338)) -((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) +((((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) |has| |#2| (-157)) (($) -3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-382 (-522))) |has| |#2| (-37 (-382 (-522)))) ((|#2|) . T)) -((($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) -((($) -3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) ((((-1018)) . T)) ((((-792)) . T)) ((($) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522)))) ((|#1|) . T)) ((($) . T)) -((($) -3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) +((($) -3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (|has| |#2| (-838)) (|has| |#1| (-838)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-157))) ((((-637)) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-157))) ((((-382 (-522))) . T) (($) . T)) (((|#1| (-522)) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-338)) (|has| |#1| (-338)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) -(-3708 (|has| |#1| (-157)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-157)) (|has| |#1| (-514))) (((|#1| (-522)) . T)) (((|#1| (-382 (-522))) . T)) (((|#1| (-708)) . T)) @@ -3016,16 +3016,16 @@ ((((-821 (-354))) . T) (((-821 (-522))) . T) (((-1085)) . T) (((-498)) . T)) (((|#1|) . T)) ((((-792)) . T)) -(-3708 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) -(-3708 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-730)) (|has| |#2| (-730)))) +(-3844 (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-338)) (|has| |#2| (-730)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-730)) (|has| |#2| (-730)))) ((((-522)) . T)) ((((-522)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3708 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) +(-3844 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-971))) ((((-1085)) -12 (|has| |#2| (-829 (-1085))) (|has| |#2| (-971)))) -(-3708 (-12 (|has| |#1| (-447)) (|has| |#2| (-447))) (-12 (|has| |#1| (-664)) (|has| |#2| (-664)))) +(-3844 (-12 (|has| |#1| (-447)) (|has| |#2| (-447))) (-12 (|has| |#1| (-664)) (|has| |#2| (-664)))) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-338)) @@ -3049,7 +3049,7 @@ ((((-1068) (-1085) (-522) (-202) (-792)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3708 (|has| |#1| (-324)) (|has| |#1| (-343))) +(-3844 (|has| |#1| (-324)) (|has| |#1| (-343))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-792)) . T)) @@ -3057,7 +3057,7 @@ ((($) . T) ((|#1|) . T) (((-382 (-522))) |has| |#1| (-37 (-382 (-522))))) (((|#2|) |has| |#2| (-1014)) (((-522)) -12 (|has| |#2| (-962 (-522))) (|has| |#2| (-1014))) (((-382 (-522))) -12 (|has| |#2| (-962 (-382 (-522)))) (|has| |#2| (-1014)))) ((((-498)) |has| |#1| (-563 (-498)))) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-784)) (|has| |#1| (-1014)))) ((($) . T) (((-382 (-522))) . T)) (|has| |#1| (-838)) (|has| |#1| (-838)) @@ -3066,14 +3066,14 @@ ((((-792)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-157))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-514))) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-782))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-514))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-782))) (((|#2|) . T)) -(-3708 (|has| |#1| (-21)) (|has| |#1| (-782))) +(-3844 (|has| |#1| (-21)) (|has| |#1| (-782))) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) (((|#1|) . T)) -((((-792)) -3708 (-12 (|has| |#1| (-562 (-792))) (|has| |#2| (-562 (-792)))) (-12 (|has| |#1| (-1014)) (|has| |#2| (-1014))))) +((((-792)) -3844 (-12 (|has| |#1| (-562 (-792))) (|has| |#2| (-562 (-792)))) (-12 (|has| |#1| (-1014)) (|has| |#2| (-1014))))) ((((-382 |#2|) |#3|) . T)) ((((-382 (-522))) . T) (($) . T)) (|has| |#1| (-37 (-382 (-522)))) @@ -3085,17 +3085,17 @@ (((|#1|) . T) (((-382 (-522))) . T) (((-522)) . T) (($) . T)) (((#0=(-522) #0#) . T)) ((($) . T) (((-382 (-522))) . T)) -(-3708 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) -(-3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) +(-3844 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) +(-3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) (|has| |#4| (-730)) -(-3708 (|has| |#4| (-730)) (|has| |#4| (-782))) +(-3844 (|has| |#4| (-730)) (|has| |#4| (-782))) (|has| |#4| (-782)) (|has| |#3| (-730)) -(-3708 (|has| |#3| (-730)) (|has| |#3| (-782))) +(-3844 (|has| |#3| (-730)) (|has| |#3| (-782))) (|has| |#3| (-782)) ((((-522)) . T)) (((|#2|) . T)) -((((-1085)) -3708 (-12 (|has| (-1083 |#1| |#2| |#3|) (-829 (-1085))) (|has| |#1| (-338))) (-12 (|has| |#1| (-15 * (|#1| (-522) |#1|))) (|has| |#1| (-829 (-1085)))))) +((((-1085)) -3844 (-12 (|has| (-1083 |#1| |#2| |#3|) (-829 (-1085))) (|has| |#1| (-338))) (-12 (|has| |#1| (-15 * (|#1| (-522) |#1|))) (|has| |#1| (-829 (-1085)))))) ((((-1085)) -12 (|has| |#1| (-15 * (|#1| (-382 (-522)) |#1|))) (|has| |#1| (-829 (-1085))))) ((((-1085)) -12 (|has| |#1| (-15 * (|#1| (-708) |#1|))) (|has| |#1| (-829 (-1085))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3110,11 +3110,11 @@ ((((-1083 |#1| |#2| |#3|)) |has| |#1| (-338))) ((((-1083 |#1| |#2| |#3|)) |has| |#1| (-338))) ((((-1050 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) ((($) . T)) (|has| |#1| (-947)) -(((|#2|) . T) (((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) ((((-792)) . T)) ((((-498)) |has| |#2| (-563 (-498))) (((-821 (-522))) |has| |#2| (-563 (-821 (-522)))) (((-821 (-354))) |has| |#2| (-563 (-821 (-354)))) (((-354)) . #0=(|has| |#2| (-947))) (((-202)) . #0#)) ((((-1085) (-51)) . T)) @@ -3126,15 +3126,15 @@ ((((-1083 |#1| |#2| |#3|)) . T)) ((((-1083 |#1| |#2| |#3|)) . T) (((-1076 |#1| |#2| |#3|)) . T)) ((((-792)) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) ((((-522) |#1|) . T)) ((((-1083 |#1| |#2| |#3|)) |has| |#1| (-338))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-338)) -(((|#3|) . T) ((|#2|) . T) (($) -3708 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) ((|#4|) -3708 (|has| |#4| (-157)) (|has| |#4| (-338)) (|has| |#4| (-971)))) -(((|#2|) . T) (($) -3708 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((|#3|) -3708 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-971)))) +(((|#3|) . T) ((|#2|) . T) (($) -3844 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-971))) ((|#4|) -3844 (|has| |#4| (-157)) (|has| |#4| (-338)) (|has| |#4| (-971)))) +(((|#2|) . T) (($) -3844 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-971))) ((|#3|) -3844 (|has| |#3| (-157)) (|has| |#3| (-338)) (|has| |#3| (-971)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-338)) @@ -3146,37 +3146,37 @@ ((((-792)) . T)) ((((-792)) . T)) (((|#1|) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) ((((-522) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-338)) (|has| |#2| (-262 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-426)) (|has| |#1| (-838))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) ((((-792)) . T)) ((((-792)) . T)) ((((-792)) . T)) (((|#1| (-494 |#2|)) . T)) -((((-2 (|:| -2530 (-1085)) (|:| -3048 (-51)))) . T)) +((((-2 (|:| -2644 (-1085)) (|:| -3149 (-51)))) . T)) (((|#1| (-522)) . T)) (((|#1| (-382 (-522))) . T)) (((|#1| (-708)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-382 (-522))) . T)) -(-3708 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) -(-3708 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) +(-3844 (|has| |#2| (-426)) (|has| |#2| (-514)) (|has| |#2| (-838))) +(-3844 (|has| |#1| (-426)) (|has| |#1| (-514)) (|has| |#1| (-838))) ((($) . T)) (((|#2| (-494 (-794 |#1|))) . T)) ((((-522) |#1|) . T)) (((|#2|) . T)) (((|#2| (-708)) . T)) -((((-792)) -3708 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) +((((-792)) -3844 (|has| |#1| (-562 (-792))) (|has| |#1| (-1014)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1068) |#1|) . T)) ((((-382 |#2|)) . T)) -((((-2 (|:| -2530 |#1|) (|:| -3048 |#2|))) . T)) +((((-2 (|:| -2644 |#1|) (|:| -3149 |#2|))) . T)) (|has| |#1| (-514)) (|has| |#1| (-514)) ((($) . T) ((|#2|) . T)) @@ -3184,12 +3184,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-262 |#2| |#2|))) (((|#1| (-588 |#1|)) |has| |#1| (-782))) -(-3708 (|has| |#1| (-210)) (|has| |#1| (-324))) -(-3708 (|has| |#1| (-338)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-210)) (|has| |#1| (-324))) +(-3844 (|has| |#1| (-338)) (|has| |#1| (-324))) (|has| |#1| (-1014)) (((|#1|) . T)) ((((-382 (-522))) . T) (($) . T)) -((((-925 |#1|)) . T) ((|#1|) . T) (((-522)) -3708 (|has| (-925 |#1|) (-962 (-522))) (|has| |#1| (-962 (-522)))) (((-382 (-522))) -3708 (|has| (-925 |#1|) (-962 (-382 (-522)))) (|has| |#1| (-962 (-382 (-522)))))) +((((-925 |#1|)) . T) ((|#1|) . T) (((-522)) -3844 (|has| (-925 |#1|) (-962 (-522))) (|has| |#1| (-962 (-522)))) (((-382 (-522))) -3844 (|has| (-925 |#1|) (-962 (-382 (-522)))) (|has| |#1| (-962 (-382 (-522)))))) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) (((|#1| |#1|) -12 (|has| |#1| (-285 |#1|)) (|has| |#1| (-1014)))) @@ -3200,9 +3200,9 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1050 |#1| |#2|) #0#) |has| (-1050 |#1| |#2|) (-285 (-1050 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) #0#) |has| (-2 (|:| -2530 |#1|) (|:| -3048 |#2|)) (-285 (-2 (|:| -2530 |#1|) (|:| -3048 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((#0=(-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) #0#) |has| (-2 (|:| -2644 |#1|) (|:| -3149 |#2|)) (-285 (-2 (|:| -2644 |#1|) (|:| -3149 |#2|))))) (((#0=(-112 |#1|)) |has| #0# (-285 #0#))) -(-3708 (|has| |#1| (-784)) (|has| |#1| (-1014))) +(-3844 (|has| |#1| (-784)) (|has| |#1| (-1014))) ((($ $) . T)) ((($ $) . T) ((#0=(-794 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-210)) ((|#2| |#1|) |has| |#1| (-210)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 5fa2086c..9bc45ab2 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3409939476) +(30 . 3410359535) (4241 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -460,645 +460,644 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |Category| |makeFloatFunction| |OMputFloat| |rquo| - |indicialEquation| |adaptive| |delta| |charClass| |upperCase?| |tab1| - |leadingSupport| |probablyZeroDim?| |iicosh| |sup| |factorFraction| - |insertMatch| |toseSquareFreePart| |constantToUnaryFunction| - |subQuasiComponent?| |intermediateResultsIF| |character?| - |returnTypeOf| |elColumn2!| |c02aff| |rootsOf| |mat| - |primitiveElement| |or?| |mirror| |lfextendedint| |showClipRegion| - |ramified?| |OMsupportsSymbol?| |rightExtendedGcd| |key?| - |KrullNumber| |subtractIfCan| |expenseOfEvaluationIF| |connect| - |declare| |subscript| |degreeSubResultant| |acosIfCan| |reify| - |isMult| |clipWithRanges| |setrest!| |complexNumeric| |imagJ| - |andOperands| |powers| |setProperty!| |integralRepresents| - |rationalPoint?| |limitedint| |taylorQuoByVar| |depth| |log| |s21bdf| - |controlPanel| |chineseRemainder| |primitivePart!| |socf2socdf| - |mapSolve| |pascalTriangle| |integers| |even?| |dmpToHdmp| |iiacoth| - |LyndonWordsList| |kernels| |setchildren!| |mainMonomials| |write!| - |sPol| |comment| |clip| |d02bbf| |uncouplingMatrices| - |lastSubResultantEuclidean| |cSin| |userOrdered?| |leaves| |summation| - |linears| |univariate| |s19acf| |readLineIfCan!| |nextNormalPoly| - |lambda| |viewDefaults| |commutator| |retractable?| - |mainDefiningPolynomial| |inverseColeman| |separant| |f07adf| - |sizeMultiplication| |fprindINFO| |showSummary| |retractIfCan| - |pointSizeDefault| |createNormalElement| |poisson| - |fortranCarriageReturn| |incrementKthElement| |expandPower| - |exprHasWeightCosWXorSinWX| |selectNonFiniteRoutines| |build| - |gcdPolynomial| |escape| |laguerreL| |generalLambert| |ratDenom| - |startTableGcd!| |mainContent| |innerSolve1| |nonQsign| - |totalDifferential| |createMultiplicationTable| |computeCycleLength| - |rotatex| |fracPart| |showAttributes| |ran| |totolex| |BumInSepFFE| - |systemSizeIF| |var2Steps| |swapColumns!| |constant?| |cCot| |makeSin| - |lastSubResultant| |integral?| |plot| |extension| |mulmod| - |leftExtendedGcd| |moduloP| |removeRedundantFactors| |moebiusMu| - |defineProperty| |sign| |powern| |shanksDiscLogAlgorithm| |e02bdf| BY - |setfirst!| |RemainderList| |addBadValue| |numberOfVariables| - |setnext!| |rst| Y |quotient| |numericalIntegration| |top| - |makeSketch| |ocf2ocdf| |deepExpand| |minIndex| |changeVar| - |definingEquations| |rule| |ipow| |discriminantEuclidean| |continue| - |matrix| |void| |trapezoidalo| |merge!| |HermiteIntegrate| - |reduceLODE| |product| |LiePolyIfCan| |anticoord| - |stiffnessAndStabilityFactor| |high| |ref| |prolateSpheroidal| - |pattern| |s17aff| |OMconnOutDevice| |formula| |generator| - |getBadValues| |minimize| |numberOfChildren| |changeBase| - |symmetricProduct| |elements| |setScreenResolution3D| |map| |lyndon?| - |unexpand| |extractIndex| |inconsistent?| |quote| |startStats!| - |tableForDiscreteLogarithm| |htrigs| |exponent| |nary?| - |univariateSolve| |replaceKthElement| |d03faf| |index?| |viewport3D| - |equivOperands| |iilog| |stoseSquareFreePart| |divideIfCan!| |nrows| - |cExp| |removeSquaresIfCan| |find| |acoshIfCan| ~= |measure2Result| - |SturmHabichtCoefficients| |f01rdf| |op| |nextSublist| |ncols| - |remove| |prinpolINFO| |linearAssociatedExp| |stopTableInvSet!| - |noncommutativeJordanAlgebra?| |c06frf| |symbolTableOf| |s21bcf| - |convert| |bivariate?| |true| |resize| |palgLODE0| |schema| - |cyclotomic| |normalizedDivide| |sech2cosh| |getPickedPoints| - |separate| |last| |s13aaf| |totalfract| |rk4a| |assoc| |toScale| - |leftZero| |cyclePartition| |lo| |initiallyReduce| |tracePowMod| - |decimal| |fixPredicate| |match?| |transform| |nextPartition| - |genericRightTraceForm| |coord| |nextsubResultant2| |incr| |edf2df| - |wronskianMatrix| |fortran| |complexEigenvalues| |e02zaf| |presuper| - |exteriorDifferential| |palglimint0| |drawToScale| |hi| - |createNormalPrimitivePoly| |solveLinearPolynomialEquation| |atom?| - |weakBiRank| |s14baf| |imagE| |normalise| |definingPolynomial| - |binomial| |idealiser| |c05nbf| |outputList| |retract| - |var2StepsDefault| |symbolIfCan| |variable?| |basisOfLeftNucloid| - |f02fjf| |symbol| |makeop| |rational| |resetVariableOrder| |isobaric?| - |iflist2Result| |dAndcExp| |realEigenvalues| |tValues| |refine| - |genericLeftTrace| ~ |makeViewport2D| |hasSolution?| |nthRoot| - |leftNorm| |null| |string| |zag| |integer| |getCurve| |lambert| - |argumentList!| |triangSolve| |interval| |OMgetEndApp| |iiperm| - |calcRanges| |yellow| |bumptab| |graphStates| |mvar| |complete| - |removeSuperfluousQuasiComponents| |numberOfHues| |entries| - |genericRightTrace| |constantKernel| |binaryTournament| |var1Steps| - |tab| = |harmonic| |findBinding| |tubePlot| |univariate?| |eq?| - |kroneckerDelta| |normalizeAtInfinity| |segment| - |LagrangeInterpolation| |pseudoDivide| |lowerPolynomial| |e04dgf| - |open| |halfExtendedResultant1| |leftTrace| |distFact| |clearCache| < - |curryLeft| |solveLinearlyOverQ| |leftFactorIfCan| |pade| |level| - |dequeue| |variationOfParameters| |OMlistCDs| > |externalList| - |varselect| |mainCharacterization| |interpret| |iisqrt2| |mapCoef| - |squareFreePolynomial| <= |cAsec| |trueEqual| |characteristicSet| - |leader| |useSingleFactorBound?| |horizConcat| |quotientByP| >= |expr| - |iisqrt3| |copyInto!| |generate| |universe| |list| |script| |satisfy?| - |cyclotomicFactorization| |s18aef| |output| |setDifference| - |selectsecond| |structuralConstants| |countRealRoots| |hessian| - |abelianGroup| |orthonormalBasis| |incrementBy| |complexIntegrate| - |setIntersection| |multiset| |firstUncouplingMatrix| |c06fqf| - |lazyPquo| |checkPrecision| |airyBi| + |createPrimitiveNormalPoly| - |expand| |setUnion| |mainVariable?| |equation| |removeSinSq| |s14abf| - |internalZeroSetSplit| |variable| - |sylvesterMatrix| |filterWhile| - |frobenius| |apply| |zerosOf| |quickSort| |nthFractionalTerm| / - |UP2ifCan| |filterUntil| |asechIfCan| |c06gbf| |numberOfComposites| - |csc2sin| |option?| |select| |size| |quasiMonic?| |bindings| |tex| - |copy!| |complementaryBasis| |deepestInitial| |rspace| |stopTableGcd!| - |rowEch| |t| |rootProduct| |tan2trig| |limit| |setClipValue| |ldf2lst| - UP2UTS |iisinh| |showTheFTable| |freeOf?| |fortranDouble| |close| - |transcendent?| |fglmIfCan| |badNum| |Ei| |f02aff| |pushucoef| - |createIrreduciblePoly| |csubst| |identity| |pmintegrate| |insert| - |shift| |redmat| |rationalIfCan| |makeEq| |bezoutResultant| - |condition| |newReduc| |cAtanh| |maxrank| |hclf| |cotIfCan| SEGMENT - |makeRecord| |messagePrint| |solid?| |fortranReal| |display| - |rightPower| |OMParseError?| |someBasis| |meshPar1Var| |seed| - |implies?| |getSyntaxFormsFromFile| |tanAn| |sizeLess?| |stFuncN| - |s17agf| |OMputAtp| |symmetricGroup| |phiCoord| |showAll?| |s01eaf| - |bandedHessian| |cschIfCan| |antisymmetric?| |front| - |extendedResultant| |infLex?| |addMatchRestricted| |s13acf| |arity| - |prem| |halfExtendedResultant2| |qroot| |wordsForStrongGenerators| - |diagonalProduct| |clipSurface| |iroot| |minPoly| |minimalPolynomial| - |rotate| |coordinate| |exprHasLogarithmicWeights| |linkToFortran| - |partialQuotients| |input| |s17dgf| |hexDigit| |OMgetEndAttr| - |sizePascalTriangle| |s18def| |mkPrim| |pToHdmp| |OMputSymbol| - |library| |subResultantsChain| |hMonic| |s17aef| |cRationalPower| - |upDateBranches| |exprHasAlgebraicWeight| |iisec| |contours| - |mergeFactors| |result| |csch| |OMgetEndBind| |listRepresentation| - |pair?| |middle| |rightZero| |changeThreshhold| |asinh| - |rightScalarTimes!| |splitNodeOf!| |mindegTerm| |children| - |totalGroebner| |csch2sinh| |acosh| |sparsityIF| |leaf?| - |getMultiplicationTable| |pile| |sortConstraints| |entry?| |atanh| - |d02cjf| |rur| |critM| |bernoulli| |set| |shufflein| |d02bhf| - |diagonal?| |acoth| |irreducible?| |rational?| |rightTraceMatrix| - |OMopenFile| |oddlambert| |superHeight| |closedCurve?| |asech| - |inrootof| |decrease| |stoseInvertible?reg| |compile| |id| |polyRDE| - |e04mbf| |f07fdf| |removeCosSq| |conjug| - |rewriteIdealWithHeadRemainder| |ksec| |readIfCan!| |beauzamyBound| - |ddFact| |s21bbf| |multiple| |e01bff| |genericRightMinimalPolynomial| - |c06gqf| |ptree| |measure| |root| |table| |Is| |prinshINFO| - |outputFixed| |coleman| |applyQuote| |rightFactorCandidate| |leftRank| - |numberOfComputedEntries| |changeWeightLevel| |e04fdf| |new| - |derivative| |startPolynomial| |c06ekf| |ParCondList| |showRegion| - |iteratedInitials| |patternVariable| |lazyPrem| |characteristicSerie| - |startTableInvSet!| |alphanumeric?| |coerceListOfPairs| |dmp2rfi| - |complexEigenvectors| |leviCivitaSymbol| |iFTable| |postfix| |besselY| - |compose| |call| |graphImage| |permutations| |acotIfCan| - |partialNumerators| |pdf2ef| |ruleset| |ScanRoman| - |reciprocalPolynomial| |checkForZero| |bracket| |mainPrimitivePart| - |pointColorPalette| |exptMod| |show| - |dimensionOfIrreducibleRepresentation| |commonDenominator| |cTan| - |groebgen| |quasiAlgebraicSet| |iidsum| |writable?| |gcdcofactprim| - |insertionSort!| |repeating?| |ratpart| |toseLastSubResultant| - |integrate| |derivationCoordinates| |row| |symmetricPower| |reverse| - |s19abf| |pushdown| |trace| |irreducibleRepresentation| |revert| - |rightUnits| |reverseLex| |suchThat| |UnVectorise| |setright!| - |unrankImproperPartitions1| |computePowers| - |removeRoughlyRedundantFactorsInPol| |strongGenerators| |numFunEvals| - |aLinear| |zoom| |OMgetBind| |critpOrder| |plenaryPower| |dot| - |rotatey| |minColIndex| |tower| |nullary| |setColumn!| - |numberOfPrimitivePoly| |hypergeometric0F1| |rdregime| |iiasech| - |center| |mapMatrixIfCan| |e01saf| |extendedint| |f04maf| |cosIfCan| - |numberOfImproperPartitions| |printHeader| |initial| |mapBivariate| - |prindINFO| |birth| |nthExpon| |printInfo| |exprToGenUPS| |viewpoint| - |lowerCase!| |nextPrime| |impliesOperands| |firstDenom| |left| - |useEisensteinCriterion| |kmax| |factor| |karatsuba| |partition| - |routines| |nand| |digit| |nextsousResultant2| |outputFloating| - |right| |deepCopy| |genericLeftNorm| |OMencodingUnknown| |s19adf| - |sqrt| |maximumExponent| |property| |expintfldpoly| - |indicialEquationAtInfinity| |reduced?| |paraboloidal| |style| |real| - |lazyPseudoDivide| |f04mcf| |makingStats?| |increasePrecision| - |noKaratsuba| |leftTraceMatrix| |fortranLiteral| |saturate| |bat| - |bitLength| |imag| |B1solve| |resultant| |fixedPointExquo| - |setleaves!| |paren| |symbolTable| |rootSimp| |lepol| |d01gaf| - |invmultisect| |f02adf| |ridHack1| |blue| |directProduct| |iicos| - |subNodeOf?| |enqueue!| |stoseIntegralLastSubResultant| |polygamma| - |units| |extractBottom!| |eigenMatrix| |cCoth| |cAsin| |ricDsolve| - |coHeight| |ef2edf| |bat1| |inRadical?| |Lazard| |iicsch| |s18aff| - |pushFortranOutputStack| |rootPower| |integerBound| |slash| - |scanOneDimSubspaces| |rangeIsFinite| |subSet| |groebnerFactorize| - |zeroDim?| |laplace| |destruct| |removeSinhSq| |patternMatchTimes| - |definingInequation| |popFortranOutputStack| FG2F |rowEchelonLocal| - |semicolonSeparate| |vspace| |OMputEndAttr| |tubeRadiusDefault| - |lfinfieldint| |optimize| |OMputBind| |addiag| |mapdiv| |leftUnit| - |twist| |outputAsFortran| |deleteProperty!| |distance| |polyPart| - |unitNormal| |maxIndex| |octon| |elliptic?| |rationalPoints| |Gamma| - |colorDef| |collectUpper| |setTex!| |unitCanonical| - |fortranCompilerName| |s13adf| |prepareDecompose| |OMencodingXML| - |selectfirst| |type| |c06eaf| |node?| |symbol?| |polygon?| |code| - |factorset| |innerint| |tanh2coth| |useEisensteinCriterion?| - |badValues| |headRemainder| |rightFactorIfCan| |expenseOfEvaluation| - |solveid| |FormatRoman| |deepestTail| |null?| |sumSquares| |nil| - |c06fpf| |setlast!| |print| |characteristicPolynomial| - |pseudoRemainder| |lineColorDefault| |unary?| |heapSort| - |setErrorBound| |fixedPoints| |absolutelyIrreducible?| |imaginary| - |cAcsch| |iicot| |laplacian| |sinhIfCan| |nullSpace| |cycleElt| - |completeEval| |cardinality| |bernoulliB| |algebraicSort| |rotate!| - |primitivePart| |mesh| |multiplyExponents| |wholeRagits| - |internalSubPolSet?| |setPoly| |fractRadix| |prepareSubResAlgo| - |symmetricDifference| |processTemplate| |second| |leadingExponent| - |printInfo!| |upperCase| |getOrder| |quasiMonicPolynomials| - |removeRedundantFactorsInContents| |splitConstant| |OMgetEndObject| - |addPoint2| |quasiComponent| |SturmHabicht| |third| |function| |hex| - |reducedSystem| |s17ajf| |positiveSolve| |s18dcf| |norm| - |expintegrate| |getRef| |linSolve| |parametric?| |sylvesterSequence| - |checkRur| |outputMeasure| |d02ejf| |regularRepresentation| - |viewPosDefault| |primeFrobenius| |numberOfMonomials| |padecf| - |taylorIfCan| |nlde| |inspect| |denomLODE| |pointPlot| |testModulus| - |lookup| |basisOfRightNucloid| |cycleEntry| |infRittWu?| |tube| - |linearMatrix| |monomialIntegrate| |increase| |representationType| - |nor| |d01alf| |LiePoly| |Vectorise| |super| |supRittWu?| - |internalAugment| |getDatabase| |ldf2vmf| |solveInField| - |drawComplexVectorField| |in?| |rootRadius| |divergence| |charthRoot| - |enterInCache| |coshIfCan| |vector| |inverse| |appendPoint| - |rewriteSetWithReduction| |logGamma| |pdct| |close!| |qinterval| - |ideal| |lazyEvaluate| |integralAtInfinity?| |differentiate| |debug3D| - |red| |merge| |ScanArabic| |bumptab1| |chebyshevU| |cCosh| - |fixedDivisor| |iiabs| |gbasis| |e01bhf| |zeroMatrix| |isPower| - |d01fcf| |traverse| |setleft!| |goto| |precision| |case| |linear| - |outlineRender| |coth2trigh| |oneDimensionalArray| |c06gcf| - |consnewpol| |ratDsolve| |e02daf| |epilogue| |hconcat| |expint| - |augment| |doubleComplex?| |coerce| |nullary?| |nthRootIfCan| |expPot| - |crest| |s18adf| |alternatingGroup| |anfactor| |purelyAlgebraic?| - |polynomial| |intensity| |construct| |linearlyDependentOverZ?| - |binarySearchTree| |primlimitedint| |updatF| |d01akf| |lyndon| - |purelyTranscendental?| |OMgetFloat| |redPo| |hasHi| |squareTop| D - |complex?| |toseInvertibleSet| |outputArgs| |realEigenvectors| - |OMopenString| |transcendenceDegree| |nextColeman| |double?| - |perfectSqrt| |ode| |lcm| |generalizedEigenvectors| - |chainSubResultants| |selectODEIVPRoutines| |completeHermite| - |wholePart| |headReduced?| |leftRecip| |exquo| |identityMatrix| - |enumerate| |pureLex| |squareFreePrim| |po| |ListOfTerms| |bright| - |rationalFunction| |abs| |initials| |div| |padicFraction| |pow| - |member?| |qqq| |critB| |is?| |zero?| |axesColorDefault| |imagK| - |extractClosed| |quo| |content| |rightRank| |f01qcf| |terms| |gcd| - |rischNormalize| |and?| |OMputEndBind| |typeLists| |rowEchelon| - |cubic| |updateStatus!| |lflimitedint| |internalDecompose| - |decomposeFunc| |union| |binary| |shiftLeft| |OMgetError| - |unprotectedRemoveRedundantFactors| |iExquo| |rdHack1| |rem| |maxrow| - |chebyshevT| |showTheSymbolTable| |fi2df| |false| |setRealSteps| - |cAcot| |selectPolynomials| |const| |direction| |s20acf| |eval| - |numberOfFractionalTerms| |internalSubQuasiComponent?| |optAttributes| - |graphState| |first| |surface| |fortranLogical| |splitDenominator| - |LazardQuotient2| |tableau| |romberg| |setPrologue!| - |leftCharacteristicPolynomial| |enterPointData| |e02dff| |normalize| - |rest| |particularSolution| |box| |tanintegrate| |viewDeltaXDefault| - |linear?| |evenInfiniteProduct| |clearTheIFTable| |low| |packageCall| - |back| |generic| |transpose| |substitute| |argscript| - |basisOfRightAnnihilator| |leadingIndex| |characteristic| |/\\| - |aQuartic| |pr2dmp| |pop!| |any| |backOldPos| |normal01| |d02gbf| - |modifyPoint| |removeDuplicates| |skewSFunction| |singleFactorBound| - |explimitedint| |sub| |resultantReduitEuclidean| |positiveRemainder| - |normFactors| |invmod| |bivariateSLPEBR| |stopMusserTrials| - |extendedIntegrate| |rroot| |cartesian| |atoms| |getCode| - |decreasePrecision| |OMgetEndBVar| |algebraic?| |preprocess| - |removeIrreducibleRedundantFactors| |OMputInteger| |integral| |rename| - |brillhartTrials| |lagrange| |iisin| |algebraicVariables| |parabolic| - |sumOfKthPowerDivisors| |newLine| |open?| |infinite?| |crushedSet| - |oblateSpheroidal| |partialDenominators| |zeroVector| |matrixConcat3D| - |diag| |f07aef| |radicalEigenvectors| |Nul| |yCoordinates| |objectOf| - |complexElementary| |rewriteSetByReducingWithParticularGenerators| - |setelt| |chvar| |e02agf| |d02gaf| |currentCategoryFrame| - |OMgetInteger| |latex| |range| |iitan| |reorder| |numeric| |lowerCase| - |bombieriNorm| |applyRules| |cycleLength| |groebner?| |color| |over| - |numberOfComponents| |powerSum| |putColorInfo| |plus| |not| |radical| - |normalizedAssociate| |copy| |real?| |linGenPos| |setAdaptive3D| - |f01rcf| |predicates| |vconcat| |factorSFBRlcUnit| |conditionP| - |setStatus!| |alphabetic| |asecIfCan| |intersect| |basisOfLeftNucleus| - |localUnquote| |setAdaptive| |properties| |completeHensel| - |shallowExpand| |expextendedint| |rangePascalTriangle| |child?| - |zeroDimPrime?| |rootPoly| |yCoord| |sncndn| ^= |signAround| - |cylindrical| |makeGraphImage| |listOfMonoms| |tanIfCan| |f02bbf| - |quotedOperators| |polCase| |exprToXXP| |laurentRep| |integerIfCan| - |autoCoerce| |pmComplexintegrate| |swapRows!| |rowEchLocal| |max| - |conjugates| |OMgetString| |wrregime| |OMreadStr| |mindeg| - |createThreeSpace| |exponential| |isList| |rk4f| |inR?| - |initializeGroupForWordProblem| |mainVariables| |say| |iicsc| |df2st| - |isTimes| |collect| |d01asf| |solveRetract| |primes| - |subResultantChain| |unitVector| |translate| |omError| |bubbleSort!| - |singularAtInfinity?| |makeFR| |reflect| |leftDiscriminant| - |leftScalarTimes!| |besselJ| |monicDivide| |allRootsOf| |setRow!| - |f02xef| |hspace| |constDsolve| |OMputEndBVar| |c05adf| |triangulate| - |times| |nextPrimitivePoly| |zeroSquareMatrix| |rootOfIrreduciblePoly| - |mathieu11| |branchIfCan| |rubiksGroup| |getOperator| - |resultantEuclideannaif| |contractSolve| |leftRankPolynomial| - |shrinkable| |squareMatrix| |seriesSolve| |coerceImages| - |setLegalFortranSourceExtensions| |getVariableOrder| |divisors| - |nextNormalPrimitivePoly| |semiResultantEuclidean2| |specialTrigs| - |pastel| |leftDivide| |singularitiesOf| |primitive?| |inHallBasis?| - |increment| |monicLeftDivide| |clearTheSymbolTable| |replace| |length| - |monom| |OMputAttr| |radix| |quartic| |expt| |check| |getButtonValue| - |setProperties!| |scripts| |square?| |musserTrials| |OMputEndError| - |key| |jacobi| |cos2sec| |df2mf| |OMputApp| - |selectSumOfSquaresRoutines| |prologue| |options| |quadratic?| - |setMinPoints| |common| |OMgetEndAtp| |idealSimplify| |e01sbf| - |stoseInvertible?| |elt| |irreducibleFactor| |changeMeasure| |solid| - |univariatePolynomial| |cycles| |clikeUniv| |lieAlgebra?| - |expressIdealMember| |filename| |xCoord| |negative?| |dn| |Si| - |complexRoots| |semiSubResultantGcdEuclidean2| |e02baf| - |semiResultantEuclidean1| |reopen!| |point?| |iisech| |uniform01| - |BasicMethod| |baseRDEsys| |iipow| |not?| |factorSquareFree| - |factorByRecursion| |setVariableOrder| |prod| |minRowIndex| - |leadingCoefficientRicDE| |showAllElements| |cyclotomicDecomposition| - |asinhIfCan| |parse| |createPrimitiveElement| |redpps| |linearPart| - |sturmVariationsOf| |s14aaf| |list?| |cond| |sumOfSquares| - |stoseInvertible?sqfreg| |d02kef| |odd?| |alphabetic?| |graphCurves| - |space| |computeBasis| |cn| |qfactor| |constantIfCan| |round| |fmecg| - |scopes| |fill!| |numericIfCan| |delay| |OMgetObject| - |semiIndiceSubResultantEuclidean| |airyAi| |addPoint| - |factorsOfDegree| |palgLODE| |monicRightFactorIfCan| |rightGcd| - |trunc| |lexTriangular| |digits| |curve| |dim| |RittWuCompare| - |edf2ef| |multiple?| |extensionDegree| |bringDown| |sechIfCan| - |mainForm| |initTable!| |operator| |Beta| |alternating| |e04gcf| - |concat!| |removeConstantTerm| |monomialIntPoly| - |basisOfLeftAnnihilator| |radPoly| |iicoth| |bsolve| - |createMultiplicationMatrix| |fullPartialFraction| |notOperand| |axes| - |useNagFunctions| |setref| |tubePoints| |makeTerm| |width| - |cycleSplit!| |rewriteIdealWithQuasiMonicGenerators| |dominantTerm| - |fortranInteger| |explogs2trigs| |extractIfCan| |rightLcm| - |nonSingularModel| |listLoops| |cap| |conditionsForIdempotents| - |evaluateInverse| |factorGroebnerBasis| |certainlySubVariety?| - |knownInfBasis| |exists?| |root?| |adaptive3D?| |fullDisplay| - |radicalRoots| |powerAssociative?| |useSingleFactorBound| |endOfFile?| - |complexSolve| |gcdcofact| |pomopo!| |palglimint| |fortranLinkerArgs| - |singRicDE| |bipolar| |powmod| |constant| |lieAdmissible?| |swap!| - |headReduce| |d01bbf| |recip| |meshFun2Var| |e01bgf| |midpoints| - |OMsetEncoding| |OMgetSymbol| |setFormula!| - |solveLinearPolynomialEquationByRecursion| |trivialIdeal?| |rename!| - |factorials| |getProperty| |palginfieldint| |doublyTransitive?| - |semiLastSubResultantEuclidean| |youngGroup| |fortranTypeOf| - |optional| |roman| |unitsColorDefault| |continuedFraction| - |infiniteProduct| |basisOfRightNucleus| |primPartElseUnitCanonical| - |erf| |infinityNorm| |e02bbf| |besselK| |selectOptimizationRoutines| - |triangularSystems| |e04naf| |parametersOf| |clipParametric| - |modularFactor| |binaryFunction| |index| |e04ucf| UTS2UP |less?| - |cfirst| |xn| |isAbsolutelyIrreducible?| |split| |viewThetaDefault| - |multiEuclideanTree| |symmetric?| |setOrder| |nthFlag| |fintegrate| - |equality| |meshPar2Var| |bitCoef| |sec2cos| |dilog| |point| - |combineFeatureCompatibility| |d02raf| |karatsubaOnce| |gethi| - |normal?| |associatedSystem| |cup| |getVariable| |listBranches| - |showScalarValues| |reducedContinuedFraction| |sin| |makeCrit| - |search| |pair| |divide| |linearlyDependent?| |radicalEigenvalues| - |stop| |alphanumeric| |getConstant| |mathieu12| |cyclic| |ReduceOrder| - |cos| |functionIsContinuousAtEndPoints| |lazyPseudoRemainder| - |chiSquare| |frst| |psolve| |\\/| |iiacosh| |discriminant| |safeFloor| - |perspective| |tan| |series| |clipBoolean| |exprToUPS| - |resultantReduit| |areEquivalent?| |geometric| |callForm?| |module| - |cot2trig| |one?| |toseInvertible?| |cot| |numberOfFactors| |f02abf| - |resetNew| |create3Space| |truncate| |select!| |getProperties| - |pToDmp| |degree| |sec| |bag| |setImagSteps| |trailingCoefficient| - |distdfact| |move| |unravel| |hexDigit?| |divisorCascade| - |rootNormalize| |csc| |numer| |removeZero| |makeViewport3D| - |figureUnits| |separateFactors| |cPower| |getMeasure| |lifting| - |prime?| |min| |asin| |denom| |mapUp!| |has?| |OMconnectTCP| - |drawCurves| |d01anf| |inGroundField?| |normalDeriv| |f04arf| |acos| - |computeInt| |primeFactor| |rightRegularRepresentation| |writeLine!| - |modularGcd| |status| |dimensionsOf| |newTypeLists| |leadingTerm| - |cyclicSubmodule| |atan| |binding| |pi| |PollardSmallFactor| |message| - |updatD| |c02agf| |composites| |safeCeiling| |magnitude| |neglist| - |innerEigenvectors| |acot| |infinity| |rightTrim| |vark| |lyndonIfCan| - |iiacsc| |coercePreimagesImages| |explicitlyFinite?| |charpol| - |perfectNthRoot| |e01baf| |viewport2D| |asec| |obj| |leftTrim| - |pointLists| |commutativeEquality| |resultantnaif| |viewZoomDefault| - |setStatus| |factorial| |usingTable?| |balancedFactorisation| - |component| |acsc| |plusInfinity| |cache| |contains?| |oddintegers| - |iitanh| |rightAlternative?| |string?| |fractionFreeGauss!| |e02bef| - |FormatArabic| |setClosed| |sinh| |insertTop!| |minusInfinity| - |wordInGenerators| |name| |flexible?| |cycle| |clearTheFTable| - |SFunction| |invertibleSet| |validExponential| |firstNumer| |cosh| - |dom| |singular?| |janko2| |principal?| |associatorDependence| - |numerator| |recolor| |iiasinh| |mathieu24| |e02ddf| |label| |tanh| - |kernel| |iiacot| |df2ef| |fibonacci| |mesh?| |lazyVariations| - |gradient| |e02ahf| |approxSqrt| |cLog| |coth| |draw| |sin?| - |supersub| |rotatez| |monicModulo| |minimumDegree| |changeName| - |generalInfiniteProduct| |associative?| |OMgetVariable| |sech| - |computeCycleEntry| |sinhcosh| |degreePartition| - |removeRedundantFactorsInPols| |subResultantGcdEuclidean| - |univariatePolynomials| |f04asf| |setTopPredicate| - |semiDiscriminantEuclidean| |pointColorDefault| |linearAssociatedLog| - |selectIntegrationRoutines| |mkAnswer| |hermiteH| |minimumExponent| - |OMputError| |lazy?| |blankSeparate| |compdegd| - |zeroSetSplitIntoTriangularSystems| |infieldIntegrate| |Lazard2| - |monicRightDivide| |atanhIfCan| |title| |makeObject| |inc| - |complexLimit| |linearPolynomials| |generators| |froot| |graeffe| - |primaryDecomp| |f01qef| |f01qdf| |keys| |e| |cAtan| |coefChoose| - |plotPolar| |algebraicDecompose| |error| |splitLinear| |secIfCan| - |rightDiscriminant| |factors| |coef| |restorePrecision| |putGraph| - |LowTriBddDenomInv| |cosSinInfo| |simplifyExp| |assert| |localReal?| - |dimensions| |randomR| |lquo| |getlo| |failed?| |sayLength| - |flagFactor| |rightMinimalPolynomial| |categoryFrame| - |currentSubProgram| |opeval| |maxPoints3D| |getGraph| - |numberOfIrreduciblePoly| |OMsupportsCD?| |bezoutMatrix| |shiftRoots| - |outputGeneral| |leftAlternative?| |nextItem| |innerSolve| |setEmpty!| - |selectAndPolynomials| |closeComponent| |newSubProgram| |modulus| - |debug| |monic?| |differentialVariables| |pleskenSplit| |leftMult| - |subresultantVector| |option| |discreteLog| |unitNormalize| - |stopTable!| |algebraicCoefficients?| |scalarMatrix| - |functionIsFracPolynomial?| |antiCommutator| |ceiling| - |jordanAdmissible?| |subPolSet?| |selectOrPolynomials| - |companionBlocks| |makeResult| |cCsch| |d01apf| |argumentListOf| - |OMUnknownCD?| |getGoodPrime| |cAsech| |node| |stirling1| |s17dcf| - |nonLinearPart| |integralDerivationMatrix| |cyclic?| |distribute| - |overlabel| |constantOperator| |df2fi| |partialFraction| |entry| - |tablePow| |rewriteIdealWithRemainder| |finiteBound| |pointColor| - |every?| |OMbindTCP| |jacobiIdentity?| |dec| |compBound| |taylor| - |tanQ| |normalDenom| ** |llprop| |resetAttributeButtons| |insertRoot!| - |antiCommutative?| |tryFunctionalDecomposition?| |OMgetEndError| - |laurent| |possiblyInfinite?| |var1StepsDefault| |float| - |problemPoints| |constantOpIfCan| |linearAssociatedOrder| - |removeRoughlyRedundantFactorsInPols| |rightNorm| - |stosePrepareSubResAlgo| |tan2cot| |puiseux| |flexibleArray| - |minordet| |rootBound| |failed| |legendreP| |ranges| |cCsc| EQ - |s18acf| |palgint0| |symmetricTensors| |scale| |lfintegrate| - |basisOfCentroid| |midpoint| |nextPrimitiveNormalPoly| |integer?| - |composite| |inv| |seriesToOutputForm| |elRow2!| |interReduce| - |overbar| |LyndonCoordinates| |SturmHabichtSequence| |elem?| - |scripted?| |cycleTail| |ground?| |hdmpToP| |mightHaveRoots| - |setOfMinN| |npcoef| |internalIntegrate| |karatsubaDivide| |An| - |imagj| |hyperelliptic| |ground| |squareFreePart| |ravel| - |realElementary| |conjugate| |directory| |countRealRootsMultiple| - |thetaCoord| |gramschmidt| |lazyGintegrate| |leadingMonomial| - |purelyAlgebraicLeadingMonomial?| |rightUnit| |exp1| |element?| - |reshape| |f01ref| |simpleBounds?| |inf| |fixedPoint| - |leadingCoefficient| |rk4| |shuffle| |getZechTable| - |selectMultiDimensionalRoutines| |Hausdorff| |ramifiedAtInfinity?| - |mainVariable| |atanIfCan| |primitiveMonomials| |setMinPoints3D| - |e02ajf| GE |float?| |weight| |compiledFunction| |quasiRegular| - |extractProperty| |reductum| |elliptic| |f02awf| GT - |subscriptedVariables| |createLowComplexityNormalBasis| |divideIfCan| - |plus!| |polynomialZeros| |OMcloseConn| |rank| |log10| |henselFact| LE - |repSq| |nthr| |stoseInvertibleSetreg| |constantLeft| |traceMatrix| - |sample| |setFieldInfo| |perfectNthPower?| |makeSeries| LT - |normalizeIfCan| |OMserve| |mix| |update| |c06ebf| |tensorProduct| - |lprop| |sqfree| |s20adf| |integralMatrixAtInfinity| |f04qaf| - |zeroDimensional?| |trim| |s21baf| |pushuconst| |exactQuotient| - |lazyPseudoQuotient| |eq| |s17dlf| GF2FG |cscIfCan| |car| |f04jgf| - |setValue!| |lazyIrreducibleFactors| |sdf2lst| |determinant| |iter| - |diophantineSystem| |makeUnit| |unit| |maxint| |cdr| |s19aaf| - |randnum| |biRank| |sort| |virtualDegree| |push!| |permutation| - |setPosition| |quasiRegular?| |e02aef| |f01brf| |slex| |hasPredicate?| - |radicalEigenvector| |baseRDE| |LyndonBasis| |leadingBasisTerm| - |cross| |mergeDifference| |gcdprim| |quadraticNorm| |OMUnknownSymbol?| - |palgextint| |digamma| |listOfLists| |position| |laguerre| |nsqfree| - |moduleSum| |shiftRight| |coefficient| |generic?| |simplify| - |standardBasisOfCyclicSubmodule| |li| |log2| |denomRicDE| |evaluate| - |lSpaceBasis| |topFortranOutputStack| |moebius| |child| |random| - |f01maf| |deref| |curve?| |palgRDE0| |physicalLength| |hermite| - |infix| |diagonal| |cyclicParents| |extractTop!| |exp| |setprevious!| - |recur| |iiacos| |createRandomElement| |OMputBVar| |OMputEndAtp| - |expandTrigProducts| |btwFact| |currentScope| |simplifyPower| - |leftPower| |OMconnInDevice| |movedPoints| |rightExactQuotient| - |gderiv| |internalIntegrate0| |inverseLaplace| |monomRDE| |isExpt| - |acscIfCan| |removeRoughlyRedundantFactorsInContents| |bottom!| - |corrPoly| |region| |e02dcf| |tanSum| - |inverseIntegralMatrixAtInfinity| |acschIfCan| |maxdeg| |OMgetBVar| - |principalIdeal| |randomLC| |rules| |e01daf| |dioSolve| - |exponentialOrder| |unrankImproperPartitions0| |algDsolve| |subst| - |permutationRepresentation| |extendIfCan| |members| |lex| |medialSet| - |cot2tan| |interpretString| |kovacic| |prinb| |critMonD1| - |numFunEvals3D| |multiEuclidean| |optional?| |integralMatrix| |f01mcf| - |taylorRep| |contract| |getOperands| |closedCurve| |datalist| |e04ycf| - |pushdterm| |optpair| |polarCoordinates| |realRoots| |stirling2| - |trapezoidal| |mathieu23| |printStats!| |showArrayValues| - |doubleResultant| |f02axf| |implies| |stFunc2| |monomial?| - |normalized?| |tryFunctionalDecomposition| |sturmSequence| - |leftQuotient| |objects| |whatInfinity| |f07fef| |associatedEquations| - |xor| |LyndonWordsList1| |exQuo| |more?| |doubleRank| |minset| |base| - |subresultantSequence| |mantissa| |normDeriv2| |functionIsOscillatory| - |OMclose| |cSech| |removeDuplicates!| |critMTonD1| |getExplanations| - |nilFactor| |c06fuf| |nextSubsetGray| |possiblyNewVariety?| |double| - |internalInfRittWu?| |cosh2sech| |monicCompleteDecompose| - |semiSubResultantGcdEuclidean1| |radicalSimplify| |prefix| - |rightRemainder| |PDESolve| |finiteBasis| |genericLeftTraceForm| - |polyRicDE| |physicalLength!| |relerror| |diff| |mkcomm| |wreath| - |genericRightNorm| |squareFreeLexTriangular| |elRow1!| |term?| |pole?| - |hdmpToDmp| |brace| |cAcoth| |generalTwoFactor| - |clearFortranOutputStack| |identitySquareMatrix| |errorInfo| |points| - |convergents| |normalElement| |bfKeys| |test| |copies| |number?| - |mainCoefficients| |algSplitSimple| |supDimElseRittWu?| |partitions| - |initiallyReduced?| |bitTruth| |irreducibleFactors| |iiasin| - |splitSquarefree| |lintgcd| |resetBadValues| |d01ajf| |difference| - |internal?| |basisOfMiddleNucleus| |iiacsch| |remainder| |vedf2vef| - |cyclicEqual?| |relationsIdeal| |declare!| |solve| |OMgetAttr| - |Frobenius| |primPartElseUnitCanonical!| |exponents| |radicalSolve| - |viewWriteAvailable| |cyclicEntries| |logpart| |value| - |clipPointsDefault| |vertConcat| |lowerCase?| - |constantCoefficientRicDE| |cons| |moreAlgebraic?| |sincos| - |highCommonTerms| |sn| |outputForm| |antisymmetricTensors| - |mainMonomial| |deleteRoutine!| |curveColor| |squareFree| |chiSquare1| - |listYoungTableaus| |setScreenResolution| |complexNumericIfCan| - |shade| |indiceSubResultantEuclidean| |arrayStack| |primextendedint| - |ord| |numberOfDivisors| |halfExtendedSubResultantGcd2| |ODESolve| - |previous| |recoverAfterFail| |padicallyExpand| |orbit| - |resultantEuclidean| |e01sef| |iomode| |leftLcm| |acothIfCan| - |drawStyle| |fortranCharacter| |tree| |euler| |dihedral| - |stoseInvertibleSetsqfreg| |setsubMatrix!| |setButtonValue| |#| - |submod| |solveLinear| |zero| |normInvertible?| |rk4qc| - |oddInfiniteProduct| |split!| |column| |ScanFloatIgnoreSpacesIfCan| - |outputSpacing| |lllip| |cSinh| |e01bef| |iiexp| |factorPolynomial| - |decompose| |nextLatticePermutation| |And| |transcendentalDecompose| - |modularGcdPrimitive| |e02adf| |term| |fortranComplex| |leadingIdeal| - |leftUnits| |Or| |setProperty| |char| |reverse!| ^ |minPoints| - |adaptive?| |clearDenominator| |numberOfOperations| |e02gaf| |s17def| - |Not| |sum| |readLine!| |OMmakeConn| |aCubic| |OMputEndApp| |lexico| - |raisePolynomial| |listConjugateBases| |light| |polygon| |printTypes| - |stFunc1| |curryRight| |OMlistSymbols| |branchPointAtInfinity?| - |denominator| |viewPhiDefault| |s17dhf| |accuracyIF| |sort!| - |roughBase?| |upperCase!| |factorOfDegree| |ptFunc| |tubeRadius| |Ci| - |generalizedContinuumHypothesisAssumed| |makeMulti| |quoByVar| - |mainSquareFreePart| |stoseInvertibleSet| |rightRankPolynomial| - |generalizedInverse| |fillPascalTriangle| |logical?| |numerators| - |power!| |mapmult| |OMreceive| |subset?| |bit?| |imagI| - |mapUnivariate| |s15aef| |basisOfCommutingElements| |sequences| - |iprint| |orbits| |Zero| |ode2| |unaryFunction| - |factorSquareFreeByRecursion| |Aleph| |clearTable!| |palgint| - |buildSyntax| |intcompBasis| |stronglyReduced?| |setMaxPoints| |One| - |rCoord| |getMultiplicationMatrix| |f2df| |smith| |minPol| |ode1| - |symmetricSquare| |e02def| |spherical| |genericPosition| |c06gsf| - |solve1| |digit?| |comp| |lazyPremWithDefault| |lhs| |rightTrace| - |curry| |rischDEsys| |rombergo| |bumprow| |hcrf| |scalarTypeOf| - |primlimintfrac| |rhs| |radicalOfLeftTraceForm| |indices| |expandLog| - |collectUnder| |stronglyReduce| |constructorName| |conical| - |associator| |f2st| |bipolarCylindrical| |matrixGcd| |belong?| - |endSubProgram| |tanNa| |minPoints3D| |logIfCan| - |numericalOptimization| |exactQuotient!| |next| |int| |showTheIFTable| - |makeSUP| |push| |groebnerIdeal| |torsionIfCan| |setvalue!| |critT| - |leftMinimalPolynomial| |qelt| |binomThmExpt| |forLoop| |mainValue| - |unparse| |primextintfrac| |rightRecip| |sts2stst| |roughUnitIdeal?| - |systemCommand| |makeCos| |reduceBasisAtInfinity| |createZechTable| - |asinIfCan| |cyclicCopy| |sinh2csch| |viewWriteDefault| |any?| - |removeCoshSq| |dequeue!| |outputAsTex| |tanh2trigh| |rightDivide| - |selectPDERoutines| |approximants| |createNormalPoly| |polar| - |generalSqFr| |perfectSquare?| |semiDegreeSubResultantEuclidean| - |SturmHabichtMultiple| |viewSizeDefault| |normal| - |genericLeftMinimalPolynomial| |f04adf| |uniform| |drawComplex| - |lfunc| |getStream| |lighting| |leftGcd| |e02bcf| - |selectFiniteRoutines| |compactFraction| |reducedDiscriminant| - |simpsono| |coordinates| |mpsode| |homogeneous?| |iiasec| |delete!| - |append| |lexGroebner| |d01amf| |univariatePolynomialsGcds| |floor| - |positive?| |safetyMargin| |genericLeftDiscriminant| |scan| - |eyeDistance| |bivariatePolynomials| |extractPoint| |dflist| NOT - |delete| |dmpToP| |duplicates| |realZeros| |mathieu22| |removeZeroes| - |bfEntry| |leftRemainder| |nextIrreduciblePoly| |minGbasis| - |primintfldpoly| |cAcosh| OR |setAttributeButtonStep| |jordanAlgebra?| - |cSec| |assign| |setMaxPoints3D| |order| |showTypeInOutput| - |repeatUntilLoop| |prime| |UpTriBddDenomInv| |extend| AND - |zeroDimPrimary?| |overset?| |e04jaf| |OMread| |squareFreeFactors| - |reseed| |bezoutDiscriminant| |complexZeros| - |factorSquareFreePolynomial| |euclideanSize| |testDim| |green| - |infieldint| |rightMult| |legendre| |printCode| |lazyIntegrate| - |halfExtendedSubResultantGcd1| |unit?| |dihedralGroup| |leftFactor| - |removeSuperfluousCases| |palgRDE| |substring?| |localAbs| - |cyclicGroup| |algint| |screenResolution3D| |fTable| |nthFactor| - |loopPoints| |duplicates?| |subTriSet?| |linearDependenceOverZ| - |evenlambert| |modifyPointData| |stiffnessAndStabilityOfODEIF| - |times!| |iiGamma| |asimpson| |OMputObject| |equiv?| |complement| - |separateDegrees| |d03edf| |represents| |OMencodingSGML| |suffix?| - 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|subMatrix| |getCurve| |factorFraction| + |cyclicParents| |complexExpand| |asinh| |mainContent| |unaryFunction| + |reducedForm| |lambert| |extractTop!| |insertMatch| |OMputVariable| + |subst| |innerSolve1| |acosh| |factorSquareFreeByRecursion| + |printStatement| |set| |argumentList!| |setprevious!| |alternative?| + |atanh| |nonQsign| |Aleph| |dfRange| |triangSolve| |recur| + |invertible?| |totalDifferential| |acoth| |clearTable!| |sorted?| + |datalist| |id| |interval| |iiacos| |generateIrredPoly| + |createMultiplicationTable| |asech| |palgint| |quatern| |compile| + |OMgetEndApp| |createRandomElement| |f04atf| |computeCycleLength| + |buildSyntax| |outputAsScript| |table| |iiperm| |OMputBVar| + |integralBasis| |objects| |rotatex| |multiple| |intcompBasis| |ptree| + |invertibleElseSplit?| |new| |calcRanges| |OMputEndAtp| |countable?| + |base| |fracPart| |applyQuote| |stronglyReduced?| |repeating| |yellow| + |space| |expandTrigProducts| |iifact| |ran| |setMaxPoints| + |modifyPoint| 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|genericRightTrace| |numericIfCan| |gderiv| + |setPredicates| |makeSin| |invmod| |e02def| |parabolic| + |firstSubsetGray| |initial| |left| |constantKernel| |delay| + |internalIntegrate0| |choosemon| |lastSubResultant| |spherical| |swap| + |sumOfKthPowerDivisors| |right| |binaryTournament| |OMgetObject| + |inverseLaplace| |factor| |mapGen| |property| |previous| |integral?| + |genericPosition| |rationalApproximation| |newLine| |var1Steps| + |semiIndiceSubResultantEuclidean| |sqrt| |monomRDE| |f02aaf| |plot| + |c06gsf| |hasoln| |airyAi| |tab| |isExpt| |real| |OMsend| |divisors| + |extension| |solve1| |unvectorise| |harmonic| |acscIfCan| |imag| + |setEpilogue!| |units| |nextNormalPrimitivePoly| |mulmod| + |lazyPremWithDefault| |besselI| |findBinding| |directProduct| + |removeRoughlyRedundantFactorsInContents| |commaSeparate| + |semiResultantEuclidean2| |leftExtendedGcd| |rightTrace| |simplifyLog| + |tubePlot| |bottom!| |rischDE| |specialTrigs| |curry| |denominators| + |rischNormalize| |optimize| |univariate?| |corrPoly| |destruct| |mdeg| + |pastel| |toseSquareFreePart| |rischDEsys| |and?| |nodeOf?| |eq?| + |bindings| |region| |normalForm| |constantToUnaryFunction| + |leftDivide| |rombergo| |mapDown!| |OMputEndBind| |kroneckerDelta| + |type| |e02dcf| |code| |extendedSubResultantGcd| |singularitiesOf| + |subQuasiComponent?| |bumprow| |typeLists| |graphs| |tanSum| + |univcase| |intermediateResultsIF| |primitive?| |nil| |hcrf| + |parabolicCylindrical| |rowEchelon| |d03faf| |integral| + |inverseIntegralMatrixAtInfinity| |root?| |meatAxe| |character?| + |inHallBasis?| |scalarTypeOf| |print| |cubic| |autoReduced?| |index?| + |adaptive3D?| |acschIfCan| |indicialEquations| |increment| + |returnTypeOf| |primlimintfrac| |leastAffineMultiple| |updateStatus!| + |viewport3D| |fullDisplay| |maxdeg| |subCase?| |second| |elColumn2!| + |monicLeftDivide| |radicalOfLeftTraceForm| |lflimitedint| |eulerE| + |equivOperands| |OMgetBVar| |radicalRoots| |multinomial| |third| + |c02aff| |clearTheSymbolTable| |asechIfCan| |indices| + |intPatternMatch| |internalDecompose| |iilog| |powerAssociative?| + |principalIdeal| |rootsOf| |hue| |function| |OMputAttr| |setFormula!| + |c06gbf| |lift| |expandLog| |torsion?| |decomposeFunc| + |stoseSquareFreePart| |randomLC| |HenselLift| |mat| |radix| + |solveLinearPolynomialEquationByRecursion| |numberOfComposites| + |reduce| |collectUnder| |binary| |cAcos| |divideIfCan!| + |goodnessOfFit| |quartic| |primitiveElement| |trivialIdeal?| |csc2sin| + |stronglyReduce| |shallowCopy| |shiftLeft| |cExp| |setFieldInfo| + |startTableInvSet!| |subHeight| |expt| |or?| |option?| |rename!| + |arguments| |conical| |OMgetError| |removeSquaresIfCan| + |alphanumeric?| |perfectNthPower?| |coefficients| |check| |mirror| + |factorials| |quasiMonic?| |associator| |qelt| |find| |makeSeries| + |coerceListOfPairs| |constantRight| |getButtonValue| |lfextendedint| + |copy!| |acoshIfCan| |normalizeIfCan| |dmp2rfi| |euclideanNormalForm| + |setProperties!| |showClipRegion| |complementaryBasis| |maxIndex| + |oddInfiniteProduct| |measure2Result| |complexEigenvectors| |OMserve| + |limitedIntegrate| |ramified?| |square?| |deepestInitial| |octon| + |split!| |leviCivitaSymbol| |SturmHabichtCoefficients| |mix| |case| + |e02akf| |coerce| |musserTrials| |OMsupportsSymbol?| |elliptic?| + |rspace| |unprotectedRemoveRedundantFactors| |column| |f01rdf| + |c06ebf| |iFTable| |construct| |rightExtendedGcd| |OMputEndError| + |rationalPoints| |stopTableGcd!| |iExquo| |ScanFloatIgnoreSpacesIfCan| + |linearDependence| |nextSublist| |postfix| |tensorProduct| |s18adf| + |asecIfCan| |jacobi| |key?| |outputSpacing| |rowEch| |rdHack1| |Gamma| + |prinpolINFO| |lprop| |besselY| |alternatingGroup| |zCoord| + |intersect| D |KrullNumber| |cos2sec| |rootProduct| |lllip| |maxrow| + |colorDef| |linearAssociatedExp| |predicate| |sqfree| |compose| + |anfactor| |unmakeSUP| |subtractIfCan| |df2mf| |lcm| |cSinh| + |tan2trig| |chebyshevT| |collectUpper| |bright| |graphImage| + |stopTableInvSet!| |s20adf| |exquo| |colorFunction| |purelyAlgebraic?| + |expenseOfEvaluationIF| |limit| |e01bef| |currentCategoryFrame| + |showTheSymbolTable| |setTex!| |ScanFloatIgnoreSpaces| + |integralMatrixAtInfinity| |noncommutativeJordanAlgebra?| |Beta| |div| + |permutations| |setCondition!| |intensity| |setClipValue| |connect| + |iiexp| |OMgetInteger| |fi2df| |unitCanonical| |exponential1| + |alternating| |c06frf| |f04qaf| |quo| |acotIfCan| |external?| + |linearlyDependentOverZ?| |setRealSteps| |gcd| |subscript| |ldf2lst| + |latex| |fortranCompilerName| |factorPolynomial| |ignore?| + |binarySearchTree| |symbolTableOf| |partialNumerators| + |zeroDimensional?| |e04gcf| |OMunhandledSymbol| |range| + |degreeSubResultant| |union| |cAcot| UP2UTS |s13adf| |decompose| + |tRange| |pdf2ef| |eval| |primlimitedint| |s21bcf| |rem| |trim| + |concat!| |nullity| |first| |false| |acosIfCan| |iitan| |iisinh| + |prepareDecompose| |nextLatticePermutation| |fortranDoubleComplex| + |updatF| |bivariate?| |s21baf| |ScanRoman| |removeConstantTerm| + |extractSplittingLeaf| |xRange| |rest| |reify| |reorder| + |showTheFTable| |OMencodingXML| |transcendentalDecompose| + |indiceSubResultant| |reciprocalPolynomial| |resize| |monomialIntPoly| + |pushuconst| |d01akf| |sinIfCan| |substitute| |yRange| |isMult| + |freeOf?| |lowerCase| |modularGcdPrimitive| |selectfirst| + |identification| |basisOfLeftAnnihilator| |palgLODE0| |checkForZero| + |exactQuotient| |lyndon| |cothIfCan| |removeDuplicates| |zRange| + |basisOfNucleus| |clipWithRanges| |fortranDouble| |bombieriNorm| + |c06eaf| |e02adf| |s17ahf| |/\\| |lists| |linear?| |radPoly| |schema| + |lazyPseudoQuotient| |bracket| |parts| |purelyTranscendental?| |map!| + |setrest!| |applyRules| |transcendent?| |term| |node?| |position!| + |evenInfiniteProduct| |elementary| |cyclotomic| |s17dlf| + |mainPrimitivePart| |iicoth| |OMgetFloat| |qsetelt!| |imagJ| + |fglmIfCan| |fortranComplex| |symbol?| |divisor| |clearTheIFTable| + |pointColorPalette| |normalizedDivide| |eigenvalues| GF2FG |redPo| + |bsolve| |andOperands| |leadingIdeal| |badNum| |selectPolynomials| + |polygon?| |noLinearFactor?| |low| |createMultiplicationMatrix| + |sech2cosh| |exptMod| |cscIfCan| |jacobian| |hasHi| |setelt| |powers| + |leftUnits| |Ei| |const| |factorset| |idealiserMatrix| + |fullPartialFraction| |getPickedPoints| + |dimensionOfIrreducibleRepresentation| |f04jgf| |nthExponent| + |squareTop| |setProperty!| |setProperty| |f02aff| |innerint| + |direction| |dark| |getProperties| |plus| |separate| |setValue!| + |commonDenominator| |scaleRoots| |notOperand| |copy| + |integralRepresents| |reverse!| |pushucoef| |s20acf| |tanh2coth| + |hasTopPredicate?| |cTan| |s13aaf| |lazyIrreducibleFactors| |not| + |f04faf| |pToDmp| |acsch| |rationalPoint?| |createIrreduciblePoly| + |useEisensteinCriterion?| |numberOfFractionalTerms| |minPoints| + |presub| |totalfract| |sdf2lst| |groebgen| + |semiResultantEuclideannaif| |degree| ^= |limitedint| |badValues| + |csubst| |symbolTable| |adaptive?| |internalSubQuasiComponent?| + |linGenPos| |overlap| |properties| |rk4a| |quasiAlgebraicSet| + |determinant| |bag| |notelem| |autoCoerce| |taylorQuoByVar| |identity| + |optAttributes| |headRemainder| |clearDenominator| |setAdaptive3D| + |zeroSetSplit| |toScale| |iidsum| |diophantineSystem| |setImagSteps| + |multisect| |numberOfOperations| |s21bdf| |pushFortranOutputStack| + |pmintegrate| |rightFactorIfCan| |graphState| |f01rcf| |f04mbf| |max| + |leftZero| |writable?| |makeUnit| |central?| |trailingCoefficient| + |expenseOfEvaluation| |popFortranOutputStack| |controlPanel| + |wrregime| |redmat| |e02gaf| |surface| |aspFilename| |predicates| + |say| |cyclePartition| |unit| |gcdcofactprim| |distdfact| |nthCoef| + |fortranLogical| |chineseRemainder| |OMreadStr| |leaves| + |rationalIfCan| |outputAsFortran| |solveid| |s17def| + |OMencodingBinary| |vconcat| |translate| |initiallyReduce| |maxint| + |insertionSort!| |f02bjf| |move| |makeEq| |keys| |primitivePart!| + |FormatRoman| |mindeg| |readLine!| |splitDenominator| + |factorSFBRlcUnit| |prefixRagits| |tracePowMod| |s19aaf| |times| + |repeating?| |unravel| |LazardQuotient| |bezoutResultant| |socf2socdf| + |OMmakeConn| |setVariableOrder| |LazardQuotient2| |deepestTail| + |eisensteinIrreducible?| |conditionP| |decimal| |ratpart| |randnum| + |hexDigit?| |att2Result| |newReduc| |mapSolve| |null?| |prod| |aCubic| + |tableau| |maxColIndex| |setStatus!| |fixPredicate| |biRank| + |toseLastSubResultant| |divisorCascade| |myDegree| |pascalTriangle| + |cAtanh| |minRowIndex| |sumSquares| |OMputEndApp| + |generalizedContinuumHypothesisAssumed?| |alphabetic| |transform| + |virtualDegree| |integrate| |rootNormalize| |createPrimitivePoly| + |integers| |leadingCoefficientRicDE| |maxrank| |c06fpf| |lexico| + |wholeRadix| |derivationCoordinates| |nextPartition| |push!| |monom| + |imagk| |removeZero| |even?| |showAllElements| |createThreeSpace| + |hclf| |raisePolynomial| |setlast!| |e01sff| |genericRightTraceForm| + |permutation| |row| |argument| |makeViewport3D| + |cyclotomicDecomposition| |packageCall| |listConjugateBases| + |dmpToHdmp| |cotIfCan| |exponential| |key| |characteristicPolynomial| + |s17acf| |coord| |setPosition| |symmetricPower| |figureUnits| |rarrow| + |iiacoth| |back| |options| |messagePrint| |isList| |asinhIfCan| + |light| |pseudoRemainder| |degreeSubResultantEuclidean| |common| + |nextsubResultant2| |s19abf| |quasiRegular?| |separateFactors| + |f01bsf| |generic| |solid?| |LyndonWordsList| |createPrimitiveElement| + |rk4f| |polygon| |lineColorDefault| |nodes| |unary?| |edf2df| |e02aef| + |pushdown| |cPower| |finite?| |fortranReal| |transpose| |elt| + |setchildren!| |inR?| |redpps| |filename| |printTypes| + |curveColorPalette| |wronskianMatrix| |irreducibleRepresentation| + |f01brf| |schwerpunkt| |getMeasure| |argscript| |heapSort| + |mainMonomials| |rightPower| |initializeGroupForWordProblem| |romberg| + |stFunc1| |triangular?| |basisOfRightAnnihilator| |complexEigenvalues| + |slex| |revert| |lifting| |leftExactQuotient| |setErrorBound| |write!| + |curryRight| |OMParseError?| |vector| |mainVariables| |not?| + |setPrologue!| |size?| |makeVariable| |iicsc| |operation| |e02zaf| + |rightUnits| |hasPredicate?| |leftCharacteristicPolynomial| |prime?| + |someBasis| |leadingIndex| |sPol| |parametersOf| |parse| + |differentiate| |OMlistSymbols| |fixedPoints| + |leftRegularRepresentation| |mapUp!| |presuper| |reverseLex| + |radicalEigenvector| |clipParametric| |eigenvector| |clip| + |characteristic| |df2st| |cond| |branchPointAtInfinity?| |meshPar1Var| + |absolutelyIrreducible?| |enterPointData| |leftOne| + |exteriorDifferential| |UnVectorise| |baseRDE| |has?| + |createLowComplexityTable| |imaginary| |aQuartic| |modularFactor| + |d02bbf| |seed| |isTimes| |e02dff| |denominator| |ffactor| |delta| + |palglimint0| |setright!| |LyndonBasis| |shellSort| |OMconnectTCP| + |cn| |cAcsch| |implies?| |collect| |normalize| |viewPhiDefault| + |trigs2explogs| |drawToScale| |leadingBasisTerm| + |unrankImproperPartitions1| |bits| |drawCurves| |iicot| |d01asf| + |getSyntaxFormsFromFile| |s17dhf| |particularSolution| |dim| |pushup| + |createNormalPrimitivePoly| |computePowers| |cross| + |euclideanGroebner| |d01anf| |accuracyIF| |tanAn| |solveRetract| + |tanintegrate| |laplacian| |parent| |solveLinearPolynomialEquation| + |mergeDifference| |removeRoughlyRedundantFactorsInPol| |gcdPrimitive| + |inGroundField?| |sizeLess?| |sort!| |primes| |sinhIfCan| + |viewDeltaXDefault| |OMwrite| |gcdprim| |strongGenerators| + |normalDeriv| RF2UTS |width| |stFuncN| |subResultantChain| + |roughBase?| |nullSpace| |equiv| |quadraticNorm| |numFunEvals| + |f04arf| |atrapezoidal| |s17agf| |unitVector| |cycleElt| |upperCase!| + |callForm?| |pseudoQuotient| |OMUnknownSymbol?| |aLinear| |computeInt| + |components| |completeEval| |OMputAtp| |omError| |module| + |factorOfDegree| |lambda| |sumOfDivisors| |palgextint| |zoom| + |primeFactor| |subNode?| |bubbleSort!| |cardinality| |ptFunc| + |cot2trig| |weierstrass| |OMgetBind| |digamma| + |rightRegularRepresentation| |complexNormalize| |constant| + |singularAtInfinity?| |tubeRadius| |bernoulliB| |one?| |weighted| + |critpOrder| |listOfLists| |OMgetAtp| |writeLine!| |makeFR| |Ci| + |optional| |algebraicSort| |ParCond| |plenaryPower| |laguerre| + |modularGcd| |cAcsc| |reflect| |generalizedContinuumHypothesisAssumed| + |rotate!| |divideExponents| |dimensionsOf| |topPredicate| |erf| + |makeMulti| |index| |primitivePart| |sqfrFactor| |cycleTail| + |newTypeLists| LODO2FUN |mesh| |quoByVar| |rootSplit| |hdmpToP| |top!| + |leadingTerm| |mainSquareFreePart| |multiplyExponents| |operators| + |mightHaveRoots| |generalPosition| |cyclicSubmodule| |dilog| |pair| + |complexForm| |setOfMinN| |binding| |basis| |sin| |cyclicEqual?| + |resultant| |pointData| |stop| |npcoef| |antiAssociative?| + |PollardSmallFactor| |formula| |cos| |relationsIdeal| + |fixedPointExquo| |reduceByQuasiMonic| |internalIntegrate| |\\/| + |updatD| |pack!| |tan| |setleaves!| |solve| |roughBasicSet| + |karatsubaDivide| |cot| |OMgetAttr| |paren| |returnType!| |An| |green| + |super| |is?| |sec| |rootSimp| |Frobenius| |d03eef| |imagj| + |infieldint| |supRittWu?| |lepol| |zero?| |pr2dmp| |csc| |numer| + |primPartElseUnitCanonical!| |nrows| |branchPoint?| |hyperelliptic| + |rightMult| |internalAugment| |exponents| |d01gaf| |pop!| |asin| + |axesColorDefault| |denom| |ncols| |squareFreePart| |getDatabase| + |legendre| |backOldPos| |imagK| |acos| |radicalSolve| |invmultisect| + |aQuadratic| |message| |realElementary| |status| |ldf2vmf| |printCode| + |f02adf| |atan| |normal01| |extractClosed| |rightTrim| |pi| + |viewWriteAvailable| |read!| |conjugate| |solveInField| + |lazyIntegrate| |obj| |d02gbf| |content| |acot| |infinity| |ridHack1| + |leftTrim| |cyclicEntries| |OMputEndObject| |countRealRootsMultiple| + |drawComplexVectorField| |halfExtendedSubResultantGcd1| |rightRank| + |blue| |linearPart| |asec| |logpart| |cache| |reduction| |thetaCoord| + |in?| |unit?| |iicos| |clipPointsDefault| |f01qcf| |acsc| + |plusInfinity| |sturmVariationsOf| |eulerPhi| |name| |rootRadius| + |gramschmidt| |dihedralGroup| |cons| |leftDiscriminant| |vertConcat| + |s14aaf| |sinh| |terms| |minusInfinity| |subNodeOf?| |f02wef| |dom| + |lazyGintegrate| |divergence| |leftFactor| |label| |lowerCase?| + |leftScalarTimes!| |cosh| |enqueue!| |list?| |monomials| + |purelyAlgebraicLeadingMonomial?| |charthRoot| + |removeSuperfluousCases| |sumOfSquares| |kernel| |tanh| + |constantCoefficientRicDE| |stoseIntegralLastSubResultant| |besselJ| + |typeList| |wholePart| |rightUnit| |palgRDE| |enterInCache| |draw| + |coth| |moreAlgebraic?| |polygamma| |stoseInvertible?sqfreg| + |monicDivide| |groebner| |headReduced?| |exp1| |localAbs| |coshIfCan| + |extractBottom!| |d02kef| |sech| |sincos| |allRootsOf| |iibinom| + |leftRecip| |element?| |cyclicGroup| |inverse| |setRow!| + |highCommonTerms| |eigenMatrix| |odd?| |iCompose| |f01ref| + |appendPoint| |algint| |title| |alphabetic?| |sn| |cCoth| |f02xef| + |goodPoint| |simpleBounds?| |screenResolution3D| + |rewriteSetWithReduction| |makeObject| |inc| |cAsin| |outputForm| + |hspace| |graphCurves| |s17akf| |e| |inf| |logGamma| |fTable| + |ricDsolve| |antisymmetricTensors| |constDsolve| |algebraicOf| |error| + |fixedPoint| |nthFactor| |pdct| |mainMonomial| |coHeight| |coef| + |critBonD| |rk4| |assert| |close!| |loopPoints| |ef2edf| + |deleteRoutine!| |quadraticForm| |shuffle| |qinterval| |duplicates?| + |curveColor| |bat1| |semiResultantReduitEuclidean| |debug| + |getZechTable| |ideal| |subTriSet?| |option| |inRadical?| |squareFree| + |limitPlus| |selectMultiDimensionalRoutines| |lazyEvaluate| + |linearDependenceOverZ| |Lazard| |chiSquare1| |twoFactor| |Hausdorff| + |integralAtInfinity?| |evenlambert| |iicsch| |listYoungTableaus| + |integralCoordinates| |node| |ramifiedAtInfinity?| |entry| |debug3D| + |modifyPointData| |s18aff| |setScreenResolution| |pdf2df| + |mainVariable| |red| |stiffnessAndStabilityOfODEIF| |rootPower| + |complexNumericIfCan| |internalLastSubResultant| |atanIfCan| |taylor| + |times!| |merge| ** |integerBound| |shade| |pquo| |setMinPoints3D| + |laurent| |iiGamma| |ScanArabic| |float| |slash| + |indiceSubResultantEuclidean| |symFunc| |e02ajf| |puiseux| |asimpson| + |bumptab1| |failed| |arrayStack| |scanOneDimSubspaces| |morphism| EQ + |float?| |OMputObject| |chebyshevU| |rangeIsFinite| |primextendedint| + |monomRDEsys| |weight| |inv| |cCosh| |equiv?| |ord| |subSet| + |monicDecomposeIfCan| |ground?| |compiledFunction| |complement| + |fixedDivisor| |ravel| |groebnerFactorize| |numberOfDivisors| + |totalLex| |ground| |quasiRegular| |separateDegrees| |iiabs| + |directory| |zeroDim?| |reshape| |halfExtendedSubResultantGcd2| + |diagonalMatrix| |leadingMonomial| |extractProperty| |gbasis| |d03edf| + |laplace| |ODESolve| |dimension| |elliptic| |leadingCoefficient| + |represents| |e01bhf| |basisOfLeftNucleus| |recoverAfterFail| + |removeSinhSq| |quadratic| |f02awf| |primitiveMonomials| |zeroMatrix| + |OMencodingSGML| GE |localUnquote| |padicallyExpand| + |patternMatchTimes| |droot| |subscriptedVariables| |reductum| + |isPower| |printingInfo?| GT |printInfo| |orbit| |setAdaptive| + |definingInequation| |credPol| |createLowComplexityNormalBasis| + |block| |d01fcf| LE |completeHensel| FG2F |resultantEuclidean| + |update| |maxPoints| |divideIfCan| |pushNewContour| |traverse| LT + |shallowExpand| |rowEchelonLocal| |e01sef| |minrank| |plus!| + |setleft!| |create| |iomode| |car| |expextendedint| + |semicolonSeparate| |edf2efi| |polynomialZeros| |goto| |eq| + |showIntensityFunctions| |binaryFunction| |rangePascalTriangle| |cdr| + |addPoint| |leftLcm| |vspace| |numberOfNormalPoly| |iter| + |OMcloseConn| |interpolate| |outlineRender| |e04ucf| |factorsOfDegree| + |OMputEndAttr| |acothIfCan| |child?| |extract!| |sort| |log10| |empty| + |coth2trigh| UTS2UP |zeroDimPrime?| |palgLODE| |drawStyle| + |tubeRadiusDefault| |rectangularMatrix| |henselFact| + |oneDimensionalArray| |palgextint0| |less?| |rootPoly| + |fortranCharacter| |lfinfieldint| |monicRightFactorIfCan| |position| + |f02aef| |moduloP| |repSq| |setLabelValue| |c06gcf| |rightGcd| + |OMputBind| |euler| |yCoord| |makeYoungTableau| + |removeRedundantFactors| |nthr| |iiatan| |consnewpol| |dihedral| + |sncndn| |trunc| |addiag| |queue| |moebiusMu| |li| + |stoseInvertibleSetreg| |GospersMethod| |ratDsolve| |signAround| + |lexTriangular| |stoseInvertibleSetsqfreg| |mapdiv| |groebSolve| + |random| |defineProperty| |constantLeft| |reindex| |e02daf| + |normalizeAtInfinity| |cylindrical| |leftUnit| |setsubMatrix!| + |digits| |regime| |sign| |traceMatrix| |exp| |totalDegree| |epilogue| + |LagrangeInterpolation| |setButtonValue| |makeGraphImage| |twist| + |curve| |insert!| |powern| |sample| |hconcat| |doubleDisc| + |pseudoDivide| |deleteProperty!| |submod| |listOfMonoms| + |ellipticCylindrical| |shanksDiscLogAlgorithm| |basisOfCenter| + |expint| |lowerPolynomial| |solveLinear| |tanIfCan| |distance| + |f02ajf| |e02bdf| |sparsityIF| |integralDerivationMatrix| |augment| + |localIntegralBasis| |e04dgf| |polyPart| |f02bbf| |normInvertible?| + |getMatch| |setfirst!| |leaf?| |cyclic?| |doubleComplex?| |adjoint| + |rules| |cfirst| |halfExtendedResultant1| |unitNormal| |rk4qc| + |quotedOperators| |cycleRagits| |RemainderList| |distribute| + |getMultiplicationTable| |nullary?| |leastMonomial| |xn| |leftTrace| + |directSum| |addBadValue| |pile| |overlabel| |brillhartIrreducible?| + |nthRootIfCan| |isAbsolutelyIrreducible?| |distFact| |critMTonD1| + |toseInvertible?| |sin2csc| |numberOfVariables| |constantOperator| + |sortConstraints| |comparison| |expPot| |split| |curryLeft| + |getExplanations| |iiatanh| |setnext!| |df2fi| |entry?| + |boundOfCauchy| |crest| |viewThetaDefault| |solveLinearlyOverQ| + |nilFactor| |generalizedEigenvector| |rst| |d02cjf| |partialFraction| + |implies| |multiEuclideanTree| |leftFactorIfCan| |c06fuf| |multMonom| + |tablePow| |quotient| |mantissa| |rur| |leftGcd| |xor| |symmetric?| + |pade| |nextSubsetGray| |c05pbf| |numericalIntegration| |critM| + |rewriteIdealWithRemainder| |e02bcf| |setOrder| |dequeue| + |possiblyNewVariety?| |expIfCan| |makeSketch| |finiteBound| + |bernoulli| |selectFiniteRoutines| |double| |nthFlag| + |variationOfParameters| |internalInfRittWu?| |ocf2ocdf| |prefix| + |pointColor| |shufflein| |compactFraction| |gradient| |OMlistCDs| + |brace| |cosh2sech| |OMputApp| |subResultantGcd| |deepExpand| |every?| + |d02bhf| |reducedDiscriminant| |e02ahf| |externalList| + |selectSumOfSquaresRoutines| |monicCompleteDecompose| |empty?| + |truncate| |minIndex| |OMbindTCP| |diagonal?| |simpsono| |monomial| + |test| |varselect| |approxSqrt| |semiSubResultantGcdEuclidean1| + |lifting1| |prologue| |changeVar| |irreducible?| |jacobiIdentity?| + |coordinates| |mainCharacterization| |quadratic?| |radicalSimplify| + |cLog| |rationalPower| |compBound| |definingEquations| |dec| + |rational?| |multivariate| |mpsode| |iisqrt2| |sin?| + |fortranLiteralLine| |rightRemainder| |value| |setMinPoints| + |declare!| |ipow| |tanQ| |rightTraceMatrix| |homogeneous?| |variables| + |mapCoef| |OMgetEndAtp| |PDESolve| |supersub| |basicSet| + |discriminantEuclidean| |normalDenom| |OMopenFile| |iiasec| + |squareFreePolynomial| |rotatez| |finiteBasis| |dictionary| + |idealSimplify| |trapezoidalo| |llprop| |oddlambert| |delete!| |cAsec| + |genericLeftTraceForm| |e01sbf| |f02agf| |monicModulo| |merge!| + |resetAttributeButtons| |superHeight| |lexGroebner| |trueEqual| + |mainKernel| |polyRicDE| |minimumDegree| |stoseInvertible?| + |HermiteIntegrate| |insertRoot!| |closedCurve?| |d01amf| |tree| + |characteristicSet| |changeName| |physicalLength!| |irreducibleFactor| + |tubePointsDefault| |inrootof| |reduceLODE| |antiCommutative?| + |polCase| |univariatePolynomialsGcds| |getProperty| + |useSingleFactorBound?| |relerror| |imagi| |changeMeasure| + |generalInfiniteProduct| |decrease| |exprToXXP| |product| + |tryFunctionalDecomposition?| |#| |floor| |palginfieldint| + |horizConcat| |solid| |diff| |associative?| |roughEqualIdeals?| + |OMgetEndError| |LiePolyIfCan| |stoseInvertible?reg| |laurentRep| + |positive?| |And| |doublyTransitive?| |quotientByP| |mkcomm| + |showFortranOutputStack| |OMgetVariable| |univariatePolynomial| + |integerIfCan| |anticoord| |polyRDE| |possiblyInfinite?| + |safetyMargin| |Or| |iisqrt3| |semiLastSubResultantEuclidean| + |computeCycleEntry| |wreath| |bandedJacobian| ^ + |stiffnessAndStabilityFactor| |pmComplexintegrate| |e04mbf| + |var1StepsDefault| |genericLeftDiscriminant| |Not| |copyInto!| + |youngGroup| |char| |genericRightNorm| |sinhcosh| |untab| + |problemPoints| |high| |swapRows!| |f07fdf| |scan| |sum| |universe| + |fortranTypeOf| |squareFreeLexTriangular| |degreePartition| |OMgetApp| + |constantOpIfCan| |ref| |rowEchLocal| |removeCosSq| |eyeDistance| + |satisfy?| |roman| |elRow1!| |removeRedundantFactorsInPols| |head| + |prolateSpheroidal| |linearAssociatedOrder| |conjug| |conjugates| + |bivariatePolynomials| |cyclotomicFactorization| |unitsColorDefault| + |term?| |integralBasisAtInfinity| |subResultantGcdEuclidean| |s17aff| + |OMgetString| |rewriteIdealWithHeadRemainder| + |removeRoughlyRedundantFactorsInPols| |extractPoint| |s18aef| |pole?| + |addmod| |univariatePolynomials| |OMconnOutDevice| |rightNorm| |ksec| + |dflist| |selectsecond| |cAsinh| |hdmpToDmp| |f04asf| |cycles| + |precision| |stosePrepareSubResAlgo| |getBadValues| |linear| + |readIfCan!| |dmpToP| |structuralConstants| |cAcoth| |setTopPredicate| + |numberOfCycles| |clikeUniv| |minimize| |beauzamyBound| |Zero| + |tan2cot| |duplicates| |retractIfCan| |countRealRoots| |lieAlgebra?| + |generalTwoFactor| |listexp| |semiDiscriminantEuclidean| + |flexibleArray| |ddFact| |numberOfChildren| |One| |polynomial| + |realZeros| |clearFortranOutputStack| |comp| |hessian| |OMputString| + |expressIdealMember| |lhs| |pointColorDefault| |changeBase| |s21bbf| + |minordet| |mathieu22| |linearAssociatedLog| |abelianGroup| + |identitySquareMatrix| |explicitEntries?| |xCoord| |rhs| |digit?| + |symmetricProduct| |rootBound| |e01bff| |constructorName| + |removeZeroes| |depth| |orthonormalBasis| |errorInfo| |patternMatch| + |selectIntegrationRoutines| |negative?| |elements| + |genericRightMinimalPolynomial| |legendreP| |bfEntry| |next| + |complexIntegrate| |dn| |points| |mkAnswer| |invertIfCan| + |useSingleFactorBound| |setScreenResolution3D| |ranges| |c06gqf| + |leftRemainder| |multiset| |convergents| |Si| |hermiteH| |deriv| + |cCsc| |lyndon?| |root| |endOfFile?| |nextIrreduciblePoly| + |firstUncouplingMatrix| |rightCharacteristicPolynomial| + |normalElement| |complexRoots| |minimumExponent| |complexSolve| + |unexpand| |s18acf| |Is| |minGbasis| |systemCommand| |c06fqf| |bfKeys| + |toroidal| |OMputError| |semiSubResultantGcdEuclidean2| |prinshINFO| + |extractIndex| |gcdcofact| |palgint0| |primintfldpoly| |lazyPquo| + |copies| |lazy?| |e02baf| |screenResolution| |pomopo!| |inconsistent?| + |OMputEndBVar| |outputFixed| |symmetricTensors| |cAcosh| |normal| + |airyBi| |number?| |blankSeparate| |orOperands| + |semiResultantEuclidean1| |palglimint| |c05adf| |quote| |coleman| + |scale| |setAttributeButtonStep| |map| |box| + |createPrimitiveNormalPoly| |reopen!| |mainCoefficients| |compdegd| + |lazyResidueClass| |lfintegrate| |append| |startStats!| |triangulate| + |fortranLinkerArgs| |rightFactorCandidate| |jordanAlgebra?| |leftRank| + |basisOfCentroid| |mainVariable?| |algSplitSimple| |point?| + |zeroSetSplitIntoTriangularSystems| |laurentIfCan| |any| NOT + |tableForDiscreteLogarithm| |nextPrimitivePoly| |delete| |singRicDE| + |cSec| |removeSinSq| |binaryTree| |supDimElseRittWu?| |iisech| + |infieldIntegrate| |bipolar| OR |zeroSquareMatrix| |htrigs| + |numberOfComputedEntries| |midpoint| |assign| |s14abf| |partitions| + |errorKind| |Lazard2| |uniform01| |rootOfIrreduciblePoly| AND + |nextPrimitiveNormalPoly| |exponent| |powmod| |changeWeightLevel| + |setMaxPoints3D| |internalZeroSetSplit| |BasicMethod| + |initiallyReduced?| |monicRightDivide| |compound?| |nary?| + |lieAdmissible?| |mathieu11| |e04fdf| |integer?| |order| |convert| + |sylvesterMatrix| |bitTruth| |substring?| |atanhIfCan| |baseRDEsys| + |stripCommentsAndBlanks| |derivative| |univariateSolve| |branchIfCan| + |swap!| |composite| |showTypeInOutput| |frobenius| |iipow| + |irreducibleFactors| |coerceP| |complexLimit| |startPolynomial| + |seriesToOutputForm| |replaceKthElement| |rubiksGroup| |numeric| + |headReduce| |repeatUntilLoop| |iiasin| |zerosOf| |suffix?| |aromberg| + |linearPolynomials| |factorSquareFree| |radical| |elRow2!| + |getOperator| |c06ekf| |d01bbf| |prime| |nextColeman| |quickSort| + |lfextlimint| |splitSquarefree| |open?| |generators| + |factorByRecursion| |ParCondList| |resultantEuclideannaif| + |interReduce| |recip| |UpTriBddDenomInv| |fintegrate| |double?| |heap| + |nthFractionalTerm| |lintgcd| |infinite?| |prefix?| |froot| + |meshFun2Var| |contractSolve| |overbar| |showRegion| |extend| + |equality| |perfectSqrt| |init| |UP2ifCan| |crushedSet| + |resetBadValues| |graeffe| |completeSmith| |leftRankPolynomial| + |LyndonCoordinates| |e01bgf| |iteratedInitials| |zeroDimPrimary?| + |meshPar2Var| |ode| |oblateSpheroidal| |d01ajf| |readable?| + |primaryDecomp| |patternVariable| |midpoints| |SturmHabichtSequence| + |overset?| |bitCoef| |generalizedEigenvectors| |partialDenominators| + |tail| |difference| |explicitlyEmpty?| |f01qef| * |elem?| + |OMsetEncoding| |lazyPrem| |e04jaf| |sec2cos| |chainSubResultants| + |zeroVector| |internal?| |zeroOf| |f01qdf| |OMgetSymbol| |scripted?| + |characteristicSerie| |OMread| |combineFeatureCompatibility| + |selectODEIVPRoutines| |flatten| |basisOfMiddleNucleus| + |matrixConcat3D| |mkIntegral| |cAtan| |squareFreeFactors| |d02raf| + |iiacsch| |commutative?| |diag| |coefChoose| |infix?| |symmetricGroup| + |cosSinInfo| |approximate| |reseed| |karatsubaOnce| |completeHermite| + |mask| |f07aef| |remainder| |approxNthRoot| |plotPolar| |complex| + |phiCoord| |simplifyExp| |bezoutDiscriminant| |gethi| |vedf2vef| + |search| |intChoose| |algebraicDecompose| |mr| |localReal?| |showAll?| + |complexZeros| |splitLinear| |fractRagits| |s01eaf| |dimensions| + |factorSquareFreePolynomial| |e01daf| |dot| |minus!| |secIfCan| + |bandedHessian| |randomR| |replace| |length| |euclideanSize| |reset| + |rotatey| |dioSolve| |rightDiscriminant| |prevPrime| |cschIfCan| + |lquo| |scripts| |testDim| |exponentialOrder| |minColIndex| + |outerProduct| |weights| |factors| |getlo| |antisymmetric?| |write| + |nullary| |unrankImproperPartitions0| |restorePrecision| |startTable!| + |currentEnv| |f2st| |failed?| |front| |wholeRagits| |stack| |save| + |setColumn!| |algDsolve| |power| |putGraph| |sayLength| + |extendedResultant| |bipolarCylindrical| |internalSubPolSet?| + |numberOfPrimitivePoly| |permutationRepresentation| |or| + |permutationGroup| |LowTriBddDenomInv| |flagFactor| |infLex?| + |matrixGcd| |setPoly| |hypergeometric0F1| |extendIfCan| |and| + |rightMinimalPolynomial| |addMatchRestricted| |belong?| |fractRadix| + |members| |rdregime| |c02agf| |se2rfi| |categoryFrame| |s13acf| + |prepareSubResAlgo| |endSubProgram| |iiasech| |lex| |isOp| + |composites| |arity| |currentSubProgram| |lp| |symmetricDifference| + |tanNa| |mapMatrixIfCan| F |medialSet| |safeCeiling| |OMreadFile| + |opeval| |prem| |processTemplate| |minPoints3D| |e01saf| |cot2tan| + |setProperties| |magnitude| |leadingExponent| |halfExtendedResultant2| + |maxPoints3D| |logIfCan| |isQuotient| |neglist| |extendedint| + |interpretString| |cCos| |arg1| |qroot| |getGraph| |abs| |varList| + |numericalOptimization| |printInfo!| |showScalarValues| + |innerEigenvectors| |kovacic| |f04maf| |primintegrate| |arg2| + |numberOfIrreduciblePoly| |wordsForStrongGenerators| |initials| + |exactQuotient!| |upperCase| |reducedContinuedFraction| |prinb| + |cosIfCan| |vark| |superscript| |OMsupportsCD?| |diagonalProduct| + |padicFraction| |int| |getOrder| |makeCrit| |numberOfFactors| + |critMonD1| |lyndonIfCan| |numberOfImproperPartitions| |c06ecf| + |conditions| |bezoutMatrix| |shrinkable| |pow| |clipSurface| + |showTheIFTable| |quasiMonicPolynomials| |divide| |iiacsc| + |factorList| |f02abf| |numFunEvals3D| |printHeader| |concat| |match| + |iroot| |shiftRoots| |hash| |removeRedundantFactorsInContents| + |member?| |squareMatrix| |makeSUP| |height| |multiEuclidean| + |mapBivariate| |d01aqf| |coercePreimagesImages| |resetNew| |minPoly| + |seriesSolve| |count| |outputGeneral| |qqq| |push| |splitConstant| + |prindINFO| |optional?| |fractionPart| |create3Space| + |explicitlyFinite?| |leftAlternative?| |critB| |minimalPolynomial| + |coerceImages| |groebnerIdeal| |OMgetEndObject| |integralMatrix| + |birth| |factorAndSplit| |charpol| |setLegalFortranSourceExtensions| + |nextItem| |rotate| |torsionIfCan| |addPoint2| |f01mcf| |nthExpon| + |mapUnivariateIfCan| |perfectNthRoot| |innerSolve| |coordinate| + |getVariableOrder| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-838) -12 (|has| |#1| (-283)) (|has| |#1| (-838))) ((-849) -3708 (|has| |#1| (-324)) (|has| |#1| (-338)) (|has| |#1| (-283))) ((-928) -12 (|has| |#1| (-928)) (|has| |#1| (-1106))) ((-962 (-382 (-522))) |has| |#1| (-962 (-382 (-522)))) ((-962 (-522)) |has| |#1| (-962 (-522))) ((-962 |#1|) . T) ((-977 #0#) -3708 (|has| |#1| (-324)) (|has| |#1| (-338))) ((-977 |#1|) . T) ((-977 $) . T) ((-971) . T) ((-978) . T) ((-1026) . T) ((-1014) . T) ((-1061) |has| |#1| (-324)) ((-1106) |has| |#1| (-1106)) ((-1109) |has| |#1| (-1106)) ((-1120) . 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-382 (-522))) -3844 (|has| |#1| (-324)) (|has| |#1| (-338))) ((-37 |#1|) . T) ((-37 $) -3844 (|has| |#1| (-514)) (|has| |#1| (-324)) (|has| |#1| (-338)) (|has| |#1| (-283))) ((-34) |has| |#1| (-1106)) ((-91) |has| |#1| (-1106)) ((-97) . T) ((-107 #0# #0#) -3844 (|has| |#1| (-324)) (|has| |#1| (-338))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-124) . T) ((-133) -3844 (|has| |#1| (-324)) (|has| |#1| (-133))) ((-135) |has| |#1| (-135)) ((-562 (-792)) . T) ((-157) . T) ((-563 (-154 (-202))) |has| |#1| (-947)) ((-563 (-154 (-354))) |has| |#1| (-947)) ((-563 (-498)) |has| |#1| (-563 (-498))) ((-563 (-821 (-354))) |has| |#1| (-563 (-821 (-354)))) ((-563 (-821 (-522))) |has| |#1| (-563 (-821 (-522)))) ((-563 #1=(-1081 |#1|)) . T) ((-208 |#1|) . 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T) ((-285 |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((-343) |has| |#2| (-343)) ((-352 |#2|) |has| |#2| (-971)) ((-386 |#2|) |has| |#2| (-1014)) ((-461 |#2|) . T) ((-555 #0# |#2|) . T) ((-483 |#2| |#2|) -12 (|has| |#2| (-285 |#2|)) (|has| |#2| (-1014))) ((-590 |#2|) -3844 (|has| |#2| (-971)) (|has| |#2| (-338)) (|has| |#2| (-157))) ((-590 $) -3844 (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-584 (-522)) -12 (|has| |#2| (-584 (-522))) (|has| |#2| (-971))) ((-584 |#2|) |has| |#2| (-971)) ((-655 |#2|) -3844 (|has| |#2| (-338)) (|has| |#2| (-157))) ((-664) -3844 (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-728) |has| |#2| (-782)) ((-729) -3844 (|has| |#2| (-782)) (|has| |#2| (-730))) ((-730) |has| |#2| (-730)) ((-731) -3844 (|has| |#2| (-782)) (|has| |#2| (-730))) ((-732) -3844 (|has| |#2| (-782)) (|has| |#2| (-730))) ((-782) |has| |#2| (-782)) ((-784) -3844 (|has| |#2| (-782)) (|has| |#2| (-730))) ((-829 (-1085)) -12 (|has| |#2| (-829 (-1085))) (|has| |#2| (-971))) ((-962 (-382 (-522))) -12 (|has| |#2| (-962 (-382 (-522)))) (|has| |#2| (-1014))) ((-962 (-522)) -12 (|has| |#2| (-962 (-522))) (|has| |#2| (-1014))) ((-962 |#2|) |has| |#2| (-1014)) ((-977 |#2|) -3844 (|has| |#2| (-971)) (|has| |#2| (-338)) (|has| |#2| (-157))) ((-977 $) |has| |#2| (-157)) ((-971) -3844 (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-978) -3844 (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-1026) -3844 (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-1014) -3844 (|has| |#2| (-1014)) (|has| |#2| (-971)) (|has| |#2| (-782)) (|has| |#2| (-730)) (|has| |#2| (-343)) (|has| |#2| (-338)) (|has| |#2| (-157)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-1120) . T) ((-1173 |#2|) |has| |#2| (-338))) +((-3639 (((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 21)) (-2153 ((|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 23)) (-3810 (((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)) 18))) +(((-216 |#1| |#2| |#3|) (-10 -7 (-15 -3639 ((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -2153 (|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -3810 ((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)))) (-708) (-1120) (-1120)) (T -216)) +((-3810 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-217 *5 *6)) (-14 *5 (-708)) (-4 *6 (-1120)) (-4 *7 (-1120)) (-5 *2 (-217 *5 *7)) (-5 *1 (-216 *5 *6 *7)))) (-2153 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-217 *5 *6)) (-14 *5 (-708)) (-4 *6 (-1120)) (-4 *2 (-1120)) (-5 *1 (-216 *5 *6 *2)))) (-3639 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-217 *6 *7)) (-14 *6 (-708)) (-4 *7 (-1120)) (-4 *5 (-1120)) (-5 *2 (-217 *6 *5)) (-5 *1 (-216 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-46 |#1| #0=(-522)) . T) ((-25) . T) ((-37 #1=(-382 (-522))) -3844 (|has| |#1| (-338)) (|has| |#1| (-37 (-382 (-522))))) ((-37 |#1|) |has| |#1| (-157)) ((-37 |#2|) |has| |#1| (-338)) ((-37 $) -3844 (|has| |#1| (-514)) (|has| |#1| (-338))) ((-34) |has| |#1| (-37 (-382 (-522)))) ((-91) |has| |#1| (-37 (-382 (-522)))) ((-97) . T) ((-107 #1# #1#) -3844 (|has| |#1| (-338)) (|has| |#1| (-37 (-382 (-522))))) ((-107 |#1| |#1|) . T) ((-107 |#2| |#2|) |has| |#1| (-338)) ((-107 $ $) -3844 (|has| |#1| (-514)) (|has| |#1| (-338)) (|has| |#1| (-157))) ((-124) . T) ((-133) -3844 (-12 (|has| |#1| (-338)) (|has| |#2| (-133))) (|has| |#1| (-133))) ((-135) -3844 (-12 (|has| |#1| (-338)) (|has| |#2| (-135))) (|has| |#1| (-135))) ((-562 (-792)) . 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T) ((-590 |#2|) |has| |#1| (-338)) ((-590 $) . T) ((-584 (-522)) -12 (|has| |#1| (-338)) (|has| |#2| (-584 (-522)))) ((-584 |#2|) |has| |#1| (-338)) ((-655 #1#) -3844 (|has| |#1| (-338)) (|has| |#1| (-37 (-382 (-522))))) ((-655 |#1|) |has| |#1| (-157)) ((-655 |#2|) |has| |#1| (-338)) ((-655 $) -3844 (|has| |#1| (-514)) (|has| |#1| (-338))) ((-664) . 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(-1102 2822703 2823219 2823458 "TEXTFILE" 2823825 T TEXTFILE (NIL) -8 NIL NIL) (-1101 2820568 2821082 2821520 "TEX" 2822287 T TEX (NIL) -8 NIL NIL) (-1100 2820349 2820380 2820452 "TEX1" 2820531 NIL TEX1 (NIL T) -7 NIL NIL) (-1099 2819997 2820060 2820150 "TEMUTL" 2820281 T TEMUTL (NIL) -7 NIL NIL) (-1098 2818151 2818431 2818756 "TBCMPPK" 2819720 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1097 2810039 2816311 2816368 "TBAGG" 2816768 NIL TBAGG (NIL T T) -9 NIL 2816979) (-1096 2805109 2806597 2808351 "TBAGG-" 2808356 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1095 2804493 2804600 2804745 "TANEXP" 2804998 NIL TANEXP (NIL T) -7 NIL NIL) (-1094 2797994 2804350 2804443 "TABLE" 2804448 NIL TABLE (NIL T T) -8 NIL NIL) (-1093 2797407 2797505 2797643 "TABLEAU" 2797891 NIL TABLEAU (NIL T) -8 NIL NIL) (-1092 2792015 2793235 2794483 "TABLBUMP" 2796193 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1091 2788478 2789173 2789956 "SYSSOLP" 2791266 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1090 2784769 2785477 2786211 "SYNTAX" 2787766 T SYNTAX (NIL) -8 NIL NIL) (-1089 2781903 2782511 2783149 "SYMTAB" 2784153 T SYMTAB (NIL) -8 NIL NIL) (-1088 2777152 2778054 2779037 "SYMS" 2780942 T SYMS (NIL) -8 NIL NIL) (-1087 2774385 2776612 2776841 "SYMPOLY" 2776957 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1086 2773905 2773980 2774102 "SYMFUNC" 2774297 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1085 2769883 2771142 2771964 "SYMBOL" 2773105 T SYMBOL (NIL) -8 NIL NIL) (-1084 2763422 2765111 2766831 "SWITCH" 2768185 T SWITCH (NIL) -8 NIL NIL) (-1083 2756655 2762249 2762551 "SUTS" 2763177 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1082 2748548 2755776 2756056 "SUPXS" 2756432 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1081 2740080 2748169 2748294 "SUP" 2748457 NIL SUP (NIL T) -8 NIL NIL) (-1080 2739239 2739366 2739583 "SUPFRACF" 2739948 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1079 2738864 2738923 2739034 "SUP2" 2739174 NIL SUP2 (NIL T T) -7 NIL NIL) (-1078 2737282 2737556 2737918 "SUMRF" 2738563 NIL SUMRF (NIL T) -7 NIL NIL) (-1077 2736599 2736665 2736863 "SUMFS" 2737203 NIL SUMFS (NIL T T) -7 NIL NIL) (-1076 2720538 2735780 2736030 "SULS" 2736406 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1075 2719860 2720063 2720203 "SUCH" 2720446 NIL SUCH (NIL T T) -8 NIL NIL) (-1074 2713787 2714799 2715757 "SUBSPACE" 2718948 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1073 2713217 2713307 2713471 "SUBRESP" 2713675 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1072 2706586 2707882 2709193 "STTF" 2711953 NIL STTF (NIL T) -7 NIL NIL) (-1071 2700759 2701879 2703026 "STTFNC" 2705486 NIL STTFNC (NIL T) -7 NIL NIL) (-1070 2692110 2693977 2695770 "STTAYLOR" 2699000 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1069 2685354 2691974 2692057 "STRTBL" 2692062 NIL STRTBL (NIL T) -8 NIL NIL) (-1068 2680745 2685309 2685340 "STRING" 2685345 T STRING (NIL) -8 NIL NIL) (-1067 2675633 2680118 2680149 "STRICAT" 2680208 T STRICAT (NIL) -9 NIL 2680270) (-1066 2668349 2673156 2673776 "STREAM" 2675048 NIL STREAM (NIL T) -8 NIL NIL) (-1065 2667859 2667936 2668080 "STREAM3" 2668266 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1064 2666841 2667024 2667259 "STREAM2" 2667672 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1063 2666529 2666581 2666674 "STREAM1" 2666783 NIL STREAM1 (NIL T) -7 NIL NIL) (-1062 2665545 2665726 2665957 "STINPROD" 2666345 NIL STINPROD (NIL T) -7 NIL NIL) (-1061 2665123 2665307 2665338 "STEP" 2665418 T STEP (NIL) -9 NIL 2665496) (-1060 2658666 2665022 2665099 "STBL" 2665104 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1059 2653841 2657888 2657932 "STAGG" 2658085 NIL STAGG (NIL T) -9 NIL 2658174) (-1058 2651543 2652145 2653017 "STAGG-" 2653022 NIL STAGG- (NIL T T) -8 NIL NIL) (-1057 2649738 2651313 2651405 "STACK" 2651486 NIL STACK (NIL T) -8 NIL NIL) (-1056 2642469 2647885 2648340 "SREGSET" 2649368 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1055 2634909 2636277 2637789 "SRDCMPK" 2641075 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1054 2627876 2632349 2632380 "SRAGG" 2633683 T SRAGG (NIL) -9 NIL 2634291) (-1053 2626893 2627148 2627527 "SRAGG-" 2627532 NIL SRAGG- (NIL T) -8 NIL NIL) (-1052 2621342 2625812 2626239 "SQMATRIX" 2626512 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1051 2615094 2618062 2618788 "SPLTREE" 2620688 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1050 2611084 2611750 2612396 "SPLNODE" 2614520 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1049 2610130 2610363 2610394 "SPFCAT" 2610838 T SPFCAT (NIL) -9 NIL NIL) (-1048 2608867 2609077 2609341 "SPECOUT" 2609888 T SPECOUT (NIL) -7 NIL NIL) (-1047 2608628 2608668 2608737 "SPADPRSR" 2608820 T SPADPRSR (NIL) -7 NIL NIL) (-1046 2600650 2602397 2602440 "SPACEC" 2606763 NIL SPACEC (NIL T) -9 NIL 2608579) (-1045 2598822 2600583 2600631 "SPACE3" 2600636 NIL SPACE3 (NIL T) -8 NIL NIL) (-1044 2597574 2597745 2598036 "SORTPAK" 2598627 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1043 2595630 2595933 2596351 "SOLVETRA" 2597238 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1042 2594641 2594863 2595137 "SOLVESER" 2595403 NIL SOLVESER (NIL T) -7 NIL NIL) (-1041 2589861 2590742 2591744 "SOLVERAD" 2593693 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1040 2585676 2586285 2587014 "SOLVEFOR" 2589228 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1039 2579975 2585027 2585124 "SNTSCAT" 2585129 NIL SNTSCAT (NIL T T T T) -9 NIL 2585199) (-1038 2574080 2578306 2578696 "SMTS" 2579665 NIL SMTS (NIL T T T) -8 NIL NIL) (-1037 2568491 2573969 2574045 "SMP" 2574050 NIL SMP (NIL T T) -8 NIL NIL) (-1036 2566650 2566951 2567349 "SMITH" 2568188 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1035 2559614 2563810 2563913 "SMATCAT" 2565253 NIL SMATCAT (NIL NIL T T T) -9 NIL 2565802) (-1034 2556555 2557378 2558555 "SMATCAT-" 2558560 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1033 2554268 2555791 2555835 "SKAGG" 2556096 NIL SKAGG (NIL T) -9 NIL 2556231) (-1032 2550326 2553372 2553650 "SINT" 2554012 T SINT (NIL) -8 NIL NIL) (-1031 2550098 2550136 2550202 "SIMPAN" 2550282 T SIMPAN (NIL) -7 NIL NIL) (-1030 2548936 2549157 2549432 "SIGNRF" 2549857 NIL SIGNRF (NIL T) -7 NIL NIL) (-1029 2547745 2547896 2548186 "SIGNEF" 2548765 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1028 2545435 2545889 2546395 "SHP" 2547286 NIL SHP (NIL T NIL) -7 NIL NIL) (-1027 2539288 2545336 2545412 "SHDP" 2545417 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1026 2538777 2538969 2539000 "SGROUP" 2539152 T SGROUP (NIL) -9 NIL 2539239) (-1025 2538547 2538599 2538703 "SGROUP-" 2538708 NIL SGROUP- (NIL T) -8 NIL NIL) (-1024 2535383 2536080 2536803 "SGCF" 2537846 T SGCF (NIL) -7 NIL NIL) (-1023 2529781 2534833 2534930 "SFRTCAT" 2534935 NIL SFRTCAT (NIL T T T T) -9 NIL 2534973) (-1022 2523241 2524256 2525390 "SFRGCD" 2528764 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1021 2516407 2517478 2518662 "SFQCMPK" 2522174 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1020 2516029 2516118 2516228 "SFORT" 2516348 NIL SFORT (NIL T T) -8 NIL NIL) (-1019 2515174 2515869 2515990 "SEXOF" 2515995 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1018 2514308 2515055 2515123 "SEX" 2515128 T SEX (NIL) -8 NIL NIL) (-1017 2509084 2509773 2509869 "SEXCAT" 2513640 NIL SEXCAT (NIL T T T T T) -9 NIL 2514259) (-1016 2506264 2509018 2509066 "SET" 2509071 NIL SET (NIL T) -8 NIL NIL) (-1015 2504515 2504977 2505282 "SETMN" 2506005 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1014 2504122 2504248 2504279 "SETCAT" 2504396 T SETCAT (NIL) -9 NIL 2504480) (-1013 2503902 2503954 2504053 "SETCAT-" 2504058 NIL SETCAT- (NIL T) -8 NIL NIL) (-1012 2500289 2502363 2502407 "SETAGG" 2503277 NIL SETAGG (NIL T) -9 NIL 2503617) (-1011 2499747 2499863 2500100 "SETAGG-" 2500105 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1010 2498950 2499243 2499305 "SEGXCAT" 2499591 NIL SEGXCAT (NIL T T) -9 NIL 2499711) (-1009 2498006 2498616 2498798 "SEG" 2498803 NIL SEG (NIL T) -8 NIL NIL) (-1008 2496912 2497125 2497169 "SEGCAT" 2497751 NIL SEGCAT (NIL T) -9 NIL 2497989) (-1007 2495961 2496291 2496491 "SEGBIND" 2496747 NIL SEGBIND (NIL T) -8 NIL NIL) (-1006 2495582 2495641 2495754 "SEGBIND2" 2495896 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1005 2494801 2494927 2495131 "SEG2" 2495426 NIL SEG2 (NIL T T) -7 NIL NIL) (-1004 2494238 2494736 2494783 "SDVAR" 2494788 NIL SDVAR (NIL T) -8 NIL NIL) (-1003 2486490 2494011 2494139 "SDPOL" 2494144 NIL SDPOL (NIL T) -8 NIL NIL) (-1002 2485083 2485349 2485668 "SCPKG" 2486205 NIL SCPKG (NIL T) -7 NIL NIL) (-1001 2484220 2484399 2484599 "SCOPE" 2484905 T SCOPE (NIL) -8 NIL NIL) (-1000 2483441 2483574 2483753 "SCACHE" 2484075 NIL SCACHE (NIL T) -7 NIL NIL) (-999 2482884 2483205 2483288 "SAOS" 2483378 T SAOS (NIL) -8 NIL NIL) (-998 2482452 2482487 2482658 "SAERFFC" 2482843 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-997 2476348 2482351 2482429 "SAE" 2482434 NIL SAE (NIL T T NIL) -8 NIL NIL) (-996 2475944 2475979 2476136 "SAEFACT" 2476307 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-995 2474270 2474584 2474983 "RURPK" 2475610 NIL RURPK (NIL T NIL) -7 NIL NIL) (-994 2472923 2473200 2473507 "RULESET" 2474106 NIL RULESET (NIL T T T) -8 NIL NIL) (-993 2470131 2470634 2471095 "RULE" 2472605 NIL RULE (NIL T T T) -8 NIL NIL) (-992 2469773 2469928 2470009 "RULECOLD" 2470083 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-991 2464665 2465459 2466375 "RSETGCD" 2468972 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-990 2453979 2459031 2459126 "RSETCAT" 2463191 NIL RSETCAT (NIL T T T T) -9 NIL 2464288) (-989 2451910 2452449 2453269 "RSETCAT-" 2453274 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-988 2444340 2445715 2447231 "RSDCMPK" 2450509 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-987 2442357 2442798 2442871 "RRCC" 2443947 NIL RRCC (NIL T T) -9 NIL 2444291) (-986 2441711 2441885 2442161 "RRCC-" 2442166 NIL RRCC- (NIL T T T) -8 NIL NIL) (-985 2416077 2425702 2425767 "RPOLCAT" 2436269 NIL RPOLCAT (NIL T T T) -9 NIL 2439427) (-984 2407581 2409919 2413037 "RPOLCAT-" 2413042 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-983 2398647 2405811 2406291 "ROUTINE" 2407121 T ROUTINE (NIL) -8 NIL NIL) (-982 2395352 2398203 2398350 "ROMAN" 2398520 T ROMAN (NIL) -8 NIL NIL) (-981 2393638 2394223 2394480 "ROIRC" 2395158 NIL ROIRC (NIL T T) -8 NIL NIL) (-980 2390042 2392346 2392375 "RNS" 2392671 T RNS (NIL) -9 NIL 2392941) (-979 2388556 2388939 2389470 "RNS-" 2389543 NIL RNS- (NIL T) -8 NIL NIL) (-978 2387981 2388389 2388418 "RNG" 2388423 T RNG (NIL) -9 NIL 2388444) (-977 2387378 2387740 2387781 "RMODULE" 2387841 NIL RMODULE (NIL T) -9 NIL 2387883) (-976 2386230 2386324 2386654 "RMCAT2" 2387279 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-975 2382944 2385413 2385734 "RMATRIX" 2385965 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-974 2375940 2378174 2378287 "RMATCAT" 2381596 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2382578) (-973 2375319 2375466 2375769 "RMATCAT-" 2375774 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-972 2374889 2374964 2375090 "RINTERP" 2375238 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-971 2373939 2374503 2374532 "RING" 2374642 T RING (NIL) -9 NIL 2374736) (-970 2373734 2373778 2373872 "RING-" 2373877 NIL RING- (NIL T) -8 NIL NIL) (-969 2372582 2372819 2373075 "RIDIST" 2373498 T RIDIST (NIL) -7 NIL NIL) (-968 2363904 2372056 2372259 "RGCHAIN" 2372431 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-967 2360909 2361523 2362191 "RF" 2363268 NIL RF (NIL T) -7 NIL NIL) (-966 2360558 2360621 2360722 "RFFACTOR" 2360840 NIL RFFACTOR (NIL T) -7 NIL NIL) (-965 2360286 2360321 2360416 "RFFACT" 2360517 NIL RFFACT (NIL T) -7 NIL NIL) (-964 2358416 2358780 2359160 "RFDIST" 2359926 T RFDIST (NIL) -7 NIL NIL) (-963 2357874 2357966 2358126 "RETSOL" 2358318 NIL RETSOL (NIL T T) -7 NIL NIL) (-962 2357466 2357546 2357588 "RETRACT" 2357778 NIL RETRACT (NIL T) -9 NIL NIL) (-961 2357318 2357343 2357427 "RETRACT-" 2357432 NIL RETRACT- (NIL T T) -8 NIL NIL) (-960 2350176 2356975 2357100 "RESULT" 2357213 T RESULT (NIL) -8 NIL NIL) (-959 2348761 2349450 2349647 "RESRING" 2350079 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-958 2348401 2348450 2348546 "RESLATC" 2348698 NIL RESLATC (NIL T) -7 NIL NIL) (-957 2348110 2348144 2348249 "REPSQ" 2348360 NIL REPSQ (NIL T) -7 NIL NIL) (-956 2345541 2346121 2346721 "REP" 2347530 T REP (NIL) -7 NIL NIL) (-955 2345242 2345276 2345385 "REPDB" 2345500 NIL REPDB (NIL T) -7 NIL NIL) (-954 2339187 2340566 2341786 "REP2" 2344054 NIL REP2 (NIL T) -7 NIL NIL) (-953 2335593 2336274 2337079 "REP1" 2338414 NIL REP1 (NIL T) -7 NIL NIL) (-952 2328339 2333754 2334206 "REGSET" 2335224 NIL REGSET (NIL T T T T) -8 NIL NIL) (-951 2327160 2327495 2327743 "REF" 2328124 NIL REF (NIL T) -8 NIL NIL) (-950 2326541 2326644 2326809 "REDORDER" 2327044 NIL REDORDER (NIL T T) -7 NIL NIL) (-949 2322510 2325775 2325996 "RECLOS" 2326372 NIL RECLOS (NIL T) -8 NIL NIL) (-948 2321567 2321748 2321961 "REALSOLV" 2322317 T REALSOLV (NIL) -7 NIL NIL) (-947 2321414 2321455 2321484 "REAL" 2321489 T REAL (NIL) -9 NIL 2321524) (-946 2317905 2318707 2319589 "REAL0Q" 2320579 NIL REAL0Q (NIL T) -7 NIL NIL) (-945 2313516 2314504 2315563 "REAL0" 2316886 NIL REAL0 (NIL T) -7 NIL NIL) (-944 2312924 2312996 2313201 "RDIV" 2313438 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-943 2311997 2312171 2312382 "RDIST" 2312746 NIL RDIST (NIL T) -7 NIL NIL) (-942 2310601 2310888 2311257 "RDETRS" 2311705 NIL RDETRS (NIL T T) -7 NIL NIL) (-941 2308422 2308876 2309411 "RDETR" 2310143 NIL RDETR (NIL T T) -7 NIL NIL) (-940 2307038 2307316 2307717 "RDEEFS" 2308138 NIL RDEEFS (NIL T T) -7 NIL NIL) (-939 2305538 2305844 2306273 "RDEEF" 2306726 NIL RDEEF (NIL T T) -7 NIL NIL) (-938 2299822 2302754 2302783 "RCFIELD" 2304060 T RCFIELD (NIL) -9 NIL 2304790) (-937 2297891 2298395 2299088 "RCFIELD-" 2299161 NIL RCFIELD- (NIL T) -8 NIL NIL) (-936 2294222 2296007 2296049 "RCAGG" 2297120 NIL RCAGG (NIL T) -9 NIL 2297585) (-935 2293853 2293947 2294107 "RCAGG-" 2294112 NIL RCAGG- (NIL T T) -8 NIL NIL) (-934 2293198 2293309 2293471 "RATRET" 2293737 NIL RATRET (NIL T) -7 NIL NIL) (-933 2292755 2292822 2292941 "RATFACT" 2293126 NIL RATFACT (NIL T) -7 NIL NIL) (-932 2292070 2292190 2292340 "RANDSRC" 2292625 T RANDSRC (NIL) -7 NIL NIL) (-931 2291807 2291851 2291922 "RADUTIL" 2292019 T RADUTIL (NIL) -7 NIL NIL) (-930 2284814 2290550 2290867 "RADIX" 2291522 NIL RADIX (NIL NIL) -8 NIL NIL) (-929 2276384 2284658 2284786 "RADFF" 2284791 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-928 2276035 2276110 2276139 "RADCAT" 2276296 T RADCAT (NIL) -9 NIL NIL) (-927 2275820 2275868 2275965 "RADCAT-" 2275970 NIL RADCAT- (NIL T) -8 NIL NIL) (-926 2273971 2275595 2275684 "QUEUE" 2275764 NIL QUEUE (NIL T) -8 NIL NIL) (-925 2270468 2273908 2273953 "QUAT" 2273958 NIL QUAT (NIL T) -8 NIL NIL) (-924 2270106 2270149 2270276 "QUATCT2" 2270419 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-923 2263899 2267279 2267320 "QUATCAT" 2268099 NIL QUATCAT (NIL T) -9 NIL 2268864) (-922 2260043 2261080 2262467 "QUATCAT-" 2262561 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-921 2257563 2259127 2259169 "QUAGG" 2259544 NIL QUAGG (NIL T) -9 NIL 2259719) (-920 2256488 2256961 2257133 "QFORM" 2257435 NIL QFORM (NIL NIL T) -8 NIL NIL) (-919 2247784 2253042 2253083 "QFCAT" 2253741 NIL QFCAT (NIL T) -9 NIL 2254734) (-918 2243356 2244557 2246148 "QFCAT-" 2246242 NIL QFCAT- (NIL T T) -8 NIL NIL) (-917 2242994 2243037 2243164 "QFCAT2" 2243307 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-916 2242454 2242564 2242694 "QEQUAT" 2242884 T QEQUAT (NIL) -8 NIL NIL) (-915 2235640 2236711 2237893 "QCMPACK" 2241387 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-914 2233216 2233637 2234065 "QALGSET" 2235295 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-913 2232461 2232635 2232867 "QALGSET2" 2233036 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-912 2231152 2231375 2231692 "PWFFINTB" 2232234 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-911 2229340 2229508 2229861 "PUSHVAR" 2230966 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-910 2225257 2226311 2226353 "PTRANFN" 2228237 NIL PTRANFN (NIL T) -9 NIL NIL) (-909 2223669 2223960 2224281 "PTPACK" 2224968 NIL PTPACK (NIL T) -7 NIL NIL) (-908 2223305 2223362 2223469 "PTFUNC2" 2223606 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-907 2217781 2222122 2222163 "PTCAT" 2222531 NIL PTCAT (NIL T) -9 NIL 2222693) (-906 2217439 2217474 2217598 "PSQFR" 2217740 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-905 2216034 2216332 2216666 "PSEUDLIN" 2217137 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-904 2202842 2205206 2207529 "PSETPK" 2213794 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-903 2195928 2198642 2198737 "PSETCAT" 2201718 NIL PSETCAT (NIL T T T T) -9 NIL 2202532) (-902 2193766 2194400 2195219 "PSETCAT-" 2195224 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-901 2193114 2193279 2193308 "PSCURVE" 2193576 T PSCURVE (NIL) -9 NIL 2193743) (-900 2189565 2191091 2191156 "PSCAT" 2191992 NIL PSCAT (NIL T T T) -9 NIL 2192232) (-899 2188629 2188845 2189244 "PSCAT-" 2189249 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-898 2187282 2187914 2188128 "PRTITION" 2188435 T PRTITION (NIL) -8 NIL NIL) (-897 2176380 2178586 2180774 "PRS" 2185144 NIL PRS (NIL T T) -7 NIL NIL) (-896 2174238 2175730 2175771 "PRQAGG" 2175954 NIL PRQAGG (NIL T) -9 NIL 2176056) (-895 2173808 2173910 2173939 "PROPLOG" 2174124 T PROPLOG (NIL) -9 NIL NIL) (-894 2170931 2171496 2172023 "PROPFRML" 2173313 NIL PROPFRML (NIL T) -8 NIL NIL) (-893 2170391 2170501 2170631 "PROPERTY" 2170821 T PROPERTY (NIL) -8 NIL NIL) (-892 2164165 2168557 2169377 "PRODUCT" 2169617 NIL 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2020893 "PDRING" 2021550 NIL PDRING (NIL T) -9 NIL 2021835) (-828 2019176 2019394 2019756 "PDRING-" 2019761 NIL PDRING- (NIL T T) -8 NIL NIL) (-827 2016318 2017068 2017759 "PDEPROB" 2018505 T PDEPROB (NIL) -8 NIL NIL) (-826 2013889 2014385 2014934 "PDEPACK" 2015789 T PDEPACK (NIL) -7 NIL NIL) (-825 2012801 2012991 2013242 "PDECOMP" 2013688 NIL PDECOMP (NIL T T) -7 NIL NIL) (-824 2010412 2011227 2011256 "PDECAT" 2012041 T PDECAT (NIL) -9 NIL 2012752) (-823 2010165 2010198 2010287 "PCOMP" 2010373 NIL PCOMP (NIL T T) -7 NIL NIL) (-822 2008372 2008968 2009264 "PBWLB" 2009895 NIL PBWLB (NIL T) -8 NIL NIL) (-821 2000881 2002449 2003785 "PATTERN" 2007057 NIL PATTERN (NIL T) -8 NIL NIL) (-820 2000513 2000570 2000679 "PATTERN2" 2000818 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-819 1998270 1998658 1999115 "PATTERN1" 2000102 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-818 1995665 1996219 1996700 "PATRES" 1997835 NIL PATRES (NIL T T) -8 NIL NIL) (-817 1995229 1995296 1995428 "PATRES2" 1995592 NIL PATRES2 (NIL 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1985380 1985499 "PAN2EXPR" 1985675 T PAN2EXPR (NIL) -7 NIL NIL) (-803 1984100 1984415 1984643 "PALETTE" 1985086 T PALETTE (NIL) -8 NIL NIL) (-802 1982568 1983105 1983465 "PAIR" 1983786 NIL PAIR (NIL T T) -8 NIL NIL) (-801 1976418 1981827 1982021 "PADICRC" 1982423 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-800 1969626 1975764 1975948 "PADICRAT" 1976266 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-799 1967930 1969563 1969608 "PADIC" 1969613 NIL PADIC (NIL NIL) -8 NIL NIL) (-798 1965134 1966708 1966749 "PADICCT" 1967330 NIL PADICCT (NIL NIL) -9 NIL 1967612) (-797 1964091 1964291 1964559 "PADEPAC" 1964921 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-796 1963303 1963436 1963642 "PADE" 1963953 NIL PADE (NIL T T T) -7 NIL NIL) (-795 1961314 1962146 1962461 "OWP" 1963071 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-794 1960423 1960919 1961091 "OVAR" 1961182 NIL OVAR (NIL NIL) -8 NIL NIL) (-793 1959687 1959808 1959969 "OUT" 1960282 T OUT (NIL) -7 NIL NIL) (-792 1948733 1950912 1953082 "OUTFORM" 1957537 T OUTFORM 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1925736 1925883 1926078 "ORDFUNS" 1926423 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-778 1925247 1925606 1925635 "ORDFIN" 1925640 T ORDFIN (NIL) -9 NIL 1925661) (-777 1921759 1923833 1924242 "ORDCOMP" 1924871 NIL ORDCOMP (NIL T) -8 NIL NIL) (-776 1921025 1921152 1921338 "ORDCOMP2" 1921619 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-775 1917533 1918415 1919252 "OPTPROB" 1920208 T OPTPROB (NIL) -8 NIL NIL) (-774 1914375 1915004 1915698 "OPTPACK" 1916859 T OPTPACK (NIL) -7 NIL NIL) (-773 1912100 1912836 1912865 "OPTCAT" 1913680 T OPTCAT (NIL) -9 NIL 1914326) (-772 1911868 1911907 1911973 "OPQUERY" 1912054 T OPQUERY (NIL) -7 NIL NIL) (-771 1909004 1910195 1910695 "OP" 1911400 NIL OP (NIL T) -8 NIL NIL) (-770 1905769 1907801 1908170 "ONECOMP" 1908668 NIL ONECOMP (NIL T) -8 NIL NIL) (-769 1905074 1905189 1905363 "ONECOMP2" 1905641 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-768 1904493 1904599 1904729 "OMSERVER" 1904964 T OMSERVER (NIL) -7 NIL NIL) (-767 1901381 1903933 1903974 "OMSAGG" 1904035 NIL OMSAGG (NIL 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NIL) (-715 1749933 1750185 1750543 "NPCOEF" 1751085 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-714 1748999 1749114 1749330 "NORMRETR" 1749814 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-713 1747052 1747342 1747749 "NORMPK" 1748707 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-712 1746737 1746765 1746889 "NORMMA" 1747018 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-711 1746564 1746694 1746723 "NONE" 1746728 T NONE (NIL) -8 NIL NIL) (-710 1746353 1746382 1746451 "NONE1" 1746528 NIL NONE1 (NIL T) -7 NIL NIL) (-709 1745838 1745900 1746085 "NODE1" 1746285 NIL NODE1 (NIL T T) -7 NIL NIL) (-708 1744131 1745001 1745256 "NNI" 1745603 T NNI (NIL) -8 NIL NIL) (-707 1742551 1742864 1743228 "NLINSOL" 1743799 NIL NLINSOL (NIL T) -7 NIL NIL) (-706 1738719 1739686 1740608 "NIPROB" 1741649 T NIPROB (NIL) -8 NIL NIL) (-705 1737476 1737710 1738012 "NFINTBAS" 1738481 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-704 1736184 1736415 1736696 "NCODIV" 1737244 NIL NCODIV (NIL T T) -7 NIL NIL) (-703 1735946 1735983 1736058 "NCNTFRAC" 1736141 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-702 1734126 1734490 1734910 "NCEP" 1735571 NIL NCEP (NIL T) -7 NIL NIL) (-701 1733037 1733776 1733805 "NASRING" 1733915 T NASRING (NIL) -9 NIL 1733989) (-700 1732832 1732876 1732970 "NASRING-" 1732975 NIL NASRING- (NIL T) -8 NIL NIL) (-699 1731985 1732484 1732513 "NARNG" 1732630 T NARNG (NIL) -9 NIL 1732721) (-698 1731677 1731744 1731878 "NARNG-" 1731883 NIL NARNG- (NIL T) -8 NIL NIL) (-697 1730556 1730763 1730998 "NAGSP" 1731462 T NAGSP (NIL) -7 NIL NIL) (-696 1721980 1723626 1725261 "NAGS" 1728941 T NAGS (NIL) -7 NIL NIL) (-695 1720544 1720848 1721175 "NAGF07" 1721673 T NAGF07 (NIL) -7 NIL NIL) (-694 1715126 1716406 1717702 "NAGF04" 1719268 T NAGF04 (NIL) -7 NIL NIL) (-693 1708158 1709756 1711373 "NAGF02" 1713529 T NAGF02 (NIL) -7 NIL NIL) (-692 1703422 1704512 1705619 "NAGF01" 1707071 T NAGF01 (NIL) -7 NIL NIL) (-691 1697082 1698640 1700217 "NAGE04" 1701865 T NAGE04 (NIL) -7 NIL NIL) (-690 1688323 1690426 1692538 "NAGE02" 1694990 T NAGE02 (NIL) -7 NIL NIL) (-689 1684316 1685253 1686207 "NAGE01" 1687389 T NAGE01 (NIL) -7 NIL NIL) (-688 1682123 1682654 1683209 "NAGD03" 1683781 T NAGD03 (NIL) -7 NIL NIL) (-687 1673909 1675828 1677773 "NAGD02" 1680198 T NAGD02 (NIL) -7 NIL NIL) (-686 1667768 1669181 1670609 "NAGD01" 1672501 T NAGD01 (NIL) -7 NIL NIL) (-685 1664025 1664835 1665660 "NAGC06" 1666963 T NAGC06 (NIL) -7 NIL NIL) (-684 1662502 1662831 1663184 "NAGC05" 1663692 T NAGC05 (NIL) -7 NIL NIL) (-683 1661886 1662003 1662145 "NAGC02" 1662380 T NAGC02 (NIL) -7 NIL NIL) (-682 1660947 1661504 1661545 "NAALG" 1661624 NIL NAALG (NIL T) -9 NIL 1661685) (-681 1660782 1660811 1660901 "NAALG-" 1660906 NIL NAALG- (NIL T T) -8 NIL NIL) (-680 1654732 1655840 1657027 "MULTSQFR" 1659678 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-679 1654051 1654126 1654310 "MULTFACT" 1654644 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-678 1647244 1651155 1651208 "MTSCAT" 1652268 NIL MTSCAT (NIL T T) -9 NIL 1652782) (-677 1646956 1647010 1647102 "MTHING" 1647184 NIL MTHING (NIL T) -7 NIL NIL) (-676 1646748 1646781 1646841 "MSYSCMD" 1646916 T MSYSCMD (NIL) -7 NIL NIL) (-675 1642860 1645503 1645823 "MSET" 1646461 NIL MSET (NIL T) -8 NIL NIL) (-674 1639955 1642421 1642463 "MSETAGG" 1642468 NIL MSETAGG (NIL T) -9 NIL 1642502) (-673 1635811 1637353 1638094 "MRING" 1639258 NIL MRING (NIL T T) -8 NIL NIL) (-672 1635381 1635448 1635577 "MRF2" 1635738 NIL MRF2 (NIL T T T) -7 NIL NIL) (-671 1634999 1635034 1635178 "MRATFAC" 1635340 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-670 1632611 1632906 1633337 "MPRFF" 1634704 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-669 1626631 1632466 1632562 "MPOLY" 1632567 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-668 1626121 1626156 1626364 "MPCPF" 1626590 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-667 1625637 1625680 1625863 "MPC3" 1626072 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-666 1624838 1624919 1625138 "MPC2" 1625552 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-665 1623139 1623476 1623866 "MONOTOOL" 1624498 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-664 1622263 1622598 1622627 "MONOID" 1622904 T MONOID (NIL) -9 NIL 1623076) (-663 1621641 1621804 1622047 "MONOID-" 1622052 NIL MONOID- (NIL T) -8 NIL NIL) (-662 1612621 1618607 1618667 "MONOGEN" 1619341 NIL MONOGEN (NIL T T) -9 NIL 1619797) (-661 1609839 1610574 1611574 "MONOGEN-" 1611693 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-660 1608698 1609118 1609147 "MONADWU" 1609539 T MONADWU (NIL) -9 NIL 1609777) (-659 1608070 1608229 1608477 "MONADWU-" 1608482 NIL MONADWU- (NIL T) -8 NIL NIL) (-658 1607455 1607673 1607702 "MONAD" 1607909 T MONAD (NIL) -9 NIL 1608021) (-657 1607140 1607218 1607350 "MONAD-" 1607355 NIL MONAD- (NIL T) -8 NIL NIL) (-656 1605391 1606053 1606332 "MOEBIUS" 1606893 NIL MOEBIUS (NIL T) -8 NIL NIL) (-655 1604784 1605162 1605203 "MODULE" 1605208 NIL MODULE (NIL T) -9 NIL 1605234) (-654 1604352 1604448 1604638 "MODULE-" 1604643 NIL MODULE- (NIL T T) -8 NIL NIL) (-653 1602023 1602718 1603044 "MODRING" 1604177 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-652 1598979 1600144 1600661 "MODOP" 1601555 NIL MODOP (NIL T T) -8 NIL NIL) (-651 1597166 1597618 1597959 "MODMONOM" 1598778 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-650 1586884 1595370 1595792 "MODMON" 1596794 NIL MODMON (NIL T T) -8 NIL NIL) (-649 1584010 1585728 1586004 "MODFIELD" 1586759 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-648 1583536 1583579 1583758 "MMAP" 1583961 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-647 1581772 1582549 1582590 "MLO" 1583007 NIL MLO (NIL T) -9 NIL 1583248) (-646 1579139 1579654 1580256 "MLIFT" 1581253 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-645 1578530 1578614 1578768 "MKUCFUNC" 1579050 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-644 1578129 1578199 1578322 "MKRECORD" 1578453 NIL MKRECORD (NIL T T) -7 NIL NIL) (-643 1577177 1577338 1577566 "MKFUNC" 1577940 NIL MKFUNC (NIL T) -7 NIL NIL) (-642 1576565 1576669 1576825 "MKFLCFN" 1577060 NIL MKFLCFN (NIL T) -7 NIL NIL) (-641 1575991 1576358 1576447 "MKCHSET" 1576509 NIL MKCHSET (NIL T) -8 NIL NIL) (-640 1575268 1575370 1575555 "MKBCFUNC" 1575884 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-639 1571952 1574822 1574958 "MINT" 1575152 T MINT (NIL) -8 NIL NIL) (-638 1570764 1571007 1571284 "MHROWRED" 1571707 NIL MHROWRED (NIL T) -7 NIL NIL) (-637 1566035 1569209 1569633 "MFLOAT" 1570360 T MFLOAT (NIL) -8 NIL NIL) (-636 1565392 1565468 1565639 "MFINFACT" 1565947 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-635 1561707 1562555 1563439 "MESH" 1564528 T MESH (NIL) -7 NIL NIL) (-634 1560097 1560409 1560762 "MDDFACT" 1561394 NIL MDDFACT (NIL T) -7 NIL NIL) (-633 1556939 1559256 1559298 "MDAGG" 1559553 NIL MDAGG (NIL T) -9 NIL 1559696) (-632 1546637 1556232 1556439 "MCMPLX" 1556752 T MCMPLX (NIL) -8 NIL NIL) (-631 1545778 1545924 1546124 "MCDEN" 1546486 NIL MCDEN (NIL T T) -7 NIL NIL) (-630 1543668 1543938 1544318 "MCALCFN" 1545508 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-629 1541290 1541813 1542374 "MATSTOR" 1543139 NIL MATSTOR (NIL T) -7 NIL NIL) (-628 1537298 1540665 1540912 "MATRIX" 1541075 NIL MATRIX (NIL T) -8 NIL NIL) (-627 1533068 1533771 1534507 "MATLIN" 1536655 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-626 1523265 1526403 1526480 "MATCAT" 1531318 NIL MATCAT (NIL T T T) -9 NIL 1532735) (-625 1519630 1520643 1521998 "MATCAT-" 1522003 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-624 1518232 1518385 1518716 "MATCAT2" 1519465 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-623 1516344 1516668 1517052 "MAPPKG3" 1517907 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-622 1515325 1515498 1515720 "MAPPKG2" 1516168 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-621 1513824 1514108 1514435 "MAPPKG1" 1515031 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-620 1513435 1513493 1513616 "MAPHACK3" 1513760 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-619 1513027 1513088 1513202 "MAPHACK2" 1513367 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-618 1512465 1512568 1512710 "MAPHACK1" 1512918 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-617 1510573 1511167 1511470 "MAGMA" 1512194 NIL MAGMA (NIL T) -8 NIL NIL) (-616 1507047 1508817 1509277 "M3D" 1510146 NIL M3D (NIL T) -8 NIL NIL) (-615 1501202 1505417 1505459 "LZSTAGG" 1506241 NIL LZSTAGG (NIL T) -9 NIL 1506536) (-614 1497175 1498333 1499790 "LZSTAGG-" 1499795 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-613 1494291 1495068 1495554 "LWORD" 1496721 NIL LWORD (NIL T) -8 NIL NIL) (-612 1487451 1494062 1494196 "LSQM" 1494201 NIL LSQM (NIL NIL T) -8 NIL NIL) (-611 1486675 1486814 1487042 "LSPP" 1487306 NIL LSPP (NIL T T T T) -7 NIL NIL) (-610 1484487 1484788 1485244 "LSMP" 1486364 NIL LSMP (NIL T T T T) -7 NIL NIL) (-609 1481266 1481940 1482670 "LSMP1" 1483789 NIL LSMP1 (NIL T) -7 NIL NIL) (-608 1475192 1480434 1480476 "LSAGG" 1480538 NIL LSAGG (NIL T) -9 NIL 1480616) (-607 1471887 1472811 1474024 "LSAGG-" 1474029 NIL LSAGG- (NIL T T) -8 NIL NIL) (-606 1469513 1471031 1471280 "LPOLY" 1471682 NIL LPOLY (NIL T T) -8 NIL NIL) (-605 1469095 1469180 1469303 "LPEFRAC" 1469422 NIL LPEFRAC (NIL T) -7 NIL NIL) (-604 1467442 1468189 1468442 "LO" 1468927 NIL LO (NIL T T T) -8 NIL NIL) (-603 1467095 1467207 1467236 "LOGIC" 1467347 T LOGIC (NIL) -9 NIL 1467427) (-602 1466957 1466980 1467051 "LOGIC-" 1467056 NIL LOGIC- (NIL T) -8 NIL NIL) (-601 1466150 1466290 1466483 "LODOOPS" 1466813 NIL LODOOPS (NIL T T) -7 NIL NIL) (-600 1463568 1466067 1466132 "LODO" 1466137 NIL LODO (NIL T NIL) -8 NIL NIL) (-599 1462114 1462349 1462700 "LODOF" 1463315 NIL LODOF (NIL T T) -7 NIL NIL) (-598 1458533 1460969 1461010 "LODOCAT" 1461442 NIL LODOCAT (NIL T) -9 NIL 1461653) (-597 1458267 1458325 1458451 "LODOCAT-" 1458456 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-596 1455581 1458108 1458226 "LODO2" 1458231 NIL LODO2 (NIL T T) -8 NIL NIL) (-595 1453010 1455518 1455563 "LODO1" 1455568 NIL LODO1 (NIL T) -8 NIL NIL) (-594 1451873 1452038 1452349 "LODEEF" 1452833 NIL LODEEF (NIL T T T) -7 NIL NIL) (-593 1447159 1450003 1450045 "LNAGG" 1450992 NIL LNAGG (NIL T) -9 NIL 1451436) (-592 1446306 1446520 1446862 "LNAGG-" 1446867 NIL LNAGG- (NIL T T) -8 NIL NIL) (-591 1442471 1443233 1443871 "LMOPS" 1445722 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-590 1441868 1442230 1442271 "LMODULE" 1442331 NIL LMODULE (NIL T) -9 NIL 1442373) (-589 1439114 1441513 1441636 "LMDICT" 1441778 NIL LMDICT (NIL T) -8 NIL NIL) (-588 1432341 1438060 1438358 "LIST" 1438849 NIL LIST (NIL T) -8 NIL NIL) (-587 1431866 1431940 1432079 "LIST3" 1432261 NIL LIST3 (NIL T T T) -7 NIL NIL) (-586 1430873 1431051 1431279 "LIST2" 1431684 NIL LIST2 (NIL T T) -7 NIL NIL) (-585 1429007 1429319 1429718 "LIST2MAP" 1430520 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-584 1427719 1428399 1428440 "LINEXP" 1428693 NIL LINEXP (NIL T) -9 NIL 1428841) (-583 1426366 1426626 1426923 "LINDEP" 1427471 NIL LINDEP (NIL T T) -7 NIL NIL) (-582 1423133 1423852 1424629 "LIMITRF" 1425621 NIL LIMITRF (NIL T) -7 NIL NIL) (-581 1421413 1421708 1422123 "LIMITPS" 1422828 NIL LIMITPS (NIL T T) -7 NIL NIL) (-580 1415868 1420924 1421152 "LIE" 1421234 NIL LIE (NIL T T) -8 NIL NIL) (-579 1414918 1415361 1415402 "LIECAT" 1415542 NIL LIECAT (NIL T) -9 NIL 1415693) (-578 1414759 1414786 1414874 "LIECAT-" 1414879 NIL LIECAT- (NIL T T) -8 NIL NIL) (-577 1407371 1414208 1414373 "LIB" 1414614 T LIB (NIL) -8 NIL NIL) (-576 1403008 1403889 1404824 "LGROBP" 1406488 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-575 1400874 1401148 1401510 "LF" 1402729 NIL LF (NIL T T) -7 NIL NIL) (-574 1399713 1400405 1400434 "LFCAT" 1400641 T LFCAT (NIL) -9 NIL 1400780) (-573 1396625 1397251 1397937 "LEXTRIPK" 1399079 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-572 1393331 1394195 1394698 "LEXP" 1396205 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-571 1391729 1392042 1392443 "LEADCDET" 1393013 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-570 1390925 1390999 1391226 "LAZM3PK" 1391650 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-569 1385841 1389004 1389541 "LAUPOL" 1390438 NIL LAUPOL (NIL T T) -8 NIL NIL) (-568 1385408 1385452 1385619 "LAPLACE" 1385791 NIL LAPLACE (NIL T T) -7 NIL NIL) (-567 1383336 1384509 1384760 "LA" 1385241 NIL LA (NIL T T T) -8 NIL NIL) (-566 1382398 1382992 1383033 "LALG" 1383094 NIL LALG (NIL T) -9 NIL 1383152) (-565 1382113 1382172 1382307 "LALG-" 1382312 NIL LALG- (NIL T T) -8 NIL NIL) (-564 1381023 1381210 1381507 "KOVACIC" 1381913 NIL KOVACIC (NIL T T) -7 NIL NIL) (-563 1380857 1380881 1380923 "KONVERT" 1380985 NIL KONVERT (NIL T) -9 NIL NIL) (-562 1380691 1380715 1380757 "KOERCE" 1380819 NIL KOERCE (NIL T) -9 NIL NIL) (-561 1378425 1379185 1379578 "KERNEL" 1380330 NIL KERNEL (NIL T) -8 NIL NIL) (-560 1377927 1378008 1378138 "KERNEL2" 1378339 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-559 1371778 1376466 1376521 "KDAGG" 1376898 NIL KDAGG (NIL T T) -9 NIL 1377104) (-558 1371307 1371431 1371636 "KDAGG-" 1371641 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-557 1364482 1370968 1371123 "KAFILE" 1371185 NIL KAFILE (NIL T) -8 NIL NIL) (-556 1358937 1363993 1364221 "JORDAN" 1364303 NIL JORDAN (NIL T T) -8 NIL NIL) (-555 1355236 1357142 1357197 "IXAGG" 1358126 NIL IXAGG (NIL T T) -9 NIL 1358585) (-554 1354155 1354461 1354880 "IXAGG-" 1354885 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-553 1349740 1354077 1354136 "IVECTOR" 1354141 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-552 1348506 1348743 1349009 "ITUPLE" 1349507 NIL ITUPLE (NIL T) -8 NIL NIL) (-551 1346942 1347119 1347425 "ITRIGMNP" 1348328 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-550 1345687 1345891 1346174 "ITFUN3" 1346718 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-549 1345319 1345376 1345485 "ITFUN2" 1345624 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-548 1343121 1344192 1344489 "ITAYLOR" 1345054 NIL ITAYLOR (NIL T) -8 NIL NIL) (-547 1332112 1337307 1338466 "ISUPS" 1341994 NIL ISUPS (NIL T) -8 NIL NIL) (-546 1331216 1331356 1331592 "ISUMP" 1331959 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-545 1326480 1331017 1331096 "ISTRING" 1331169 NIL ISTRING (NIL NIL) -8 NIL NIL) (-544 1325693 1325774 1325989 "IRURPK" 1326394 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-543 1324629 1324830 1325070 "IRSN" 1325473 T IRSN (NIL) -7 NIL NIL) (-542 1322664 1323019 1323454 "IRRF2F" 1324267 NIL IRRF2F (NIL T) -7 NIL NIL) (-541 1322411 1322449 1322525 "IRREDFFX" 1322620 NIL IRREDFFX (NIL T) -7 NIL NIL) (-540 1321026 1321285 1321584 "IROOT" 1322144 NIL IROOT (NIL T) -7 NIL NIL) (-539 1317664 1318715 1319405 "IR" 1320368 NIL IR (NIL T) -8 NIL NIL) (-538 1315277 1315772 1316338 "IR2" 1317142 NIL IR2 (NIL T T) -7 NIL NIL) (-537 1314353 1314466 1314686 "IR2F" 1315160 NIL IR2F (NIL T T) -7 NIL NIL) (-536 1314144 1314178 1314238 "IPRNTPK" 1314313 T IPRNTPK (NIL) -7 NIL NIL) (-535 1310698 1314033 1314102 "IPF" 1314107 NIL IPF (NIL NIL) -8 NIL NIL) (-534 1309015 1310623 1310680 "IPADIC" 1310685 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-533 1308514 1308572 1308761 "INVLAPLA" 1308951 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-532 1298163 1300516 1302902 "INTTR" 1306178 NIL INTTR (NIL T T) -7 NIL NIL) (-531 1294511 1295252 1296115 "INTTOOLS" 1297349 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-530 1294097 1294188 1294305 "INTSLPE" 1294414 T INTSLPE (NIL) -7 NIL NIL) (-529 1292047 1294020 1294079 "INTRVL" 1294084 NIL INTRVL (NIL T) -8 NIL NIL) (-528 1289654 1290166 1290740 "INTRF" 1291532 NIL INTRF (NIL T) -7 NIL NIL) (-527 1289069 1289166 1289307 "INTRET" 1289552 NIL INTRET (NIL T) -7 NIL NIL) (-526 1287071 1287460 1287929 "INTRAT" 1288677 NIL INTRAT (NIL T T) -7 NIL NIL) (-525 1284304 1284887 1285512 "INTPM" 1286556 NIL INTPM (NIL T T) -7 NIL NIL) (-524 1281013 1281612 1282356 "INTPAF" 1283690 NIL INTPAF (NIL T T T) -7 NIL NIL) (-523 1276256 1277202 1278237 "INTPACK" 1279998 T INTPACK (NIL) -7 NIL NIL) (-522 1273110 1275985 1276112 "INT" 1276149 T INT (NIL) -8 NIL NIL) (-521 1272362 1272514 1272722 "INTHERTR" 1272952 NIL INTHERTR (NIL T T) -7 NIL NIL) (-520 1271801 1271881 1272069 "INTHERAL" 1272276 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-519 1269647 1270090 1270547 "INTHEORY" 1271364 T INTHEORY (NIL) -7 NIL NIL) (-518 1260970 1262590 1264368 "INTG0" 1267999 NIL INTG0 (NIL T T T) -7 NIL NIL) (-517 1241543 1246333 1251143 "INTFTBL" 1256180 T INTFTBL (NIL) -8 NIL NIL) (-516 1240792 1240930 1241103 "INTFACT" 1241402 NIL INTFACT (NIL T) -7 NIL NIL) (-515 1238183 1238629 1239192 "INTEF" 1240346 NIL INTEF (NIL T T) -7 NIL NIL) (-514 1236644 1237393 1237422 "INTDOM" 1237723 T INTDOM (NIL) -9 NIL 1237930) (-513 1236013 1236187 1236429 "INTDOM-" 1236434 NIL INTDOM- (NIL T) -8 NIL NIL) (-512 1232505 1234437 1234492 "INTCAT" 1235291 NIL INTCAT (NIL T) -9 NIL 1235610) (-511 1231978 1232080 1232208 "INTBIT" 1232397 T INTBIT (NIL) -7 NIL NIL) (-510 1230653 1230807 1231120 "INTALG" 1231823 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-509 1230110 1230200 1230370 "INTAF" 1230557 NIL INTAF (NIL T T) -7 NIL NIL) (-508 1223564 1229920 1230060 "INTABL" 1230065 NIL INTABL (NIL T T T) -8 NIL NIL) (-507 1218514 1221243 1221272 "INS" 1222240 T INS (NIL) -9 NIL 1222921) (-506 1215754 1216525 1217499 "INS-" 1217572 NIL INS- (NIL T) -8 NIL NIL) (-505 1214533 1214760 1215057 "INPSIGN" 1215507 NIL INPSIGN (NIL T T) -7 NIL NIL) (-504 1213651 1213768 1213965 "INPRODPF" 1214413 NIL INPRODPF (NIL T T) -7 NIL NIL) (-503 1212545 1212662 1212899 "INPRODFF" 1213531 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-502 1211545 1211697 1211957 "INNMFACT" 1212381 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-501 1210742 1210839 1211027 "INMODGCD" 1211444 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-500 1209251 1209495 1209819 "INFSP" 1210487 NIL INFSP (NIL T T T) -7 NIL NIL) (-499 1208435 1208552 1208735 "INFPROD0" 1209131 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-498 1205445 1206604 1207095 "INFORM" 1207952 T INFORM (NIL) -8 NIL NIL) (-497 1205055 1205115 1205213 "INFORM1" 1205380 NIL INFORM1 (NIL T) -7 NIL NIL) (-496 1204578 1204667 1204781 "INFINITY" 1204961 T INFINITY (NIL) -7 NIL NIL) (-495 1203196 1203444 1203765 "INEP" 1204326 NIL INEP (NIL T T T) -7 NIL NIL) (-494 1202472 1203093 1203158 "INDE" 1203163 NIL INDE (NIL T) -8 NIL NIL) (-493 1202036 1202104 1202221 "INCRMAPS" 1202399 NIL INCRMAPS (NIL T) -7 NIL NIL) (-492 1197347 1198272 1199216 "INBFF" 1201124 NIL INBFF (NIL T) -7 NIL NIL) (-491 1193842 1197192 1197295 "IMATRIX" 1197300 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-490 1192554 1192677 1192992 "IMATQF" 1193698 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-489 1190774 1191001 1191338 "IMATLIN" 1192310 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-488 1185400 1190698 1190756 "ILIST" 1190761 NIL ILIST (NIL T NIL) -8 NIL NIL) (-487 1183353 1185260 1185373 "IIARRAY2" 1185378 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-486 1178721 1183264 1183328 "IFF" 1183333 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-485 1173764 1178013 1178201 "IFARRAY" 1178578 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-484 1172971 1173668 1173741 "IFAMON" 1173746 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-483 1172554 1172619 1172674 "IEVALAB" 1172881 NIL IEVALAB (NIL T T) -9 NIL NIL) (-482 1172229 1172297 1172457 "IEVALAB-" 1172462 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-481 1171887 1172143 1172206 "IDPO" 1172211 NIL IDPO (NIL T T) -8 NIL NIL) (-480 1171164 1171776 1171851 "IDPOAMS" 1171856 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-479 1170498 1171053 1171128 "IDPOAM" 1171133 NIL IDPOAM (NIL T T) -8 NIL NIL) (-478 1169583 1169833 1169887 "IDPC" 1170300 NIL IDPC (NIL T T) -9 NIL 1170449) (-477 1169079 1169475 1169548 "IDPAM" 1169553 NIL IDPAM (NIL T T) -8 NIL NIL) (-476 1168482 1168971 1169044 "IDPAG" 1169049 NIL IDPAG (NIL T T) -8 NIL NIL) (-475 1164737 1165585 1166480 "IDECOMP" 1167639 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-474 1157611 1158660 1159707 "IDEAL" 1163773 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-473 1156775 1156887 1157086 "ICDEN" 1157495 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-472 1155874 1156255 1156402 "ICARD" 1156648 T ICARD (NIL) -8 NIL NIL) (-471 1153946 1154259 1154662 "IBPTOOLS" 1155551 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-470 1149560 1153566 1153679 "IBITS" 1153865 NIL IBITS (NIL NIL) -8 NIL NIL) (-469 1146283 1146859 1147554 "IBATOOL" 1148977 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-468 1144063 1144524 1145057 "IBACHIN" 1145818 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-467 1141940 1143909 1144012 "IARRAY2" 1144017 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-466 1138093 1141866 1141923 "IARRAY1" 1141928 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-465 1132032 1136511 1136989 "IAN" 1137635 T IAN (NIL) -8 NIL NIL) (-464 1131543 1131600 1131773 "IALGFACT" 1131969 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-463 1131070 1131183 1131212 "HYPCAT" 1131419 T HYPCAT (NIL) -9 NIL NIL) (-462 1130608 1130725 1130911 "HYPCAT-" 1130916 NIL HYPCAT- (NIL T) -8 NIL NIL) (-461 1127287 1128618 1128660 "HOAGG" 1129641 NIL HOAGG (NIL T) -9 NIL 1130320) (-460 1125881 1126280 1126806 "HOAGG-" 1126811 NIL HOAGG- (NIL T T) -8 NIL NIL) (-459 1119712 1125322 1125488 "HEXADEC" 1125735 T HEXADEC (NIL) -8 NIL NIL) (-458 1118460 1118682 1118945 "HEUGCD" 1119489 NIL HEUGCD (NIL T) -7 NIL NIL) (-457 1117563 1118297 1118427 "HELLFDIV" 1118432 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-456 1115791 1117340 1117428 "HEAP" 1117507 NIL HEAP (NIL T) -8 NIL NIL) (-455 1109658 1115706 1115768 "HDP" 1115773 NIL HDP (NIL NIL T) -8 NIL NIL) (-454 1103370 1109295 1109446 "HDMP" 1109559 NIL HDMP (NIL NIL T) -8 NIL NIL) (-453 1102695 1102834 1102998 "HB" 1103226 T HB (NIL) -7 NIL NIL) (-452 1096192 1102541 1102645 "HASHTBL" 1102650 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-451 1093945 1095820 1095999 "HACKPI" 1096033 T HACKPI (NIL) -8 NIL NIL) (-450 1089641 1093799 1093911 "GTSET" 1093916 NIL GTSET (NIL T T T T) -8 NIL NIL) (-449 1083167 1089519 1089617 "GSTBL" 1089622 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-448 1075403 1082203 1082467 "GSERIES" 1082958 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-447 1074425 1074878 1074907 "GROUP" 1075168 T GROUP (NIL) -9 NIL 1075327) (-446 1073541 1073764 1074108 "GROUP-" 1074113 NIL GROUP- (NIL T) -8 NIL NIL) (-445 1071910 1072229 1072616 "GROEBSOL" 1073218 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-444 1070850 1071112 1071164 "GRMOD" 1071693 NIL GRMOD (NIL T T) -9 NIL 1071861) (-443 1070618 1070654 1070782 "GRMOD-" 1070787 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-442 1065946 1066972 1067972 "GRIMAGE" 1069638 T GRIMAGE (NIL) -8 NIL NIL) (-441 1064413 1064673 1064997 "GRDEF" 1065642 T GRDEF (NIL) -7 NIL NIL) (-440 1063857 1063973 1064114 "GRAY" 1064292 T GRAY (NIL) -7 NIL NIL) (-439 1063090 1063470 1063522 "GRALG" 1063675 NIL GRALG (NIL T T) -9 NIL 1063767) (-438 1062751 1062824 1062987 "GRALG-" 1062992 NIL GRALG- (NIL T T T) -8 NIL NIL) (-437 1059559 1062340 1062516 "GPOLSET" 1062658 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-436 1058915 1058972 1059229 "GOSPER" 1059496 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-435 1054674 1055353 1055879 "GMODPOL" 1058614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-434 1053679 1053863 1054101 "GHENSEL" 1054486 NIL GHENSEL (NIL T T) -7 NIL NIL) (-433 1047745 1048588 1049614 "GENUPS" 1052763 NIL GENUPS (NIL T T) -7 NIL NIL) (-432 1047442 1047493 1047582 "GENUFACT" 1047688 NIL GENUFACT (NIL T) -7 NIL NIL) (-431 1046854 1046931 1047096 "GENPGCD" 1047360 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-430 1046328 1046363 1046576 "GENMFACT" 1046813 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-429 1044896 1045151 1045458 "GENEEZ" 1046071 NIL GENEEZ (NIL T T) -7 NIL NIL) (-428 1038770 1044509 1044670 "GDMP" 1044819 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-427 1028152 1032541 1033647 "GCNAALG" 1037753 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-426 1026573 1027445 1027474 "GCDDOM" 1027729 T GCDDOM (NIL) -9 NIL 1027886) (-425 1026043 1026170 1026385 "GCDDOM-" 1026390 NIL GCDDOM- (NIL T) -8 NIL NIL) (-424 1024715 1024900 1025204 "GB" 1025822 NIL GB (NIL T T T T) -7 NIL NIL) (-423 1013335 1015661 1018053 "GBINTERN" 1022406 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-422 1011172 1011464 1011885 "GBF" 1013010 NIL GBF (NIL T T T T) -7 NIL NIL) (-421 1009953 1010118 1010385 "GBEUCLID" 1010988 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-420 1009302 1009427 1009576 "GAUSSFAC" 1009824 T GAUSSFAC (NIL) -7 NIL NIL) (-419 1007679 1007981 1008294 "GALUTIL" 1009021 NIL GALUTIL (NIL T) -7 NIL NIL) (-418 1005996 1006270 1006593 "GALPOLYU" 1007406 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-417 1003385 1003675 1004080 "GALFACTU" 1005693 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-416 995191 996690 998298 "GALFACT" 1001817 NIL GALFACT (NIL T) -7 NIL NIL) (-415 992578 993236 993265 "FVFUN" 994421 T FVFUN (NIL) -9 NIL 995141) (-414 991843 992025 992054 "FVC" 992345 T FVC (NIL) -9 NIL 992528) (-413 991485 991640 991721 "FUNCTION" 991795 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-412 989155 989706 990195 "FT" 991016 T FT (NIL) -8 NIL NIL) (-411 987973 988456 988659 "FTEM" 988972 T FTEM (NIL) -8 NIL NIL) (-410 986238 986526 986928 "FSUPFACT" 987665 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-409 984635 984924 985256 "FST" 985926 T FST (NIL) -8 NIL NIL) (-408 983810 983916 984110 "FSRED" 984517 NIL FSRED (NIL T T) -7 NIL NIL) (-407 982489 982744 983098 "FSPRMELT" 983525 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-406 979574 980012 980511 "FSPECF" 982052 NIL FSPECF (NIL T T) -7 NIL NIL) (-405 961947 970504 970545 "FS" 974383 NIL FS (NIL T) -9 NIL 976665) (-404 950597 953587 957643 "FS-" 957940 NIL FS- (NIL T T) -8 NIL NIL) (-403 950113 950167 950343 "FSINT" 950538 NIL FSINT (NIL T T) -7 NIL NIL) (-402 948394 949106 949409 "FSERIES" 949892 NIL FSERIES (NIL T T) -8 NIL NIL) (-401 947412 947528 947758 "FSCINT" 948274 NIL FSCINT (NIL T T) -7 NIL NIL) (-400 943646 946356 946398 "FSAGG" 946768 NIL FSAGG (NIL T) -9 NIL 947027) (-399 941408 942009 942805 "FSAGG-" 942900 NIL FSAGG- (NIL T T) -8 NIL NIL) (-398 940450 940593 940820 "FSAGG2" 941261 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-397 938109 938388 938941 "FS2UPS" 940168 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-396 937695 937738 937891 "FS2" 938060 NIL FS2 (NIL T T T T) -7 NIL NIL) (-395 936555 936726 937034 "FS2EXPXP" 937520 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-394 935981 936096 936248 "FRUTIL" 936435 NIL FRUTIL (NIL T) -7 NIL NIL) (-393 927402 931480 932836 "FR" 934657 NIL FR (NIL T) -8 NIL NIL) (-392 922478 925121 925162 "FRNAALG" 926558 NIL FRNAALG (NIL T) -9 NIL 927165) (-391 918157 919227 920502 "FRNAALG-" 921252 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-390 917795 917838 917965 "FRNAAF2" 918108 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-389 916160 916652 916946 "FRMOD" 917608 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-388 913883 914551 914867 "FRIDEAL" 915951 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-387 913082 913169 913456 "FRIDEAL2" 913790 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-386 912339 912747 912789 "FRETRCT" 912794 NIL FRETRCT (NIL T) -9 NIL 912965) (-385 911451 911682 912033 "FRETRCT-" 912038 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-384 908660 909880 909940 "FRAMALG" 910822 NIL FRAMALG (NIL T T) -9 NIL 911114) (-383 906793 907249 907879 "FRAMALG-" 908102 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-382 900695 906268 906544 "FRAC" 906549 NIL FRAC (NIL T) -8 NIL NIL) (-381 900331 900388 900495 "FRAC2" 900632 NIL FRAC2 (NIL T T) -7 NIL NIL) (-380 899967 900024 900131 "FR2" 900268 NIL FR2 (NIL T T) -7 NIL NIL) (-379 894640 897553 897582 "FPS" 898701 T FPS (NIL) -9 NIL 899257) (-378 894089 894198 894362 "FPS-" 894508 NIL FPS- (NIL T) -8 NIL NIL) (-377 891537 893234 893263 "FPC" 893488 T FPC (NIL) -9 NIL 893630) (-376 891330 891370 891467 "FPC-" 891472 NIL FPC- (NIL T) -8 NIL NIL) (-375 890208 890818 890860 "FPATMAB" 890865 NIL FPATMAB (NIL T) -9 NIL 891017) (-374 887908 888384 888810 "FPARFRAC" 889845 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-373 883303 883800 884482 "FORTRAN" 887340 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-372 881019 881519 882058 "FORT" 882784 T FORT (NIL) -7 NIL NIL) (-371 878694 879256 879285 "FORTFN" 880345 T FORTFN (NIL) -9 NIL 880969) (-370 878457 878507 878536 "FORTCAT" 878595 T FORTCAT (NIL) -9 NIL 878657) (-369 876517 877000 877399 "FORMULA" 878078 T FORMULA (NIL) -8 NIL NIL) (-368 876305 876335 876404 "FORMULA1" 876481 NIL FORMULA1 (NIL T) -7 NIL NIL) (-367 875828 875880 876053 "FORDER" 876247 NIL FORDER (NIL T T T T) -7 NIL NIL) (-366 874924 875088 875281 "FOP" 875655 T FOP (NIL) -7 NIL NIL) (-365 873532 874204 874378 "FNLA" 874806 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-364 872200 872589 872618 "FNCAT" 873190 T FNCAT (NIL) -9 NIL 873483) (-363 871766 872159 872187 "FNAME" 872192 T FNAME (NIL) -8 NIL NIL) (-362 870425 871398 871427 "FMTC" 871432 T FMTC (NIL) -9 NIL 871467) (-361 866743 867950 868578 "FMONOID" 869830 NIL FMONOID (NIL T) -8 NIL NIL) (-360 865963 866486 866634 "FM" 866639 NIL FM (NIL T T) -8 NIL NIL) (-359 863386 864032 864061 "FMFUN" 865205 T FMFUN (NIL) -9 NIL 865913) (-358 862654 862835 862864 "FMC" 863154 T FMC (NIL) -9 NIL 863336) (-357 859883 860717 860771 "FMCAT" 861953 NIL FMCAT (NIL T T) -9 NIL 862447) (-356 858778 859651 859750 "FM1" 859828 NIL FM1 (NIL T T) -8 NIL NIL) (-355 856552 856968 857462 "FLOATRP" 858329 NIL FLOATRP (NIL T) -7 NIL NIL) (-354 850038 854208 854838 "FLOAT" 855942 T FLOAT (NIL) -8 NIL NIL) (-353 847476 847976 848554 "FLOATCP" 849505 NIL FLOATCP (NIL T) -7 NIL NIL) (-352 846264 847112 847153 "FLINEXP" 847158 NIL FLINEXP (NIL T) -9 NIL 847251) (-351 845419 845654 845981 "FLINEXP-" 845986 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-350 844495 844639 844863 "FLASORT" 845271 NIL FLASORT (NIL T T) -7 NIL NIL) (-349 841713 842555 842608 "FLALG" 843835 NIL FLALG (NIL T T) -9 NIL 844302) (-348 835497 839199 839241 "FLAGG" 840503 NIL FLAGG (NIL T) -9 NIL 841155) (-347 834223 834562 835052 "FLAGG-" 835057 NIL FLAGG- (NIL T T) -8 NIL NIL) (-346 833265 833408 833635 "FLAGG2" 834076 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-345 830237 831255 831315 "FINRALG" 832443 NIL FINRALG (NIL T T) -9 NIL 832951) (-344 829397 829626 829965 "FINRALG-" 829970 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-343 828803 829016 829045 "FINITE" 829241 T FINITE (NIL) -9 NIL 829348) (-342 821262 823423 823464 "FINAALG" 827131 NIL FINAALG (NIL T) -9 NIL 828584) (-341 816603 817644 818788 "FINAALG-" 820167 NIL FINAALG- (NIL T T) -8 NIL NIL) (-340 815998 816358 816461 "FILE" 816533 NIL FILE (NIL T) -8 NIL NIL) (-339 814682 814994 815049 "FILECAT" 815733 NIL FILECAT (NIL T T) -9 NIL 815949) (-338 812544 814100 814129 "FIELD" 814169 T FIELD (NIL) -9 NIL 814249) (-337 811164 811549 812060 "FIELD-" 812065 NIL FIELD- (NIL T) -8 NIL NIL) (-336 808979 809801 810147 "FGROUP" 810851 NIL FGROUP (NIL T) -8 NIL NIL) (-335 808069 808233 808453 "FGLMICPK" 808811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-334 803871 807994 808051 "FFX" 808056 NIL FFX (NIL T NIL) -8 NIL NIL) (-333 803472 803533 803668 "FFSLPE" 803804 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-332 799467 800244 801040 "FFPOLY" 802708 NIL FFPOLY (NIL T) -7 NIL NIL) (-331 798971 799007 799216 "FFPOLY2" 799425 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-330 794793 798890 798953 "FFP" 798958 NIL FFP (NIL T NIL) -8 NIL NIL) (-329 790161 794704 794768 "FF" 794773 NIL FF (NIL NIL NIL) -8 NIL NIL) (-328 785257 789504 789694 "FFNBX" 790015 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-327 780167 784392 784650 "FFNBP" 785111 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-326 774770 779451 779662 "FFNB" 780000 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-325 773602 773800 774115 "FFINTBAS" 774567 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-324 769825 772065 772094 "FFIELDC" 772714 T FFIELDC (NIL) -9 NIL 773090) (-323 768488 768858 769355 "FFIELDC-" 769360 NIL FFIELDC- (NIL T) -8 NIL NIL) (-322 768058 768103 768227 "FFHOM" 768430 NIL FFHOM (NIL T T T) -7 NIL NIL) (-321 765756 766240 766757 "FFF" 767573 NIL FFF (NIL T) -7 NIL NIL) (-320 761344 765498 765599 "FFCGX" 765699 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-319 756946 761076 761183 "FFCGP" 761287 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-318 752099 756673 756781 "FFCG" 756882 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-317 734044 743167 743254 "FFCAT" 748419 NIL FFCAT (NIL T T T) -9 NIL 749906) (-316 729242 730289 731603 "FFCAT-" 732833 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-315 728653 728696 728931 "FFCAT2" 729193 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-314 717853 721643 722860 "FEXPR" 727508 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-313 716852 717287 717329 "FEVALAB" 717413 NIL FEVALAB (NIL T) -9 NIL 717674) (-312 716011 716221 716559 "FEVALAB-" 716564 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-311 714604 715394 715597 "FDIV" 715910 NIL FDIV (NIL T T T T) -8 NIL NIL) (-310 711670 712385 712501 "FDIVCAT" 714069 NIL FDIVCAT (NIL T T T T) -9 NIL 714506) (-309 711432 711459 711629 "FDIVCAT-" 711634 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-308 710652 710739 711016 "FDIV2" 711339 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-307 709338 709597 709886 "FCPAK1" 710383 T FCPAK1 (NIL) -7 NIL NIL) (-306 708466 708838 708979 "FCOMP" 709229 NIL FCOMP (NIL T) -8 NIL NIL) (-305 692094 695509 699072 "FC" 704923 T FC (NIL) -8 NIL NIL) (-304 684689 688735 688776 "FAXF" 690578 NIL FAXF (NIL T) -9 NIL 691269) (-303 681968 682623 683448 "FAXF-" 683913 NIL FAXF- (NIL T T) -8 NIL NIL) (-302 677068 681344 681520 "FARRAY" 681825 NIL FARRAY (NIL T) -8 NIL NIL) (-301 672458 674529 674582 "FAMR" 675594 NIL FAMR (NIL T T) -9 NIL 676054) (-300 671349 671651 672085 "FAMR-" 672090 NIL FAMR- (NIL T T T) -8 NIL NIL) (-299 670545 671271 671324 "FAMONOID" 671329 NIL FAMONOID (NIL T) -8 NIL NIL) (-298 668377 669061 669115 "FAMONC" 670056 NIL FAMONC (NIL T T) -9 NIL 670441) (-297 667069 668131 668268 "FAGROUP" 668273 NIL FAGROUP (NIL T) -8 NIL NIL) (-296 664872 665191 665593 "FACUTIL" 666750 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-295 663971 664156 664378 "FACTFUNC" 664682 NIL FACTFUNC (NIL T) -7 NIL NIL) (-294 656294 663222 663434 "EXPUPXS" 663827 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-293 653777 654317 654903 "EXPRTUBE" 655728 T EXPRTUBE (NIL) -7 NIL NIL) (-292 649971 650563 651300 "EXPRODE" 653116 NIL EXPRODE (NIL T T) -7 NIL NIL) (-291 635130 648630 649056 "EXPR" 649577 NIL EXPR (NIL T) -8 NIL NIL) (-290 629558 630145 630957 "EXPR2UPS" 634428 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-289 629194 629251 629358 "EXPR2" 629495 NIL EXPR2 (NIL T T) -7 NIL NIL) (-288 620548 628331 628626 "EXPEXPAN" 629032 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-287 620375 620505 620534 "EXIT" 620539 T EXIT (NIL) -8 NIL NIL) (-286 620002 620064 620177 "EVALCYC" 620307 NIL EVALCYC (NIL T) -7 NIL NIL) (-285 619542 619660 619702 "EVALAB" 619872 NIL EVALAB (NIL T) -9 NIL 619976) (-284 619023 619145 619366 "EVALAB-" 619371 NIL EVALAB- (NIL T T) -8 NIL NIL) (-283 616485 617797 617826 "EUCDOM" 618381 T EUCDOM (NIL) -9 NIL 618731) (-282 614890 615332 615922 "EUCDOM-" 615927 NIL EUCDOM- (NIL T) -8 NIL NIL) (-281 602468 605216 607956 "ESTOOLS" 612170 T ESTOOLS (NIL) -7 NIL NIL) (-280 602104 602161 602268 "ESTOOLS2" 602405 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-279 601855 601897 601977 "ESTOOLS1" 602056 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-278 595792 597516 597545 "ES" 600309 T ES (NIL) -9 NIL 601715) (-277 590740 592026 593843 "ES-" 594007 NIL ES- (NIL T) -8 NIL NIL) (-276 587115 587875 588655 "ESCONT" 589980 T ESCONT (NIL) -7 NIL NIL) (-275 586860 586892 586974 "ESCONT1" 587077 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-274 586535 586585 586685 "ES2" 586804 NIL ES2 (NIL T T) -7 NIL NIL) (-273 586165 586223 586332 "ES1" 586471 NIL ES1 (NIL T T) -7 NIL NIL) (-272 585381 585510 585686 "ERROR" 586009 T ERROR (NIL) -7 NIL NIL) (-271 578884 585240 585331 "EQTBL" 585336 NIL EQTBL (NIL T T) -8 NIL NIL) (-270 571321 574202 575649 "EQ" 577470 NIL -3087 (NIL T) -8 NIL NIL) (-269 570953 571010 571119 "EQ2" 571258 NIL EQ2 (NIL T T) -7 NIL NIL) (-268 566245 567291 568384 "EP" 569892 NIL EP (NIL T) -7 NIL NIL) (-267 564828 565128 565445 "ENV" 565948 T ENV (NIL) -8 NIL NIL) (-266 563987 564551 564580 "ENTIRER" 564585 T ENTIRER (NIL) -9 NIL 564630) (-265 560443 561942 562312 "EMR" 563786 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-264 559586 559771 559826 "ELTAGG" 560206 NIL ELTAGG (NIL T T) -9 NIL 560417) (-263 559305 559367 559508 "ELTAGG-" 559513 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-262 559093 559122 559177 "ELTAB" 559261 NIL ELTAB (NIL T T) -9 NIL NIL) (-261 558219 558365 558564 "ELFUTS" 558944 NIL ELFUTS (NIL T T) -7 NIL NIL) (-260 557960 558016 558045 "ELEMFUN" 558150 T ELEMFUN (NIL) -9 NIL NIL) (-259 557830 557851 557919 "ELEMFUN-" 557924 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-258 552721 555930 555972 "ELAGG" 556912 NIL ELAGG (NIL T) -9 NIL 557375) (-257 551006 551440 552103 "ELAGG-" 552108 NIL ELAGG- (NIL T T) -8 NIL NIL) (-256 549662 549943 550238 "ELABEXPR" 550731 T ELABEXPR (NIL) -8 NIL NIL) (-255 542530 544329 545156 "EFUPXS" 548938 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-254 535980 537781 538591 "EFULS" 541806 NIL EFULS (NIL T T T) -8 NIL NIL) (-253 533411 533769 534247 "EFSTRUC" 535612 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-252 522483 524048 525608 "EF" 531926 NIL EF (NIL T T) -7 NIL NIL) (-251 521584 521968 522117 "EAB" 522354 T EAB (NIL) -8 NIL NIL) (-250 520797 521543 521571 "E04UCFA" 521576 T E04UCFA (NIL) -8 NIL NIL) (-249 520010 520756 520784 "E04NAFA" 520789 T E04NAFA (NIL) -8 NIL NIL) (-248 519223 519969 519997 "E04MBFA" 520002 T E04MBFA (NIL) -8 NIL NIL) (-247 518436 519182 519210 "E04JAFA" 519215 T E04JAFA (NIL) -8 NIL NIL) (-246 517651 518395 518423 "E04GCFA" 518428 T E04GCFA (NIL) -8 NIL NIL) (-245 516866 517610 517638 "E04FDFA" 517643 T E04FDFA (NIL) -8 NIL NIL) (-244 516079 516825 516853 "E04DGFA" 516858 T E04DGFA (NIL) -8 NIL NIL) (-243 510264 511609 512971 "E04AGNT" 514737 T E04AGNT (NIL) -7 NIL NIL) (-242 508990 509470 509511 "DVARCAT" 509986 NIL DVARCAT (NIL T) -9 NIL 510184) (-241 508194 508406 508720 "DVARCAT-" 508725 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-240 501056 507996 508123 "DSMP" 508128 NIL DSMP (NIL T T T) -8 NIL NIL) (-239 495866 497001 498069 "DROPT" 500008 T DROPT (NIL) -8 NIL NIL) (-238 495531 495590 495688 "DROPT1" 495801 NIL DROPT1 (NIL T) -7 NIL NIL) (-237 490646 491772 492909 "DROPT0" 494414 T DROPT0 (NIL) -7 NIL NIL) (-236 488991 489316 489702 "DRAWPT" 490280 T DRAWPT (NIL) -7 NIL NIL) (-235 483578 484501 485580 "DRAW" 487965 NIL DRAW (NIL T) -7 NIL NIL) (-234 483211 483264 483382 "DRAWHACK" 483519 NIL DRAWHACK (NIL T) -7 NIL NIL) (-233 481942 482211 482502 "DRAWCX" 482940 T DRAWCX (NIL) -7 NIL NIL) (-232 481460 481528 481678 "DRAWCURV" 481868 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-231 471932 473890 476005 "DRAWCFUN" 479365 T DRAWCFUN (NIL) -7 NIL NIL) (-230 468745 470627 470669 "DQAGG" 471298 NIL DQAGG (NIL T) -9 NIL 471571) (-229 457251 463989 464072 "DPOLCAT" 465910 NIL DPOLCAT (NIL T T T T) -9 NIL 466454) (-228 452091 453437 455394 "DPOLCAT-" 455399 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-227 446175 451953 452050 "DPMO" 452055 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-226 440162 445956 446122 "DPMM" 446127 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-225 439675 439773 439893 "DOMAIN" 440062 T DOMAIN (NIL) -8 NIL NIL) (-224 433387 439312 439463 "DMP" 439576 NIL DMP (NIL NIL T) -8 NIL NIL) (-223 432987 433043 433187 "DLP" 433325 NIL DLP (NIL T) -7 NIL NIL) (-222 426631 432088 432315 "DLIST" 432792 NIL DLIST (NIL T) -8 NIL NIL) (-221 423477 425486 425528 "DLAGG" 426078 NIL DLAGG (NIL T) -9 NIL 426307) (-220 422186 422878 422907 "DIVRING" 423057 T DIVRING (NIL) -9 NIL 423165) (-219 421174 421427 421820 "DIVRING-" 421825 NIL DIVRING- (NIL T) -8 NIL NIL) (-218 419276 419633 420039 "DISPLAY" 420788 T DISPLAY (NIL) -7 NIL NIL) (-217 413165 419190 419253 "DIRPROD" 419258 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-216 412013 412216 412481 "DIRPROD2" 412958 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-215 401643 407648 407702 "DIRPCAT" 408110 NIL DIRPCAT (NIL NIL T) -9 NIL 408937) (-214 398969 399611 400492 "DIRPCAT-" 400829 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-213 398256 398416 398602 "DIOSP" 398803 T DIOSP (NIL) -7 NIL NIL) (-212 394958 397168 397210 "DIOPS" 397644 NIL DIOPS (NIL T) -9 NIL 397873) (-211 394507 394621 394812 "DIOPS-" 394817 NIL DIOPS- (NIL T T) -8 NIL NIL) (-210 393378 394016 394045 "DIFRING" 394232 T DIFRING (NIL) -9 NIL 394341) (-209 393024 393101 393253 "DIFRING-" 393258 NIL DIFRING- (NIL T) -8 NIL NIL) (-208 390813 392095 392136 "DIFEXT" 392495 NIL DIFEXT (NIL T) -9 NIL 392788) (-207 389099 389527 390192 "DIFEXT-" 390197 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-206 386421 388631 388673 "DIAGG" 388678 NIL DIAGG (NIL T) -9 NIL 388698) (-205 385805 385962 386214 "DIAGG-" 386219 NIL DIAGG- (NIL T T) -8 NIL NIL) (-204 381270 384764 385041 "DHMATRIX" 385574 NIL DHMATRIX (NIL T) -8 NIL NIL) (-203 376882 377791 378801 "DFSFUN" 380280 T DFSFUN (NIL) -7 NIL NIL) (-202 371668 375596 375961 "DFLOAT" 376537 T DFLOAT (NIL) -8 NIL NIL) (-201 369901 370182 370577 "DFINTTLS" 371376 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-200 366934 367936 368334 "DERHAM" 369568 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-199 364783 366709 366798 "DEQUEUE" 366878 NIL DEQUEUE (NIL T) -8 NIL NIL) (-198 364001 364134 364329 "DEGRED" 364645 NIL DEGRED (NIL T T) -7 NIL NIL) (-197 360401 361146 361998 "DEFINTRF" 363229 NIL DEFINTRF (NIL T) -7 NIL NIL) (-196 357932 358401 358999 "DEFINTEF" 359920 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-195 351763 357373 357539 "DECIMAL" 357786 T DECIMAL (NIL) -8 NIL NIL) (-194 349275 349733 350239 "DDFACT" 351307 NIL DDFACT (NIL T T) -7 NIL NIL) (-193 348871 348914 349065 "DBLRESP" 349226 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-192 346581 346915 347284 "DBASE" 348629 NIL DBASE (NIL T) -8 NIL NIL) (-191 345716 346540 346568 "D03FAFA" 346573 T D03FAFA (NIL) -8 NIL NIL) (-190 344852 345675 345703 "D03EEFA" 345708 T D03EEFA (NIL) -8 NIL NIL) (-189 342802 343268 343757 "D03AGNT" 344383 T D03AGNT (NIL) -7 NIL NIL) (-188 342120 342761 342789 "D02EJFA" 342794 T D02EJFA (NIL) -8 NIL NIL) (-187 341438 342079 342107 "D02CJFA" 342112 T D02CJFA (NIL) -8 NIL NIL) (-186 340756 341397 341425 "D02BHFA" 341430 T D02BHFA (NIL) -8 NIL NIL) (-185 340074 340715 340743 "D02BBFA" 340748 T D02BBFA (NIL) -8 NIL NIL) (-184 333272 334860 336466 "D02AGNT" 338488 T D02AGNT (NIL) -7 NIL NIL) (-183 331041 331563 332109 "D01WGTS" 332746 T D01WGTS (NIL) -7 NIL NIL) (-182 330144 331000 331028 "D01TRNS" 331033 T D01TRNS (NIL) -8 NIL NIL) (-181 329247 330103 330131 "D01GBFA" 330136 T D01GBFA (NIL) -8 NIL NIL) (-180 328350 329206 329234 "D01FCFA" 329239 T D01FCFA (NIL) -8 NIL NIL) (-179 327453 328309 328337 "D01ASFA" 328342 T D01ASFA (NIL) -8 NIL NIL) (-178 326556 327412 327440 "D01AQFA" 327445 T D01AQFA (NIL) -8 NIL NIL) (-177 325659 326515 326543 "D01APFA" 326548 T D01APFA (NIL) -8 NIL NIL) (-176 324762 325618 325646 "D01ANFA" 325651 T D01ANFA (NIL) -8 NIL NIL) (-175 323865 324721 324749 "D01AMFA" 324754 T D01AMFA (NIL) -8 NIL NIL) (-174 322968 323824 323852 "D01ALFA" 323857 T D01ALFA (NIL) -8 NIL NIL) (-173 322071 322927 322955 "D01AKFA" 322960 T D01AKFA (NIL) -8 NIL NIL) (-172 321174 322030 322058 "D01AJFA" 322063 T D01AJFA (NIL) -8 NIL NIL) (-171 314478 316027 317586 "D01AGNT" 319635 T D01AGNT (NIL) -7 NIL NIL) (-170 313815 313943 314095 "CYCLOTOM" 314346 T CYCLOTOM (NIL) -7 NIL NIL) (-169 310550 311263 311990 "CYCLES" 313108 T CYCLES (NIL) -7 NIL NIL) (-168 309862 309996 310167 "CVMP" 310411 NIL CVMP (NIL T) -7 NIL NIL) (-167 307644 307901 308276 "CTRIGMNP" 309590 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-166 307249 307332 307437 "CTORCALL" 307559 T CTORCALL (NIL) -8 NIL NIL) (-165 306623 306722 306875 "CSTTOOLS" 307146 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-164 302422 303079 303837 "CRFP" 305935 NIL CRFP (NIL T T) -7 NIL NIL) (-163 301469 301654 301882 "CRAPACK" 302226 NIL CRAPACK (NIL T) -7 NIL NIL) (-162 300853 300954 301158 "CPMATCH" 301345 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-161 300578 300606 300712 "CPIMA" 300819 NIL CPIMA (NIL T T T) -7 NIL NIL) (-160 296942 297614 298332 "COORDSYS" 299913 NIL COORDSYS (NIL T) -7 NIL NIL) (-159 296326 296455 296605 "CONTOUR" 296812 T CONTOUR (NIL) -8 NIL NIL) (-158 292187 294329 294821 "CONTFRAC" 295866 NIL CONTFRAC (NIL T) -8 NIL NIL) (-157 291340 291904 291933 "COMRING" 291938 T COMRING (NIL) -9 NIL 291989) (-156 290421 290698 290882 "COMPPROP" 291176 T COMPPROP (NIL) -8 NIL NIL) (-155 290082 290117 290245 "COMPLPAT" 290380 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-154 280063 289891 290000 "COMPLEX" 290005 NIL COMPLEX (NIL T) -8 NIL NIL) (-153 279699 279756 279863 "COMPLEX2" 280000 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-152 279417 279452 279550 "COMPFACT" 279658 NIL COMPFACT (NIL T T) -7 NIL NIL) (-151 263751 274045 274086 "COMPCAT" 275088 NIL COMPCAT (NIL T) -9 NIL 276481) (-150 253266 256190 259817 "COMPCAT-" 260173 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-149 252997 253025 253127 "COMMUPC" 253232 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-148 252792 252825 252884 "COMMONOP" 252958 T COMMONOP (NIL) -7 NIL NIL) (-147 252375 252543 252630 "COMM" 252725 T COMM (NIL) -8 NIL NIL) (-146 251623 251817 251846 "COMBOPC" 252184 T COMBOPC (NIL) -9 NIL 252359) (-145 250519 250729 250971 "COMBINAT" 251413 NIL COMBINAT (NIL T) -7 NIL NIL) (-144 246717 247290 247930 "COMBF" 249941 NIL COMBF (NIL T T) -7 NIL NIL) (-143 245503 245833 246068 "COLOR" 246502 T COLOR (NIL) -8 NIL NIL) (-142 245143 245190 245315 "CMPLXRT" 245450 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-141 240645 241673 242753 "CLIP" 244083 T CLIP (NIL) -7 NIL NIL) (-140 238983 239753 239991 "CLIF" 240473 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-139 235205 237129 237171 "CLAGG" 238100 NIL CLAGG (NIL T) -9 NIL 238636) (-138 233627 234084 234667 "CLAGG-" 234672 NIL CLAGG- (NIL T T) -8 NIL NIL) (-137 233171 233256 233396 "CINTSLPE" 233536 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-136 230672 231143 231691 "CHVAR" 232699 NIL CHVAR (NIL T T T) -7 NIL NIL) (-135 229894 230458 230487 "CHARZ" 230492 T CHARZ (NIL) -9 NIL 230506) (-134 229648 229688 229766 "CHARPOL" 229848 NIL CHARPOL (NIL T) -7 NIL NIL) (-133 228754 229351 229380 "CHARNZ" 229427 T CHARNZ (NIL) -9 NIL 229482) (-132 226777 227444 227779 "CHAR" 228439 T CHAR (NIL) -8 NIL NIL) (-131 226502 226563 226592 "CFCAT" 226703 T CFCAT (NIL) -9 NIL NIL) (-130 225747 225858 226040 "CDEN" 226386 NIL CDEN (NIL T T T) -7 NIL NIL) (-129 221739 224900 225180 "CCLASS" 225487 T CCLASS (NIL) -8 NIL NIL) (-128 216792 217768 218521 "CARTEN" 221042 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 215900 216048 216269 "CARTEN2" 216639 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214197 215052 215308 "CARD" 215664 T CARD (NIL) -8 NIL NIL) (-125 213569 213897 213926 "CACHSET" 214058 T CACHSET (NIL) -9 NIL 214135) (-124 213065 213361 213390 "CABMON" 213440 T CABMON (NIL) -9 NIL 213496) (-123 210622 212757 212864 "BTREE" 212991 NIL BTREE (NIL T) -8 NIL NIL) (-122 208120 210270 210392 "BTOURN" 210532 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205538 207591 207633 "BTCAT" 207701 NIL BTCAT (NIL T) -9 NIL 207778) (-120 205205 205285 205434 "BTCAT-" 205439 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200425 204296 204325 "BTAGG" 204581 T BTAGG (NIL) -9 NIL 204760) (-118 199848 199992 200222 "BTAGG-" 200227 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 196892 199126 199341 "BSTREE" 199665 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196030 196156 196340 "BRILL" 196748 NIL BRILL (NIL T) -7 NIL NIL) (-115 192731 194758 194800 "BRAGG" 195449 NIL BRAGG (NIL T) -9 NIL 195706) (-114 191260 191666 192221 "BRAGG-" 192226 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184468 190606 190790 "BPADICRT" 191108 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 182772 184405 184450 "BPADIC" 184455 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182472 182502 182615 "BOUNDZRO" 182736 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 177987 179078 179945 "BOP" 181625 T BOP (NIL) -8 NIL NIL) (-109 175608 176052 176572 "BOP1" 177500 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174227 174938 175161 "BOOLEAN" 175405 T BOOLEAN (NIL) -8 NIL NIL) (-107 173593 173971 174024 "BMODULE" 174029 NIL BMODULE (NIL T T) -9 NIL 174093) (-106 169403 173391 173464 "BITS" 173540 T BITS (NIL) -8 NIL NIL) (-105 168500 168935 169087 "BINFILE" 169271 T BINFILE (NIL) -8 NIL NIL) (-104 167912 168034 168176 "BINDING" 168378 T BINDING (NIL) -8 NIL NIL) (-103 161747 167356 167521 "BINARY" 167767 T BINARY (NIL) -8 NIL NIL) (-102 159574 161002 161044 "BGAGG" 161304 NIL BGAGG (NIL T) -9 NIL 161441) (-101 159405 159437 159528 "BGAGG-" 159533 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158503 158789 158994 "BFUNCT" 159220 T BFUNCT (NIL) -8 NIL NIL) (-99 157204 157382 157667 "BEZOUT" 158327 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 153729 156064 156392 "BBTREE" 156907 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153466 153519 153546 "BASTYPE" 153663 T BASTYPE (NIL) -9 NIL NIL) (-96 153321 153350 153420 "BASTYPE-" 153425 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 152759 152835 152985 "BALFACT" 153232 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151581 152178 152363 "AUTOMOR" 152604 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151306 151311 151338 "ATTREG" 151343 T ATTREG (NIL) -9 NIL NIL) (-92 149585 150003 150355 "ATTRBUT" 150972 T ATTRBUT (NIL) -8 NIL NIL) (-91 149120 149233 149260 "ATRIG" 149461 T ATRIG (NIL) -9 NIL NIL) (-90 148929 148970 149057 "ATRIG-" 149062 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147126 148705 148793 "ASTACK" 148872 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145631 145928 146293 "ASSOCEQ" 146808 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144663 145290 145414 "ASP9" 145538 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144427 144611 144650 "ASP8" 144655 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143297 144032 144174 "ASP80" 144316 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142196 142932 143064 "ASP7" 143196 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141152 141873 141991 "ASP78" 142109 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140123 140832 140949 "ASP77" 141066 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139038 139761 139892 "ASP74" 140023 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137939 138673 138805 "ASP73" 138937 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136894 137616 137734 "ASP6" 137852 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135843 136571 136689 "ASP55" 136807 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134793 135517 135636 "ASP50" 135755 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133881 134494 134604 "ASP4" 134714 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132969 133582 133692 "ASP49" 133802 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131754 132508 132676 "ASP42" 132858 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130532 131287 131457 "ASP41" 131641 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129484 130209 130327 "ASP35" 130445 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129249 129432 129471 "ASP34" 129476 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128986 129053 129129 "ASP33" 129204 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127882 128621 128753 "ASP31" 128885 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127647 127830 127869 "ASP30" 127874 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127382 127451 127527 "ASP29" 127602 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127147 127330 127369 "ASP28" 127374 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126912 127095 127134 "ASP27" 127139 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125996 126610 126721 "ASP24" 126832 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124913 125637 125767 "ASP20" 125897 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124001 124614 124724 "ASP1" 124834 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122945 123675 123794 "ASP19" 123913 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122682 122749 122825 "ASP12" 122900 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121535 122281 122425 "ASP10" 122569 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119434 121379 121470 "ARRAY2" 121475 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115250 119082 119196 "ARRAY1" 119351 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114282 114455 114676 "ARRAY12" 115073 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108641 110512 110588 "ARR2CAT" 113218 NIL ARR2CAT (NIL T T T) -9 NIL 113976) (-54 106075 106819 107773 "ARR2CAT-" 107778 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 104835 104985 105288 "APPRULE" 105913 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104488 104536 104654 "APPLYORE" 104781 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103462 103753 103948 "ANY" 104311 T ANY (NIL) -8 NIL NIL) (-50 102740 102863 103020 "ANY1" 103336 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100272 101190 101515 "ANTISYM" 102465 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100099 100231 100258 "ANON" 100263 T ANON (NIL) -8 NIL NIL) (-47 94176 98644 99095 "AN" 99666 T AN (NIL) -8 NIL NIL) (-46 90529 91927 91978 "AMR" 92717 NIL AMR (NIL T T) -9 NIL 93316) (-45 89642 89863 90225 "AMR-" 90230 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74192 89559 89620 "ALIST" 89625 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71029 73786 73955 "ALGSC" 74110 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67585 68139 68746 "ALGPKG" 70469 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66862 66963 67147 "ALGMFACT" 67471 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62612 63292 63946 "ALGMANIP" 66386 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53931 62238 62388 "ALGFF" 62545 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53127 53258 53437 "ALGFACT" 53789 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52117 52727 52766 "ALGEBRA" 52826 NIL ALGEBRA (NIL T) -9 NIL 52884) (-36 51835 51894 52026 "ALGEBRA-" 52031 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34095 49838 49891 "ALAGG" 50027 NIL ALAGG (NIL T T) -9 NIL 50188) (-34 33630 33743 33770 "AHYP" 33971 T AHYP (NIL) -9 NIL NIL) (-33 32560 32808 32835 "AGG" 33334 T AGG (NIL) -9 NIL 33613) (-32 31994 32156 32370 "AGG-" 32375 NIL AGG- (NIL T) -8 NIL NIL) (-31 29681 30099 30516 "AF" 31637 NIL AF (NIL T T) -7 NIL NIL) (-30 28950 29208 29364 "ACPLOT" 29543 T ACPLOT (NIL) -8 NIL NIL) (-29 18416 26362 26414 "ACFS" 27125 NIL ACFS (NIL T) -9 NIL 27364) (-28 16430 16920 17695 "ACFS-" 17700 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14653 14680 "ACF" 15559 T ACF (NIL) -9 NIL 15971) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11195 "ABELSG" 11287 T ABELSG (NIL) -9 NIL 11352) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10523 "ABELMON" 10693 T ABELMON (NIL) -9 NIL 10805) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9606 "ABELGRP" 9731 T ABELGRP (NIL) -9 NIL 9813) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8075 "A1AGG" 8080 NIL A1AGG (NIL T) -9 NIL 8120) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-1197 3137810 3137815 3137820 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3137795 3137800 3137805 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3137780 3137785 3137790 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3137765 3137770 3137775 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3137750 3137755 3137760 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1192 3136880 3137625 3137702 "ZMOD" 3137707 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1191 3135990 3136154 3136363 "ZLINDEP" 3136712 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1190 3125394 3127139 3129091 "ZDSOLVE" 3134139 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1189 3124640 3124781 3124970 "YSTREAM" 3125240 NIL YSTREAM (NIL T) -7 NIL NIL) (-1188 3122408 3123945 3124148 "XRPOLY" 3124483 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1187 3118870 3120199 3120781 "XPR" 3121872 NIL XPR (NIL T T) -8 NIL NIL) (-1186 3116584 3118205 3118408 "XPOLY" 3118701 NIL XPOLY (NIL T) -8 NIL NIL) (-1185 3114397 3115775 3115830 "XPOLYC" 3116115 NIL XPOLYC (NIL T T) -9 NIL 3116228) (-1184 3110769 3112914 3113302 "XPBWPOLY" 3114055 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1183 3106696 3109009 3109052 "XF" 3109673 NIL XF (NIL T) -9 NIL 3110072) (-1182 3106317 3106405 3106574 "XF-" 3106579 NIL XF- (NIL T T) -8 NIL NIL) (-1181 3101696 3102995 3103050 "XFALG" 3105198 NIL XFALG (NIL T T) -9 NIL 3105985) (-1180 3100833 3100937 3101141 "XEXPPKG" 3101588 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1179 3098931 3100684 3100779 "XDPOLY" 3100784 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1178 3097809 3098419 3098462 "XALG" 3098524 NIL XALG (NIL T) -9 NIL 3098643) (-1177 3091285 3095793 3096286 "WUTSET" 3097401 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1176 3089097 3089904 3090255 "WP" 3091067 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1175 3087983 3088181 3088476 "WFFINTBS" 3088894 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1174 3085887 3086314 3086776 "WEIER" 3087555 NIL WEIER (NIL T) -7 NIL NIL) (-1173 3085035 3085459 3085502 "VSPACE" 3085638 NIL VSPACE (NIL T) -9 NIL 3085712) (-1172 3084873 3084900 3084991 "VSPACE-" 3084996 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1171 3084619 3084662 3084733 "VOID" 3084824 T VOID (NIL) -8 NIL NIL) (-1170 3082755 3083114 3083520 "VIEW" 3084235 T VIEW (NIL) -7 NIL NIL) (-1169 3079180 3079818 3080555 "VIEWDEF" 3082040 T VIEWDEF (NIL) -7 NIL NIL) (-1168 3068519 3070728 3072901 "VIEW3D" 3077029 T VIEW3D (NIL) -8 NIL NIL) (-1167 3060801 3062430 3064009 "VIEW2D" 3066962 T VIEW2D (NIL) -8 NIL NIL) (-1166 3056210 3060571 3060663 "VECTOR" 3060744 NIL VECTOR (NIL T) -8 NIL NIL) (-1165 3054787 3055046 3055364 "VECTOR2" 3055940 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1164 3048326 3052578 3052622 "VECTCAT" 3053610 NIL VECTCAT (NIL T) -9 NIL 3054194) (-1163 3047340 3047594 3047984 "VECTCAT-" 3047989 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1162 3046821 3046991 3047111 "VARIABLE" 3047255 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1161 3046753 3046758 3046789 "UTYPE" 3046794 T UTYPE (NIL) -9 NIL NIL) (-1160 3045588 3045742 3046003 "UTSODETL" 3046579 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1159 3043028 3043488 3044012 "UTSODE" 3045129 NIL UTSODE (NIL T T) -7 NIL NIL) (-1158 3034875 3040668 3041156 "UTS" 3042597 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1157 3026223 3031585 3031628 "UTSCAT" 3032729 NIL UTSCAT (NIL T) -9 NIL 3033486) (-1156 3023579 3024294 3025282 "UTSCAT-" 3025287 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1155 3023210 3023253 3023384 "UTS2" 3023530 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1154 3017485 3020050 3020094 "URAGG" 3022164 NIL URAGG (NIL T) -9 NIL 3022886) (-1153 3014424 3015287 3016410 "URAGG-" 3016415 NIL URAGG- (NIL T T) -8 NIL NIL) (-1152 3010110 3013041 3013512 "UPXSSING" 3014088 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1151 3002004 3009231 3009511 "UPXS" 3009887 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1150 2995036 3001909 3001980 "UPXSCONS" 3001985 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1149 2985328 2992155 2992217 "UPXSCCA" 2992866 NIL UPXSCCA (NIL T T) -9 NIL 2993107) (-1148 2984967 2985052 2985225 "UPXSCCA-" 2985230 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1147 2975181 2981781 2981824 "UPXSCAT" 2982467 NIL UPXSCAT (NIL T) -9 NIL 2983075) (-1146 2974615 2974694 2974871 "UPXS2" 2975096 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1145 2973269 2973522 2973873 "UPSQFREE" 2974358 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1144 2967164 2970216 2970271 "UPSCAT" 2971420 NIL UPSCAT (NIL T T) -9 NIL 2972193) (-1143 2966378 2966582 2966905 "UPSCAT-" 2966910 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1142 2952510 2960507 2960550 "UPOLYC" 2962628 NIL UPOLYC (NIL T) -9 NIL 2963848) (-1141 2943903 2946307 2949432 "UPOLYC-" 2949437 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1140 2943534 2943577 2943708 "UPOLYC2" 2943854 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1139 2934993 2943103 2943240 "UP" 2943444 NIL UP (NIL NIL T) -8 NIL NIL) (-1138 2934336 2934443 2934606 "UPMP" 2934882 NIL UPMP (NIL T T) -7 NIL NIL) (-1137 2933889 2933970 2934109 "UPDIVP" 2934249 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1136 2932457 2932706 2933022 "UPDECOMP" 2933638 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1135 2931692 2931804 2931989 "UPCDEN" 2932341 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1134 2931215 2931284 2931431 "UP2" 2931617 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1133 2929732 2930419 2930696 "UNISEG" 2930973 NIL UNISEG (NIL T) -8 NIL NIL) (-1132 2928947 2929074 2929279 "UNISEG2" 2929575 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1131 2928007 2928187 2928413 "UNIFACT" 2928763 NIL UNIFACT (NIL T) -7 NIL NIL) (-1130 2911906 2927188 2927438 "ULS" 2927814 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1129 2899874 2911811 2911882 "ULSCONS" 2911887 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1128 2882627 2894637 2894699 "ULSCCAT" 2895411 NIL ULSCCAT (NIL T T) -9 NIL 2895707) (-1127 2881678 2881923 2882310 "ULSCCAT-" 2882315 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1126 2871671 2878185 2878228 "ULSCAT" 2879084 NIL ULSCAT (NIL T) -9 NIL 2879814) (-1125 2871105 2871184 2871361 "ULS2" 2871586 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1124 2869502 2870469 2870500 "UFD" 2870712 T UFD (NIL) -9 NIL 2870826) (-1123 2869296 2869342 2869437 "UFD-" 2869442 NIL UFD- (NIL T) -8 NIL NIL) (-1122 2868378 2868561 2868777 "UDVO" 2869102 T UDVO (NIL) -7 NIL NIL) (-1121 2866194 2866603 2867074 "UDPO" 2867942 NIL UDPO (NIL T) -7 NIL NIL) (-1120 2866126 2866131 2866162 "TYPE" 2866167 T TYPE (NIL) -9 NIL NIL) (-1119 2865097 2865299 2865539 "TWOFACT" 2865920 NIL TWOFACT (NIL T) -7 NIL NIL) (-1118 2864035 2864372 2864635 "TUPLE" 2864869 NIL TUPLE (NIL T) -8 NIL NIL) (-1117 2861726 2862245 2862784 "TUBETOOL" 2863518 T TUBETOOL (NIL) -7 NIL NIL) (-1116 2860575 2860780 2861021 "TUBE" 2861519 NIL TUBE (NIL T) -8 NIL NIL) (-1115 2855299 2859553 2859835 "TS" 2860327 NIL TS (NIL T) -8 NIL NIL) (-1114 2844002 2848094 2848191 "TSETCAT" 2853425 NIL TSETCAT (NIL T T T T) -9 NIL 2854956) (-1113 2838737 2840335 2842225 "TSETCAT-" 2842230 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1112 2833000 2833846 2834788 "TRMANIP" 2837873 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1111 2832441 2832504 2832667 "TRIMAT" 2832932 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1110 2830247 2830484 2830847 "TRIGMNIP" 2832190 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1109 2829766 2829879 2829910 "TRIGCAT" 2830123 T TRIGCAT (NIL) -9 NIL NIL) (-1108 2829435 2829514 2829655 "TRIGCAT-" 2829660 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1107 2826334 2828295 2828575 "TREE" 2829190 NIL TREE (NIL T) -8 NIL NIL) (-1106 2825607 2826135 2826166 "TRANFUN" 2826201 T TRANFUN (NIL) -9 NIL 2826267) (-1105 2824886 2825077 2825357 "TRANFUN-" 2825362 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1104 2824690 2824722 2824783 "TOPSP" 2824847 T TOPSP (NIL) -7 NIL NIL) (-1103 2824042 2824157 2824310 "TOOLSIGN" 2824571 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1102 2822703 2823219 2823458 "TEXTFILE" 2823825 T TEXTFILE (NIL) -8 NIL NIL) (-1101 2820568 2821082 2821520 "TEX" 2822287 T TEX (NIL) -8 NIL NIL) (-1100 2820349 2820380 2820452 "TEX1" 2820531 NIL TEX1 (NIL T) -7 NIL NIL) (-1099 2819997 2820060 2820150 "TEMUTL" 2820281 T TEMUTL (NIL) -7 NIL NIL) (-1098 2818151 2818431 2818756 "TBCMPPK" 2819720 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1097 2810039 2816311 2816368 "TBAGG" 2816768 NIL TBAGG (NIL T T) -9 NIL 2816979) (-1096 2805109 2806597 2808351 "TBAGG-" 2808356 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1095 2804493 2804600 2804745 "TANEXP" 2804998 NIL TANEXP (NIL T) -7 NIL NIL) (-1094 2797994 2804350 2804443 "TABLE" 2804448 NIL TABLE (NIL T T) -8 NIL NIL) (-1093 2797407 2797505 2797643 "TABLEAU" 2797891 NIL TABLEAU (NIL T) -8 NIL NIL) (-1092 2792015 2793235 2794483 "TABLBUMP" 2796193 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1091 2788478 2789173 2789956 "SYSSOLP" 2791266 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1090 2784769 2785477 2786211 "SYNTAX" 2787766 T SYNTAX (NIL) -8 NIL NIL) (-1089 2781903 2782511 2783149 "SYMTAB" 2784153 T SYMTAB (NIL) -8 NIL NIL) (-1088 2777152 2778054 2779037 "SYMS" 2780942 T SYMS (NIL) -8 NIL NIL) (-1087 2774385 2776612 2776841 "SYMPOLY" 2776957 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1086 2773905 2773980 2774102 "SYMFUNC" 2774297 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1085 2769883 2771142 2771964 "SYMBOL" 2773105 T SYMBOL (NIL) -8 NIL NIL) (-1084 2763422 2765111 2766831 "SWITCH" 2768185 T SWITCH (NIL) -8 NIL NIL) (-1083 2756655 2762249 2762551 "SUTS" 2763177 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1082 2748548 2755776 2756056 "SUPXS" 2756432 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1081 2740080 2748169 2748294 "SUP" 2748457 NIL SUP (NIL T) -8 NIL NIL) (-1080 2739239 2739366 2739583 "SUPFRACF" 2739948 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1079 2738864 2738923 2739034 "SUP2" 2739174 NIL SUP2 (NIL T T) -7 NIL NIL) (-1078 2737282 2737556 2737918 "SUMRF" 2738563 NIL SUMRF (NIL T) -7 NIL NIL) (-1077 2736599 2736665 2736863 "SUMFS" 2737203 NIL SUMFS (NIL T T) -7 NIL NIL) (-1076 2720538 2735780 2736030 "SULS" 2736406 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1075 2719860 2720063 2720203 "SUCH" 2720446 NIL SUCH (NIL T T) -8 NIL NIL) (-1074 2713787 2714799 2715757 "SUBSPACE" 2718948 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1073 2713217 2713307 2713471 "SUBRESP" 2713675 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1072 2706586 2707882 2709193 "STTF" 2711953 NIL STTF (NIL T) -7 NIL NIL) (-1071 2700759 2701879 2703026 "STTFNC" 2705486 NIL STTFNC (NIL T) -7 NIL NIL) (-1070 2692110 2693977 2695770 "STTAYLOR" 2699000 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1069 2685354 2691974 2692057 "STRTBL" 2692062 NIL STRTBL (NIL T) -8 NIL NIL) (-1068 2680745 2685309 2685340 "STRING" 2685345 T STRING (NIL) -8 NIL NIL) (-1067 2675633 2680118 2680149 "STRICAT" 2680208 T STRICAT (NIL) -9 NIL 2680270) (-1066 2668349 2673156 2673776 "STREAM" 2675048 NIL STREAM (NIL T) -8 NIL NIL) (-1065 2667859 2667936 2668080 "STREAM3" 2668266 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1064 2666841 2667024 2667259 "STREAM2" 2667672 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1063 2666529 2666581 2666674 "STREAM1" 2666783 NIL STREAM1 (NIL T) -7 NIL NIL) (-1062 2665545 2665726 2665957 "STINPROD" 2666345 NIL STINPROD (NIL T) -7 NIL NIL) (-1061 2665123 2665307 2665338 "STEP" 2665418 T STEP (NIL) -9 NIL 2665496) (-1060 2658666 2665022 2665099 "STBL" 2665104 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1059 2653841 2657888 2657932 "STAGG" 2658085 NIL STAGG (NIL T) -9 NIL 2658174) (-1058 2651543 2652145 2653017 "STAGG-" 2653022 NIL STAGG- (NIL T T) -8 NIL NIL) (-1057 2649738 2651313 2651405 "STACK" 2651486 NIL STACK (NIL T) -8 NIL NIL) (-1056 2642469 2647885 2648340 "SREGSET" 2649368 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1055 2634909 2636277 2637789 "SRDCMPK" 2641075 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1054 2627876 2632349 2632380 "SRAGG" 2633683 T SRAGG (NIL) -9 NIL 2634291) (-1053 2626893 2627148 2627527 "SRAGG-" 2627532 NIL SRAGG- (NIL T) -8 NIL NIL) (-1052 2621342 2625812 2626239 "SQMATRIX" 2626512 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1051 2615094 2618062 2618788 "SPLTREE" 2620688 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1050 2611084 2611750 2612396 "SPLNODE" 2614520 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1049 2610130 2610363 2610394 "SPFCAT" 2610838 T SPFCAT (NIL) -9 NIL NIL) (-1048 2608867 2609077 2609341 "SPECOUT" 2609888 T SPECOUT (NIL) -7 NIL NIL) (-1047 2608628 2608668 2608737 "SPADPRSR" 2608820 T SPADPRSR (NIL) -7 NIL NIL) (-1046 2600650 2602397 2602440 "SPACEC" 2606763 NIL SPACEC (NIL T) -9 NIL 2608579) (-1045 2598822 2600583 2600631 "SPACE3" 2600636 NIL SPACE3 (NIL T) -8 NIL NIL) (-1044 2597574 2597745 2598036 "SORTPAK" 2598627 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1043 2595630 2595933 2596351 "SOLVETRA" 2597238 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1042 2594641 2594863 2595137 "SOLVESER" 2595403 NIL SOLVESER (NIL T) -7 NIL NIL) (-1041 2589861 2590742 2591744 "SOLVERAD" 2593693 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1040 2585676 2586285 2587014 "SOLVEFOR" 2589228 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1039 2579975 2585027 2585124 "SNTSCAT" 2585129 NIL SNTSCAT (NIL T T T T) -9 NIL 2585199) (-1038 2574080 2578306 2578696 "SMTS" 2579665 NIL SMTS (NIL T T T) -8 NIL NIL) (-1037 2568491 2573969 2574045 "SMP" 2574050 NIL SMP (NIL T T) -8 NIL NIL) (-1036 2566650 2566951 2567349 "SMITH" 2568188 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1035 2559614 2563810 2563913 "SMATCAT" 2565253 NIL SMATCAT (NIL NIL T T T) -9 NIL 2565802) (-1034 2556555 2557378 2558555 "SMATCAT-" 2558560 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1033 2554268 2555791 2555835 "SKAGG" 2556096 NIL SKAGG (NIL T) -9 NIL 2556231) (-1032 2550326 2553372 2553650 "SINT" 2554012 T SINT (NIL) -8 NIL NIL) (-1031 2550098 2550136 2550202 "SIMPAN" 2550282 T SIMPAN (NIL) -7 NIL NIL) (-1030 2548936 2549157 2549432 "SIGNRF" 2549857 NIL SIGNRF (NIL T) -7 NIL NIL) (-1029 2547745 2547896 2548186 "SIGNEF" 2548765 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1028 2545435 2545889 2546395 "SHP" 2547286 NIL SHP (NIL T NIL) -7 NIL NIL) (-1027 2539288 2545336 2545412 "SHDP" 2545417 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1026 2538777 2538969 2539000 "SGROUP" 2539152 T SGROUP (NIL) -9 NIL 2539239) (-1025 2538547 2538599 2538703 "SGROUP-" 2538708 NIL SGROUP- (NIL T) -8 NIL NIL) (-1024 2535383 2536080 2536803 "SGCF" 2537846 T SGCF (NIL) -7 NIL NIL) (-1023 2529781 2534833 2534930 "SFRTCAT" 2534935 NIL SFRTCAT (NIL T T T T) -9 NIL 2534973) (-1022 2523241 2524256 2525390 "SFRGCD" 2528764 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1021 2516407 2517478 2518662 "SFQCMPK" 2522174 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1020 2516029 2516118 2516228 "SFORT" 2516348 NIL SFORT (NIL T T) -8 NIL NIL) (-1019 2515174 2515869 2515990 "SEXOF" 2515995 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1018 2514308 2515055 2515123 "SEX" 2515128 T SEX (NIL) -8 NIL NIL) (-1017 2509084 2509773 2509869 "SEXCAT" 2513640 NIL SEXCAT (NIL T T T T T) -9 NIL 2514259) (-1016 2506264 2509018 2509066 "SET" 2509071 NIL SET (NIL T) -8 NIL NIL) (-1015 2504515 2504977 2505282 "SETMN" 2506005 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1014 2504122 2504248 2504279 "SETCAT" 2504396 T SETCAT (NIL) -9 NIL 2504480) (-1013 2503902 2503954 2504053 "SETCAT-" 2504058 NIL SETCAT- (NIL T) -8 NIL NIL) (-1012 2500289 2502363 2502407 "SETAGG" 2503277 NIL SETAGG (NIL T) -9 NIL 2503617) (-1011 2499747 2499863 2500100 "SETAGG-" 2500105 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1010 2498950 2499243 2499305 "SEGXCAT" 2499591 NIL SEGXCAT (NIL T T) -9 NIL 2499711) (-1009 2498006 2498616 2498798 "SEG" 2498803 NIL SEG (NIL T) -8 NIL NIL) (-1008 2496912 2497125 2497169 "SEGCAT" 2497751 NIL SEGCAT (NIL T) -9 NIL 2497989) (-1007 2495961 2496291 2496491 "SEGBIND" 2496747 NIL SEGBIND (NIL T) -8 NIL NIL) (-1006 2495582 2495641 2495754 "SEGBIND2" 2495896 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1005 2494801 2494927 2495131 "SEG2" 2495426 NIL SEG2 (NIL T T) -7 NIL NIL) (-1004 2494238 2494736 2494783 "SDVAR" 2494788 NIL SDVAR (NIL T) -8 NIL NIL) (-1003 2486490 2494011 2494139 "SDPOL" 2494144 NIL SDPOL (NIL T) -8 NIL NIL) (-1002 2485083 2485349 2485668 "SCPKG" 2486205 NIL SCPKG (NIL T) -7 NIL NIL) (-1001 2484220 2484399 2484599 "SCOPE" 2484905 T SCOPE (NIL) -8 NIL NIL) (-1000 2483441 2483574 2483753 "SCACHE" 2484075 NIL SCACHE (NIL T) -7 NIL NIL) (-999 2482884 2483205 2483288 "SAOS" 2483378 T SAOS (NIL) -8 NIL NIL) (-998 2482452 2482487 2482658 "SAERFFC" 2482843 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-997 2476348 2482351 2482429 "SAE" 2482434 NIL SAE (NIL T T NIL) -8 NIL NIL) (-996 2475944 2475979 2476136 "SAEFACT" 2476307 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-995 2474270 2474584 2474983 "RURPK" 2475610 NIL RURPK (NIL T NIL) -7 NIL NIL) (-994 2472923 2473200 2473507 "RULESET" 2474106 NIL RULESET (NIL T T T) -8 NIL NIL) (-993 2470131 2470634 2471095 "RULE" 2472605 NIL RULE (NIL T T T) -8 NIL NIL) (-992 2469773 2469928 2470009 "RULECOLD" 2470083 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-991 2464665 2465459 2466375 "RSETGCD" 2468972 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-990 2453979 2459031 2459126 "RSETCAT" 2463191 NIL RSETCAT (NIL T T T T) -9 NIL 2464288) (-989 2451910 2452449 2453269 "RSETCAT-" 2453274 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-988 2444340 2445715 2447231 "RSDCMPK" 2450509 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-987 2442357 2442798 2442871 "RRCC" 2443947 NIL RRCC (NIL T T) -9 NIL 2444291) (-986 2441711 2441885 2442161 "RRCC-" 2442166 NIL RRCC- (NIL T T T) -8 NIL NIL) (-985 2416077 2425702 2425767 "RPOLCAT" 2436269 NIL RPOLCAT (NIL T T T) -9 NIL 2439427) (-984 2407581 2409919 2413037 "RPOLCAT-" 2413042 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-983 2398647 2405811 2406291 "ROUTINE" 2407121 T ROUTINE (NIL) -8 NIL NIL) (-982 2395352 2398203 2398350 "ROMAN" 2398520 T ROMAN (NIL) -8 NIL NIL) (-981 2393638 2394223 2394480 "ROIRC" 2395158 NIL ROIRC (NIL T T) -8 NIL NIL) (-980 2390042 2392346 2392375 "RNS" 2392671 T RNS (NIL) -9 NIL 2392941) (-979 2388556 2388939 2389470 "RNS-" 2389543 NIL RNS- (NIL T) -8 NIL NIL) (-978 2387981 2388389 2388418 "RNG" 2388423 T RNG (NIL) -9 NIL 2388444) (-977 2387378 2387740 2387781 "RMODULE" 2387841 NIL RMODULE (NIL T) -9 NIL 2387883) (-976 2386230 2386324 2386654 "RMCAT2" 2387279 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-975 2382944 2385413 2385734 "RMATRIX" 2385965 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-974 2375940 2378174 2378287 "RMATCAT" 2381596 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2382578) (-973 2375319 2375466 2375769 "RMATCAT-" 2375774 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-972 2374889 2374964 2375090 "RINTERP" 2375238 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-971 2373939 2374503 2374532 "RING" 2374642 T RING (NIL) -9 NIL 2374736) (-970 2373734 2373778 2373872 "RING-" 2373877 NIL RING- (NIL T) -8 NIL NIL) (-969 2372582 2372819 2373075 "RIDIST" 2373498 T RIDIST (NIL) -7 NIL NIL) (-968 2363904 2372056 2372259 "RGCHAIN" 2372431 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-967 2360909 2361523 2362191 "RF" 2363268 NIL RF (NIL T) -7 NIL NIL) (-966 2360558 2360621 2360722 "RFFACTOR" 2360840 NIL RFFACTOR (NIL T) -7 NIL NIL) (-965 2360286 2360321 2360416 "RFFACT" 2360517 NIL RFFACT (NIL T) -7 NIL NIL) (-964 2358416 2358780 2359160 "RFDIST" 2359926 T RFDIST (NIL) -7 NIL NIL) (-963 2357874 2357966 2358126 "RETSOL" 2358318 NIL RETSOL (NIL T T) -7 NIL NIL) (-962 2357466 2357546 2357588 "RETRACT" 2357778 NIL RETRACT (NIL T) -9 NIL NIL) (-961 2357318 2357343 2357427 "RETRACT-" 2357432 NIL RETRACT- (NIL T T) -8 NIL NIL) (-960 2350176 2356975 2357100 "RESULT" 2357213 T RESULT (NIL) -8 NIL NIL) (-959 2348761 2349450 2349647 "RESRING" 2350079 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-958 2348401 2348450 2348546 "RESLATC" 2348698 NIL RESLATC (NIL T) -7 NIL NIL) (-957 2348110 2348144 2348249 "REPSQ" 2348360 NIL REPSQ (NIL T) -7 NIL NIL) (-956 2345541 2346121 2346721 "REP" 2347530 T REP (NIL) -7 NIL NIL) (-955 2345242 2345276 2345385 "REPDB" 2345500 NIL REPDB (NIL T) -7 NIL NIL) (-954 2339187 2340566 2341786 "REP2" 2344054 NIL REP2 (NIL T) -7 NIL NIL) (-953 2335593 2336274 2337079 "REP1" 2338414 NIL REP1 (NIL T) -7 NIL NIL) (-952 2328339 2333754 2334206 "REGSET" 2335224 NIL REGSET (NIL T T T T) -8 NIL NIL) (-951 2327160 2327495 2327743 "REF" 2328124 NIL REF (NIL T) -8 NIL NIL) (-950 2326541 2326644 2326809 "REDORDER" 2327044 NIL REDORDER (NIL T T) -7 NIL NIL) (-949 2322510 2325775 2325996 "RECLOS" 2326372 NIL RECLOS (NIL T) -8 NIL NIL) (-948 2321567 2321748 2321961 "REALSOLV" 2322317 T REALSOLV (NIL) -7 NIL NIL) (-947 2321414 2321455 2321484 "REAL" 2321489 T REAL (NIL) -9 NIL 2321524) (-946 2317905 2318707 2319589 "REAL0Q" 2320579 NIL REAL0Q (NIL T) -7 NIL NIL) (-945 2313516 2314504 2315563 "REAL0" 2316886 NIL REAL0 (NIL T) -7 NIL NIL) (-944 2312924 2312996 2313201 "RDIV" 2313438 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-943 2311997 2312171 2312382 "RDIST" 2312746 NIL RDIST (NIL T) -7 NIL NIL) (-942 2310601 2310888 2311257 "RDETRS" 2311705 NIL RDETRS (NIL T T) -7 NIL NIL) (-941 2308422 2308876 2309411 "RDETR" 2310143 NIL RDETR (NIL T T) -7 NIL NIL) (-940 2307038 2307316 2307717 "RDEEFS" 2308138 NIL RDEEFS (NIL T T) -7 NIL NIL) (-939 2305538 2305844 2306273 "RDEEF" 2306726 NIL RDEEF (NIL T T) -7 NIL NIL) (-938 2299822 2302754 2302783 "RCFIELD" 2304060 T RCFIELD (NIL) -9 NIL 2304790) (-937 2297891 2298395 2299088 "RCFIELD-" 2299161 NIL RCFIELD- (NIL T) -8 NIL NIL) (-936 2294222 2296007 2296049 "RCAGG" 2297120 NIL RCAGG (NIL T) -9 NIL 2297585) (-935 2293853 2293947 2294107 "RCAGG-" 2294112 NIL RCAGG- (NIL T T) -8 NIL NIL) (-934 2293198 2293309 2293471 "RATRET" 2293737 NIL RATRET (NIL T) -7 NIL NIL) (-933 2292755 2292822 2292941 "RATFACT" 2293126 NIL RATFACT (NIL T) -7 NIL NIL) (-932 2292070 2292190 2292340 "RANDSRC" 2292625 T RANDSRC (NIL) -7 NIL NIL) (-931 2291807 2291851 2291922 "RADUTIL" 2292019 T RADUTIL (NIL) -7 NIL NIL) (-930 2284814 2290550 2290867 "RADIX" 2291522 NIL RADIX (NIL NIL) -8 NIL NIL) (-929 2276384 2284658 2284786 "RADFF" 2284791 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-928 2276035 2276110 2276139 "RADCAT" 2276296 T RADCAT (NIL) -9 NIL NIL) (-927 2275820 2275868 2275965 "RADCAT-" 2275970 NIL RADCAT- (NIL T) -8 NIL NIL) (-926 2273971 2275595 2275684 "QUEUE" 2275764 NIL QUEUE (NIL T) -8 NIL NIL) (-925 2270468 2273908 2273953 "QUAT" 2273958 NIL QUAT (NIL T) -8 NIL NIL) (-924 2270106 2270149 2270276 "QUATCT2" 2270419 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-923 2263899 2267279 2267320 "QUATCAT" 2268099 NIL QUATCAT (NIL T) -9 NIL 2268864) (-922 2260043 2261080 2262467 "QUATCAT-" 2262561 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-921 2257563 2259127 2259169 "QUAGG" 2259544 NIL QUAGG (NIL T) -9 NIL 2259719) (-920 2256488 2256961 2257133 "QFORM" 2257435 NIL QFORM (NIL NIL T) -8 NIL NIL) (-919 2247784 2253042 2253083 "QFCAT" 2253741 NIL QFCAT (NIL T) -9 NIL 2254734) (-918 2243356 2244557 2246148 "QFCAT-" 2246242 NIL QFCAT- (NIL T T) -8 NIL NIL) (-917 2242994 2243037 2243164 "QFCAT2" 2243307 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-916 2242454 2242564 2242694 "QEQUAT" 2242884 T QEQUAT (NIL) -8 NIL NIL) (-915 2235640 2236711 2237893 "QCMPACK" 2241387 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-914 2233216 2233637 2234065 "QALGSET" 2235295 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-913 2232461 2232635 2232867 "QALGSET2" 2233036 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-912 2231152 2231375 2231692 "PWFFINTB" 2232234 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-911 2229340 2229508 2229861 "PUSHVAR" 2230966 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-910 2225257 2226311 2226353 "PTRANFN" 2228237 NIL PTRANFN (NIL T) -9 NIL NIL) (-909 2223669 2223960 2224281 "PTPACK" 2224968 NIL PTPACK (NIL T) -7 NIL NIL) (-908 2223305 2223362 2223469 "PTFUNC2" 2223606 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-907 2217781 2222122 2222163 "PTCAT" 2222531 NIL PTCAT (NIL T) -9 NIL 2222693) (-906 2217439 2217474 2217598 "PSQFR" 2217740 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-905 2216034 2216332 2216666 "PSEUDLIN" 2217137 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-904 2202842 2205206 2207529 "PSETPK" 2213794 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-903 2195928 2198642 2198737 "PSETCAT" 2201718 NIL PSETCAT (NIL T T T T) -9 NIL 2202532) (-902 2193766 2194400 2195219 "PSETCAT-" 2195224 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-901 2193114 2193279 2193308 "PSCURVE" 2193576 T PSCURVE (NIL) -9 NIL 2193743) (-900 2189565 2191091 2191156 "PSCAT" 2191992 NIL PSCAT (NIL T T T) -9 NIL 2192232) (-899 2188629 2188845 2189244 "PSCAT-" 2189249 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-898 2187282 2187914 2188128 "PRTITION" 2188435 T PRTITION (NIL) -8 NIL NIL) (-897 2176380 2178586 2180774 "PRS" 2185144 NIL PRS (NIL T T) -7 NIL NIL) (-896 2174238 2175730 2175771 "PRQAGG" 2175954 NIL PRQAGG (NIL T) -9 NIL 2176056) (-895 2173808 2173910 2173939 "PROPLOG" 2174124 T PROPLOG (NIL) -9 NIL NIL) (-894 2170931 2171496 2172023 "PROPFRML" 2173313 NIL PROPFRML (NIL T) -8 NIL NIL) (-893 2170391 2170501 2170631 "PROPERTY" 2170821 T PROPERTY (NIL) -8 NIL NIL) (-892 2164165 2168557 2169377 "PRODUCT" 2169617 NIL PRODUCT (NIL T T) -8 NIL NIL) (-891 2161441 2163625 2163858 "PR" 2163976 NIL PR (NIL T T) -8 NIL NIL) (-890 2161237 2161269 2161328 "PRINT" 2161402 T PRINT (NIL) -7 NIL NIL) (-889 2160577 2160694 2160846 "PRIMES" 2161117 NIL PRIMES (NIL T) -7 NIL NIL) (-888 2158642 2159043 2159509 "PRIMELT" 2160156 NIL PRIMELT (NIL T) -7 NIL NIL) (-887 2158370 2158419 2158448 "PRIMCAT" 2158572 T PRIMCAT (NIL) -9 NIL NIL) (-886 2154531 2158308 2158353 "PRIMARR" 2158358 NIL PRIMARR (NIL T) -8 NIL NIL) (-885 2153538 2153716 2153944 "PRIMARR2" 2154349 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-884 2153181 2153237 2153348 "PREASSOC" 2153476 NIL PREASSOC (NIL T T) -7 NIL NIL) (-883 2152655 2152788 2152817 "PPCURVE" 2153022 T PPCURVE (NIL) -9 NIL 2153158) (-882 2150014 2150413 2151005 "POLYROOT" 2152236 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-881 2143920 2149620 2149779 "POLY" 2149887 NIL POLY (NIL T) -8 NIL NIL) (-880 2143305 2143363 2143596 "POLYLIFT" 2143856 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-879 2139590 2140039 2140667 "POLYCATQ" 2142850 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-878 2126630 2132027 2132092 "POLYCAT" 2135577 NIL POLYCAT (NIL T T T) -9 NIL 2137504) (-877 2120081 2121942 2124325 "POLYCAT-" 2124330 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-876 2119670 2119738 2119857 "POLY2UP" 2120007 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-875 2119306 2119363 2119470 "POLY2" 2119607 NIL POLY2 (NIL T T) -7 NIL NIL) (-874 2117991 2118230 2118506 "POLUTIL" 2119080 NIL POLUTIL (NIL T T) -7 NIL NIL) (-873 2116353 2116630 2116960 "POLTOPOL" 2117713 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-872 2111876 2116290 2116335 "POINT" 2116340 NIL POINT (NIL T) -8 NIL NIL) (-871 2110063 2110420 2110795 "PNTHEORY" 2111521 T PNTHEORY (NIL) -7 NIL NIL) (-870 2108491 2108788 2109197 "PMTOOLS" 2109761 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-869 2108084 2108162 2108279 "PMSYM" 2108407 NIL PMSYM (NIL T) -7 NIL NIL) (-868 2107594 2107663 2107837 "PMQFCAT" 2108009 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-867 2106949 2107059 2107215 "PMPRED" 2107471 NIL PMPRED (NIL T) -7 NIL NIL) (-866 2106345 2106431 2106592 "PMPREDFS" 2106850 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-865 2104991 2105199 2105583 "PMPLCAT" 2106107 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-864 2104523 2104602 2104754 "PMLSAGG" 2104906 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-863 2104000 2104076 2104256 "PMKERNEL" 2104441 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-862 2103617 2103692 2103805 "PMINS" 2103919 NIL PMINS (NIL T) -7 NIL NIL) (-861 2103047 2103116 2103331 "PMFS" 2103542 NIL PMFS (NIL T T T) -7 NIL NIL) (-860 2102278 2102396 2102600 "PMDOWN" 2102924 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-859 2101441 2101600 2101782 "PMASS" 2102116 T PMASS (NIL) -7 NIL NIL) (-858 2100715 2100826 2100989 "PMASSFS" 2101327 NIL PMASSFS (NIL T T) -7 NIL NIL) (-857 2100370 2100438 2100532 "PLOTTOOL" 2100641 T PLOTTOOL (NIL) -7 NIL NIL) (-856 2094992 2096181 2097329 "PLOT" 2099242 T PLOT (NIL) -8 NIL NIL) (-855 2090806 2091840 2092761 "PLOT3D" 2094091 T PLOT3D (NIL) -8 NIL NIL) (-854 2089718 2089895 2090130 "PLOT1" 2090610 NIL PLOT1 (NIL T) -7 NIL NIL) (-853 2065113 2069784 2074635 "PLEQN" 2084984 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-852 2064431 2064553 2064733 "PINTERP" 2064978 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-851 2064124 2064171 2064274 "PINTERPA" 2064378 NIL PINTERPA (NIL T T) -7 NIL NIL) (-850 2063351 2063918 2064011 "PI" 2064051 T PI (NIL) -8 NIL NIL) (-849 2061742 2062727 2062756 "PID" 2062938 T PID (NIL) -9 NIL 2063072) (-848 2061467 2061504 2061592 "PICOERCE" 2061699 NIL PICOERCE (NIL T) -7 NIL NIL) (-847 2060788 2060926 2061102 "PGROEB" 2061323 NIL PGROEB (NIL T) -7 NIL NIL) (-846 2056375 2057189 2058094 "PGE" 2059903 T PGE (NIL) -7 NIL NIL) (-845 2054499 2054745 2055111 "PGCD" 2056092 NIL PGCD (NIL T T T T) -7 NIL NIL) (-844 2053837 2053940 2054101 "PFRPAC" 2054383 NIL PFRPAC (NIL T) -7 NIL NIL) (-843 2050452 2052385 2052738 "PFR" 2053516 NIL PFR (NIL T) -8 NIL NIL) (-842 2048841 2049085 2049410 "PFOTOOLS" 2050199 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-841 2047374 2047613 2047964 "PFOQ" 2048598 NIL PFOQ (NIL T T T) -7 NIL NIL) (-840 2045851 2046063 2046425 "PFO" 2047158 NIL PFO (NIL T T T T T) -7 NIL NIL) (-839 2042374 2045740 2045809 "PF" 2045814 NIL PF (NIL NIL) -8 NIL NIL) (-838 2039802 2041083 2041112 "PFECAT" 2041697 T PFECAT (NIL) -9 NIL 2042081) (-837 2039247 2039401 2039615 "PFECAT-" 2039620 NIL PFECAT- (NIL T) -8 NIL NIL) (-836 2037851 2038102 2038403 "PFBRU" 2038996 NIL PFBRU (NIL T T) -7 NIL NIL) (-835 2035718 2036069 2036501 "PFBR" 2037502 NIL PFBR (NIL T T T T) -7 NIL NIL) (-834 2031570 2033094 2033770 "PERM" 2035075 NIL PERM (NIL T) -8 NIL NIL) (-833 2026836 2027777 2028647 "PERMGRP" 2030733 NIL PERMGRP (NIL T) -8 NIL NIL) (-832 2024906 2025899 2025941 "PERMCAT" 2026387 NIL PERMCAT (NIL T) -9 NIL 2026692) (-831 2024561 2024602 2024725 "PERMAN" 2024859 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-830 2022001 2024130 2024261 "PENDTREE" 2024463 NIL PENDTREE (NIL T) -8 NIL NIL) (-829 2020073 2020851 2020893 "PDRING" 2021550 NIL PDRING (NIL T) -9 NIL 2021835) (-828 2019176 2019394 2019756 "PDRING-" 2019761 NIL PDRING- (NIL T T) -8 NIL NIL) (-827 2016318 2017068 2017759 "PDEPROB" 2018505 T PDEPROB (NIL) -8 NIL NIL) (-826 2013889 2014385 2014934 "PDEPACK" 2015789 T PDEPACK (NIL) -7 NIL NIL) (-825 2012801 2012991 2013242 "PDECOMP" 2013688 NIL PDECOMP (NIL T T) -7 NIL NIL) (-824 2010412 2011227 2011256 "PDECAT" 2012041 T PDECAT (NIL) -9 NIL 2012752) (-823 2010165 2010198 2010287 "PCOMP" 2010373 NIL PCOMP (NIL T T) -7 NIL NIL) (-822 2008372 2008968 2009264 "PBWLB" 2009895 NIL PBWLB (NIL T) -8 NIL NIL) (-821 2000881 2002449 2003785 "PATTERN" 2007057 NIL PATTERN (NIL T) -8 NIL NIL) (-820 2000513 2000570 2000679 "PATTERN2" 2000818 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-819 1998270 1998658 1999115 "PATTERN1" 2000102 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-818 1995665 1996219 1996700 "PATRES" 1997835 NIL PATRES (NIL T T) -8 NIL NIL) (-817 1995229 1995296 1995428 "PATRES2" 1995592 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-816 1993126 1993526 1993931 "PATMATCH" 1994898 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-815 1992662 1992845 1992887 "PATMAB" 1992994 NIL PATMAB (NIL T) -9 NIL 1993077) (-814 1991207 1991516 1991774 "PATLRES" 1992467 NIL PATLRES (NIL T T T) -8 NIL NIL) (-813 1990752 1990875 1990917 "PATAB" 1990922 NIL PATAB (NIL T) -9 NIL 1991094) (-812 1988233 1988765 1989338 "PARTPERM" 1990199 T PARTPERM (NIL) -7 NIL NIL) (-811 1987854 1987917 1988019 "PARSURF" 1988164 NIL PARSURF (NIL T) -8 NIL NIL) (-810 1987486 1987543 1987652 "PARSU2" 1987791 NIL PARSU2 (NIL T T) -7 NIL NIL) (-809 1987250 1987290 1987357 "PARSER" 1987439 T PARSER (NIL) -7 NIL NIL) (-808 1986871 1986934 1987036 "PARSCURV" 1987181 NIL PARSCURV (NIL T) -8 NIL NIL) (-807 1986503 1986560 1986669 "PARSC2" 1986808 NIL PARSC2 (NIL T T) -7 NIL NIL) (-806 1986142 1986200 1986297 "PARPCURV" 1986439 NIL PARPCURV (NIL T) -8 NIL NIL) (-805 1985774 1985831 1985940 "PARPC2" 1986079 NIL PARPC2 (NIL T T) -7 NIL NIL) (-804 1985294 1985380 1985499 "PAN2EXPR" 1985675 T PAN2EXPR (NIL) -7 NIL NIL) (-803 1984100 1984415 1984643 "PALETTE" 1985086 T PALETTE (NIL) -8 NIL NIL) (-802 1982568 1983105 1983465 "PAIR" 1983786 NIL PAIR (NIL T T) -8 NIL NIL) (-801 1976418 1981827 1982021 "PADICRC" 1982423 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-800 1969626 1975764 1975948 "PADICRAT" 1976266 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-799 1967930 1969563 1969608 "PADIC" 1969613 NIL PADIC (NIL NIL) -8 NIL NIL) (-798 1965134 1966708 1966749 "PADICCT" 1967330 NIL PADICCT (NIL NIL) -9 NIL 1967612) (-797 1964091 1964291 1964559 "PADEPAC" 1964921 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-796 1963303 1963436 1963642 "PADE" 1963953 NIL PADE (NIL T T T) -7 NIL NIL) (-795 1961314 1962146 1962461 "OWP" 1963071 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-794 1960423 1960919 1961091 "OVAR" 1961182 NIL OVAR (NIL NIL) -8 NIL NIL) (-793 1959687 1959808 1959969 "OUT" 1960282 T OUT (NIL) -7 NIL NIL) (-792 1948733 1950912 1953082 "OUTFORM" 1957537 T OUTFORM (NIL) -8 NIL NIL) (-791 1948141 1948462 1948551 "OSI" 1948664 T OSI (NIL) -8 NIL NIL) (-790 1946886 1947113 1947398 "ORTHPOL" 1947888 NIL ORTHPOL (NIL T) -7 NIL NIL) (-789 1944257 1946547 1946685 "OREUP" 1946829 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-788 1941653 1943950 1944076 "ORESUP" 1944199 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-787 1939188 1939688 1940248 "OREPCTO" 1941142 NIL OREPCTO (NIL T T) -7 NIL NIL) (-786 1933097 1935303 1935344 "OREPCAT" 1937665 NIL OREPCAT (NIL T) -9 NIL 1938768) (-785 1930245 1931027 1932084 "OREPCAT-" 1932089 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-784 1929422 1929694 1929723 "ORDSET" 1930032 T ORDSET (NIL) -9 NIL 1930196) (-783 1928941 1929063 1929256 "ORDSET-" 1929261 NIL ORDSET- (NIL T) -8 NIL NIL) (-782 1927554 1928355 1928384 "ORDRING" 1928586 T ORDRING (NIL) -9 NIL 1928710) (-781 1927199 1927293 1927437 "ORDRING-" 1927442 NIL ORDRING- (NIL T) -8 NIL NIL) (-780 1926574 1927055 1927084 "ORDMON" 1927089 T ORDMON (NIL) -9 NIL 1927110) (-779 1925736 1925883 1926078 "ORDFUNS" 1926423 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-778 1925247 1925606 1925635 "ORDFIN" 1925640 T ORDFIN (NIL) -9 NIL 1925661) (-777 1921759 1923833 1924242 "ORDCOMP" 1924871 NIL ORDCOMP (NIL T) -8 NIL NIL) (-776 1921025 1921152 1921338 "ORDCOMP2" 1921619 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-775 1917533 1918415 1919252 "OPTPROB" 1920208 T OPTPROB (NIL) -8 NIL NIL) (-774 1914375 1915004 1915698 "OPTPACK" 1916859 T OPTPACK (NIL) -7 NIL NIL) (-773 1912100 1912836 1912865 "OPTCAT" 1913680 T OPTCAT (NIL) -9 NIL 1914326) (-772 1911868 1911907 1911973 "OPQUERY" 1912054 T OPQUERY (NIL) -7 NIL NIL) (-771 1909004 1910195 1910695 "OP" 1911400 NIL OP (NIL T) -8 NIL NIL) (-770 1905769 1907801 1908170 "ONECOMP" 1908668 NIL ONECOMP (NIL T) -8 NIL NIL) (-769 1905074 1905189 1905363 "ONECOMP2" 1905641 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-768 1904493 1904599 1904729 "OMSERVER" 1904964 T OMSERVER (NIL) -7 NIL NIL) (-767 1901381 1903933 1903974 "OMSAGG" 1904035 NIL OMSAGG (NIL T) -9 NIL 1904099) (-766 1900004 1900267 1900549 "OMPKG" 1901119 T OMPKG (NIL) -7 NIL NIL) (-765 1899433 1899536 1899565 "OM" 1899864 T OM (NIL) -9 NIL NIL) (-764 1897972 1898985 1899153 "OMLO" 1899314 NIL OMLO (NIL T T) -8 NIL NIL) (-763 1896902 1897049 1897275 "OMEXPR" 1897798 NIL OMEXPR (NIL T) -7 NIL NIL) (-762 1896220 1896448 1896584 "OMERR" 1896786 T OMERR (NIL) -8 NIL NIL) (-761 1895398 1895641 1895801 "OMERRK" 1896080 T OMERRK (NIL) -8 NIL NIL) (-760 1894876 1895075 1895183 "OMENC" 1895310 T OMENC (NIL) -8 NIL NIL) (-759 1888771 1889956 1891127 "OMDEV" 1893725 T OMDEV (NIL) -8 NIL NIL) (-758 1887840 1888011 1888205 "OMCONN" 1888597 T OMCONN (NIL) -8 NIL NIL) (-757 1886455 1887441 1887470 "OINTDOM" 1887475 T OINTDOM (NIL) -9 NIL 1887496) (-756 1882217 1883447 1884162 "OFMONOID" 1885772 NIL OFMONOID (NIL T) -8 NIL NIL) (-755 1881655 1882154 1882199 "ODVAR" 1882204 NIL ODVAR (NIL T) -8 NIL NIL) (-754 1878780 1881152 1881337 "ODR" 1881530 NIL ODR (NIL T T NIL) -8 NIL NIL) (-753 1871086 1878559 1878683 "ODPOL" 1878688 NIL ODPOL (NIL T) -8 NIL NIL) (-752 1864909 1870958 1871063 "ODP" 1871068 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-751 1863675 1863890 1864165 "ODETOOLS" 1864683 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-750 1860644 1861300 1862016 "ODESYS" 1863008 NIL ODESYS (NIL T T) -7 NIL NIL) (-749 1855548 1856456 1857479 "ODERTRIC" 1859719 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-748 1854974 1855056 1855250 "ODERED" 1855460 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-747 1851876 1852424 1853099 "ODERAT" 1854397 NIL ODERAT (NIL T T) -7 NIL NIL) (-746 1848844 1849308 1849904 "ODEPRRIC" 1851405 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-745 1846715 1847282 1847791 "ODEPROB" 1848355 T ODEPROB (NIL) -8 NIL NIL) (-744 1843247 1843730 1844376 "ODEPRIM" 1846194 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-743 1842500 1842602 1842860 "ODEPAL" 1843139 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-742 1838702 1839483 1840337 "ODEPACK" 1841666 T ODEPACK (NIL) -7 NIL NIL) (-741 1837739 1837846 1838074 "ODEINT" 1838591 NIL ODEINT (NIL T T) -7 NIL NIL) (-740 1831840 1833265 1834712 "ODEIFTBL" 1836312 T ODEIFTBL (NIL) -8 NIL NIL) (-739 1827184 1827970 1828928 "ODEEF" 1830999 NIL ODEEF (NIL T T) -7 NIL NIL) (-738 1826521 1826610 1826839 "ODECONST" 1827089 NIL ODECONST (NIL T T T) -7 NIL NIL) (-737 1824678 1825311 1825340 "ODECAT" 1825943 T ODECAT (NIL) -9 NIL 1826472) (-736 1821550 1824390 1824509 "OCT" 1824591 NIL OCT (NIL T) -8 NIL NIL) (-735 1821188 1821231 1821358 "OCTCT2" 1821501 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-734 1816021 1818459 1818500 "OC" 1819596 NIL OC (NIL T) -9 NIL 1820453) (-733 1813248 1813996 1814986 "OC-" 1815080 NIL OC- (NIL T T) -8 NIL NIL) (-732 1812626 1813068 1813097 "OCAMON" 1813102 T OCAMON (NIL) -9 NIL 1813123) (-731 1812079 1812486 1812515 "OASGP" 1812520 T OASGP (NIL) -9 NIL 1812540) (-730 1811366 1811829 1811858 "OAMONS" 1811898 T OAMONS (NIL) -9 NIL 1811941) (-729 1810806 1811213 1811242 "OAMON" 1811247 T OAMON (NIL) -9 NIL 1811267) (-728 1810110 1810602 1810631 "OAGROUP" 1810636 T OAGROUP (NIL) -9 NIL 1810656) (-727 1809800 1809850 1809938 "NUMTUBE" 1810054 NIL NUMTUBE (NIL T) -7 NIL NIL) (-726 1803373 1804891 1806427 "NUMQUAD" 1808284 T NUMQUAD (NIL) -7 NIL NIL) (-725 1799129 1800117 1801142 "NUMODE" 1802368 T NUMODE (NIL) -7 NIL NIL) (-724 1796532 1797378 1797407 "NUMINT" 1798324 T NUMINT (NIL) -9 NIL 1799080) (-723 1795480 1795677 1795895 "NUMFMT" 1796334 T NUMFMT (NIL) -7 NIL NIL) (-722 1781862 1784796 1787326 "NUMERIC" 1792989 NIL NUMERIC (NIL T) -7 NIL NIL) (-721 1776262 1781314 1781409 "NTSCAT" 1781414 NIL NTSCAT (NIL T T T T) -9 NIL 1781452) (-720 1775456 1775621 1775814 "NTPOLFN" 1776101 NIL NTPOLFN (NIL T) -7 NIL NIL) (-719 1763312 1772298 1773108 "NSUP" 1774678 NIL NSUP (NIL T) -8 NIL NIL) (-718 1762948 1763005 1763112 "NSUP2" 1763249 NIL NSUP2 (NIL T T) -7 NIL NIL) (-717 1752910 1762727 1762857 "NSMP" 1762862 NIL NSMP (NIL T T) -8 NIL NIL) (-716 1751342 1751643 1752000 "NREP" 1752598 NIL NREP (NIL T) -7 NIL NIL) (-715 1749933 1750185 1750543 "NPCOEF" 1751085 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-714 1748999 1749114 1749330 "NORMRETR" 1749814 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-713 1747052 1747342 1747749 "NORMPK" 1748707 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-712 1746737 1746765 1746889 "NORMMA" 1747018 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-711 1746564 1746694 1746723 "NONE" 1746728 T NONE (NIL) -8 NIL NIL) (-710 1746353 1746382 1746451 "NONE1" 1746528 NIL NONE1 (NIL T) -7 NIL NIL) (-709 1745838 1745900 1746085 "NODE1" 1746285 NIL NODE1 (NIL T T) -7 NIL NIL) (-708 1744131 1745001 1745256 "NNI" 1745603 T NNI (NIL) -8 NIL NIL) (-707 1742551 1742864 1743228 "NLINSOL" 1743799 NIL NLINSOL (NIL T) -7 NIL NIL) (-706 1738719 1739686 1740608 "NIPROB" 1741649 T NIPROB (NIL) -8 NIL NIL) (-705 1737476 1737710 1738012 "NFINTBAS" 1738481 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-704 1736184 1736415 1736696 "NCODIV" 1737244 NIL NCODIV (NIL T T) -7 NIL NIL) (-703 1735946 1735983 1736058 "NCNTFRAC" 1736141 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-702 1734126 1734490 1734910 "NCEP" 1735571 NIL NCEP (NIL T) -7 NIL NIL) (-701 1733037 1733776 1733805 "NASRING" 1733915 T NASRING (NIL) -9 NIL 1733989) (-700 1732832 1732876 1732970 "NASRING-" 1732975 NIL NASRING- (NIL T) -8 NIL NIL) (-699 1731985 1732484 1732513 "NARNG" 1732630 T NARNG (NIL) -9 NIL 1732721) (-698 1731677 1731744 1731878 "NARNG-" 1731883 NIL NARNG- (NIL T) -8 NIL NIL) (-697 1730556 1730763 1730998 "NAGSP" 1731462 T NAGSP (NIL) -7 NIL NIL) (-696 1721980 1723626 1725261 "NAGS" 1728941 T NAGS (NIL) -7 NIL NIL) (-695 1720544 1720848 1721175 "NAGF07" 1721673 T NAGF07 (NIL) -7 NIL NIL) (-694 1715126 1716406 1717702 "NAGF04" 1719268 T NAGF04 (NIL) -7 NIL NIL) (-693 1708158 1709756 1711373 "NAGF02" 1713529 T NAGF02 (NIL) -7 NIL NIL) (-692 1703422 1704512 1705619 "NAGF01" 1707071 T NAGF01 (NIL) -7 NIL NIL) (-691 1697082 1698640 1700217 "NAGE04" 1701865 T NAGE04 (NIL) -7 NIL NIL) (-690 1688323 1690426 1692538 "NAGE02" 1694990 T NAGE02 (NIL) -7 NIL NIL) (-689 1684316 1685253 1686207 "NAGE01" 1687389 T NAGE01 (NIL) -7 NIL NIL) (-688 1682123 1682654 1683209 "NAGD03" 1683781 T NAGD03 (NIL) -7 NIL NIL) (-687 1673909 1675828 1677773 "NAGD02" 1680198 T NAGD02 (NIL) -7 NIL NIL) (-686 1667768 1669181 1670609 "NAGD01" 1672501 T NAGD01 (NIL) -7 NIL NIL) (-685 1664025 1664835 1665660 "NAGC06" 1666963 T NAGC06 (NIL) -7 NIL NIL) (-684 1662502 1662831 1663184 "NAGC05" 1663692 T NAGC05 (NIL) -7 NIL NIL) (-683 1661886 1662003 1662145 "NAGC02" 1662380 T NAGC02 (NIL) -7 NIL NIL) (-682 1660947 1661504 1661545 "NAALG" 1661624 NIL NAALG (NIL T) -9 NIL 1661685) (-681 1660782 1660811 1660901 "NAALG-" 1660906 NIL NAALG- (NIL T T) -8 NIL NIL) (-680 1654732 1655840 1657027 "MULTSQFR" 1659678 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-679 1654051 1654126 1654310 "MULTFACT" 1654644 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-678 1647244 1651155 1651208 "MTSCAT" 1652268 NIL MTSCAT (NIL T T) -9 NIL 1652782) (-677 1646956 1647010 1647102 "MTHING" 1647184 NIL MTHING (NIL T) -7 NIL NIL) (-676 1646748 1646781 1646841 "MSYSCMD" 1646916 T MSYSCMD (NIL) -7 NIL NIL) (-675 1642860 1645503 1645823 "MSET" 1646461 NIL MSET (NIL T) -8 NIL NIL) (-674 1639955 1642421 1642463 "MSETAGG" 1642468 NIL MSETAGG (NIL T) -9 NIL 1642502) (-673 1635811 1637353 1638094 "MRING" 1639258 NIL MRING (NIL T T) -8 NIL NIL) (-672 1635381 1635448 1635577 "MRF2" 1635738 NIL MRF2 (NIL T T T) -7 NIL NIL) (-671 1634999 1635034 1635178 "MRATFAC" 1635340 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-670 1632611 1632906 1633337 "MPRFF" 1634704 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-669 1626631 1632466 1632562 "MPOLY" 1632567 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-668 1626121 1626156 1626364 "MPCPF" 1626590 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-667 1625637 1625680 1625863 "MPC3" 1626072 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-666 1624838 1624919 1625138 "MPC2" 1625552 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-665 1623139 1623476 1623866 "MONOTOOL" 1624498 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-664 1622263 1622598 1622627 "MONOID" 1622904 T MONOID (NIL) -9 NIL 1623076) (-663 1621641 1621804 1622047 "MONOID-" 1622052 NIL MONOID- (NIL T) -8 NIL NIL) (-662 1612621 1618607 1618667 "MONOGEN" 1619341 NIL MONOGEN (NIL T T) -9 NIL 1619797) (-661 1609839 1610574 1611574 "MONOGEN-" 1611693 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-660 1608698 1609118 1609147 "MONADWU" 1609539 T MONADWU (NIL) -9 NIL 1609777) (-659 1608070 1608229 1608477 "MONADWU-" 1608482 NIL MONADWU- (NIL T) -8 NIL NIL) (-658 1607455 1607673 1607702 "MONAD" 1607909 T MONAD (NIL) -9 NIL 1608021) (-657 1607140 1607218 1607350 "MONAD-" 1607355 NIL MONAD- (NIL T) -8 NIL NIL) (-656 1605391 1606053 1606332 "MOEBIUS" 1606893 NIL MOEBIUS (NIL T) -8 NIL NIL) (-655 1604784 1605162 1605203 "MODULE" 1605208 NIL MODULE (NIL T) -9 NIL 1605234) (-654 1604352 1604448 1604638 "MODULE-" 1604643 NIL MODULE- (NIL T T) -8 NIL NIL) (-653 1602023 1602718 1603044 "MODRING" 1604177 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-652 1598979 1600144 1600661 "MODOP" 1601555 NIL MODOP (NIL T T) -8 NIL NIL) (-651 1597166 1597618 1597959 "MODMONOM" 1598778 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-650 1586884 1595370 1595792 "MODMON" 1596794 NIL MODMON (NIL T T) -8 NIL NIL) (-649 1584010 1585728 1586004 "MODFIELD" 1586759 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-648 1583536 1583579 1583758 "MMAP" 1583961 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-647 1581772 1582549 1582590 "MLO" 1583007 NIL MLO (NIL T) -9 NIL 1583248) (-646 1579139 1579654 1580256 "MLIFT" 1581253 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-645 1578530 1578614 1578768 "MKUCFUNC" 1579050 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-644 1578129 1578199 1578322 "MKRECORD" 1578453 NIL MKRECORD (NIL T T) -7 NIL NIL) (-643 1577177 1577338 1577566 "MKFUNC" 1577940 NIL MKFUNC (NIL T) -7 NIL NIL) (-642 1576565 1576669 1576825 "MKFLCFN" 1577060 NIL MKFLCFN (NIL T) -7 NIL NIL) (-641 1575991 1576358 1576447 "MKCHSET" 1576509 NIL MKCHSET (NIL T) -8 NIL NIL) (-640 1575268 1575370 1575555 "MKBCFUNC" 1575884 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-639 1571952 1574822 1574958 "MINT" 1575152 T MINT (NIL) -8 NIL NIL) (-638 1570764 1571007 1571284 "MHROWRED" 1571707 NIL MHROWRED (NIL T) -7 NIL NIL) (-637 1566035 1569209 1569633 "MFLOAT" 1570360 T MFLOAT (NIL) -8 NIL NIL) (-636 1565392 1565468 1565639 "MFINFACT" 1565947 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-635 1561707 1562555 1563439 "MESH" 1564528 T MESH (NIL) -7 NIL NIL) (-634 1560097 1560409 1560762 "MDDFACT" 1561394 NIL MDDFACT (NIL T) -7 NIL NIL) (-633 1556939 1559256 1559298 "MDAGG" 1559553 NIL MDAGG (NIL T) -9 NIL 1559696) (-632 1546637 1556232 1556439 "MCMPLX" 1556752 T MCMPLX (NIL) -8 NIL NIL) (-631 1545778 1545924 1546124 "MCDEN" 1546486 NIL MCDEN (NIL T T) -7 NIL NIL) (-630 1543668 1543938 1544318 "MCALCFN" 1545508 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-629 1541290 1541813 1542374 "MATSTOR" 1543139 NIL MATSTOR (NIL T) -7 NIL NIL) (-628 1537298 1540665 1540912 "MATRIX" 1541075 NIL MATRIX (NIL T) -8 NIL NIL) (-627 1533068 1533771 1534507 "MATLIN" 1536655 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-626 1523265 1526403 1526480 "MATCAT" 1531318 NIL MATCAT (NIL T T T) -9 NIL 1532735) (-625 1519630 1520643 1521998 "MATCAT-" 1522003 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-624 1518232 1518385 1518716 "MATCAT2" 1519465 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-623 1516344 1516668 1517052 "MAPPKG3" 1517907 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-622 1515325 1515498 1515720 "MAPPKG2" 1516168 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-621 1513824 1514108 1514435 "MAPPKG1" 1515031 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-620 1513435 1513493 1513616 "MAPHACK3" 1513760 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-619 1513027 1513088 1513202 "MAPHACK2" 1513367 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-618 1512465 1512568 1512710 "MAPHACK1" 1512918 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-617 1510573 1511167 1511470 "MAGMA" 1512194 NIL MAGMA (NIL T) -8 NIL NIL) (-616 1507047 1508817 1509277 "M3D" 1510146 NIL M3D (NIL T) -8 NIL NIL) (-615 1501202 1505417 1505459 "LZSTAGG" 1506241 NIL LZSTAGG (NIL T) -9 NIL 1506536) (-614 1497175 1498333 1499790 "LZSTAGG-" 1499795 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-613 1494291 1495068 1495554 "LWORD" 1496721 NIL LWORD (NIL T) -8 NIL NIL) (-612 1487451 1494062 1494196 "LSQM" 1494201 NIL LSQM (NIL NIL T) -8 NIL NIL) (-611 1486675 1486814 1487042 "LSPP" 1487306 NIL LSPP (NIL T T T T) -7 NIL NIL) (-610 1484487 1484788 1485244 "LSMP" 1486364 NIL LSMP (NIL T T T T) -7 NIL NIL) (-609 1481266 1481940 1482670 "LSMP1" 1483789 NIL LSMP1 (NIL T) -7 NIL NIL) (-608 1475192 1480434 1480476 "LSAGG" 1480538 NIL LSAGG (NIL T) -9 NIL 1480616) (-607 1471887 1472811 1474024 "LSAGG-" 1474029 NIL LSAGG- (NIL T T) -8 NIL NIL) (-606 1469513 1471031 1471280 "LPOLY" 1471682 NIL LPOLY (NIL T T) -8 NIL NIL) (-605 1469095 1469180 1469303 "LPEFRAC" 1469422 NIL LPEFRAC (NIL T) -7 NIL NIL) (-604 1467442 1468189 1468442 "LO" 1468927 NIL LO (NIL T T T) -8 NIL NIL) (-603 1467095 1467207 1467236 "LOGIC" 1467347 T LOGIC (NIL) -9 NIL 1467427) (-602 1466957 1466980 1467051 "LOGIC-" 1467056 NIL LOGIC- (NIL T) -8 NIL NIL) (-601 1466150 1466290 1466483 "LODOOPS" 1466813 NIL LODOOPS (NIL T T) -7 NIL NIL) (-600 1463568 1466067 1466132 "LODO" 1466137 NIL LODO (NIL T NIL) -8 NIL NIL) (-599 1462114 1462349 1462700 "LODOF" 1463315 NIL LODOF (NIL T T) -7 NIL NIL) (-598 1458533 1460969 1461010 "LODOCAT" 1461442 NIL LODOCAT (NIL T) -9 NIL 1461653) (-597 1458267 1458325 1458451 "LODOCAT-" 1458456 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-596 1455581 1458108 1458226 "LODO2" 1458231 NIL LODO2 (NIL T T) -8 NIL NIL) (-595 1453010 1455518 1455563 "LODO1" 1455568 NIL LODO1 (NIL T) -8 NIL NIL) (-594 1451873 1452038 1452349 "LODEEF" 1452833 NIL LODEEF (NIL T T T) -7 NIL NIL) (-593 1447159 1450003 1450045 "LNAGG" 1450992 NIL LNAGG (NIL T) -9 NIL 1451436) (-592 1446306 1446520 1446862 "LNAGG-" 1446867 NIL LNAGG- (NIL T T) -8 NIL NIL) (-591 1442471 1443233 1443871 "LMOPS" 1445722 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-590 1441868 1442230 1442271 "LMODULE" 1442331 NIL LMODULE (NIL T) -9 NIL 1442373) (-589 1439114 1441513 1441636 "LMDICT" 1441778 NIL LMDICT (NIL T) -8 NIL NIL) (-588 1432341 1438060 1438358 "LIST" 1438849 NIL LIST (NIL T) -8 NIL NIL) (-587 1431866 1431940 1432079 "LIST3" 1432261 NIL LIST3 (NIL T T T) -7 NIL NIL) (-586 1430873 1431051 1431279 "LIST2" 1431684 NIL LIST2 (NIL T T) -7 NIL NIL) (-585 1429007 1429319 1429718 "LIST2MAP" 1430520 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-584 1427719 1428399 1428440 "LINEXP" 1428693 NIL LINEXP (NIL T) -9 NIL 1428841) (-583 1426366 1426626 1426923 "LINDEP" 1427471 NIL LINDEP (NIL T T) -7 NIL NIL) (-582 1423133 1423852 1424629 "LIMITRF" 1425621 NIL LIMITRF (NIL T) -7 NIL NIL) (-581 1421413 1421708 1422123 "LIMITPS" 1422828 NIL LIMITPS (NIL T T) -7 NIL NIL) (-580 1415868 1420924 1421152 "LIE" 1421234 NIL LIE (NIL T T) -8 NIL NIL) (-579 1414918 1415361 1415402 "LIECAT" 1415542 NIL LIECAT (NIL T) -9 NIL 1415693) (-578 1414759 1414786 1414874 "LIECAT-" 1414879 NIL LIECAT- (NIL T T) -8 NIL NIL) (-577 1407371 1414208 1414373 "LIB" 1414614 T LIB (NIL) -8 NIL NIL) (-576 1403008 1403889 1404824 "LGROBP" 1406488 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-575 1400874 1401148 1401510 "LF" 1402729 NIL LF (NIL T T) -7 NIL NIL) (-574 1399713 1400405 1400434 "LFCAT" 1400641 T LFCAT (NIL) -9 NIL 1400780) (-573 1396625 1397251 1397937 "LEXTRIPK" 1399079 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-572 1393331 1394195 1394698 "LEXP" 1396205 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-571 1391729 1392042 1392443 "LEADCDET" 1393013 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-570 1390925 1390999 1391226 "LAZM3PK" 1391650 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-569 1385841 1389004 1389541 "LAUPOL" 1390438 NIL LAUPOL (NIL T T) -8 NIL NIL) (-568 1385408 1385452 1385619 "LAPLACE" 1385791 NIL LAPLACE (NIL T T) -7 NIL NIL) (-567 1383336 1384509 1384760 "LA" 1385241 NIL LA (NIL T T T) -8 NIL NIL) (-566 1382398 1382992 1383033 "LALG" 1383094 NIL LALG (NIL T) -9 NIL 1383152) (-565 1382113 1382172 1382307 "LALG-" 1382312 NIL LALG- (NIL T T) -8 NIL NIL) (-564 1381023 1381210 1381507 "KOVACIC" 1381913 NIL KOVACIC (NIL T T) -7 NIL NIL) (-563 1380857 1380881 1380923 "KONVERT" 1380985 NIL KONVERT (NIL T) -9 NIL NIL) (-562 1380691 1380715 1380757 "KOERCE" 1380819 NIL KOERCE (NIL T) -9 NIL NIL) (-561 1378425 1379185 1379578 "KERNEL" 1380330 NIL KERNEL (NIL T) -8 NIL NIL) (-560 1377927 1378008 1378138 "KERNEL2" 1378339 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-559 1371778 1376466 1376521 "KDAGG" 1376898 NIL KDAGG (NIL T T) -9 NIL 1377104) (-558 1371307 1371431 1371636 "KDAGG-" 1371641 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-557 1364482 1370968 1371123 "KAFILE" 1371185 NIL KAFILE (NIL T) -8 NIL NIL) (-556 1358937 1363993 1364221 "JORDAN" 1364303 NIL JORDAN (NIL T T) -8 NIL NIL) (-555 1355236 1357142 1357197 "IXAGG" 1358126 NIL IXAGG (NIL T T) -9 NIL 1358585) (-554 1354155 1354461 1354880 "IXAGG-" 1354885 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-553 1349740 1354077 1354136 "IVECTOR" 1354141 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-552 1348506 1348743 1349009 "ITUPLE" 1349507 NIL ITUPLE (NIL T) -8 NIL NIL) (-551 1346942 1347119 1347425 "ITRIGMNP" 1348328 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-550 1345687 1345891 1346174 "ITFUN3" 1346718 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-549 1345319 1345376 1345485 "ITFUN2" 1345624 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-548 1343121 1344192 1344489 "ITAYLOR" 1345054 NIL ITAYLOR (NIL T) -8 NIL NIL) (-547 1332112 1337307 1338466 "ISUPS" 1341994 NIL ISUPS (NIL T) -8 NIL NIL) (-546 1331216 1331356 1331592 "ISUMP" 1331959 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-545 1326480 1331017 1331096 "ISTRING" 1331169 NIL ISTRING (NIL NIL) -8 NIL NIL) (-544 1325693 1325774 1325989 "IRURPK" 1326394 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-543 1324629 1324830 1325070 "IRSN" 1325473 T IRSN (NIL) -7 NIL NIL) (-542 1322664 1323019 1323454 "IRRF2F" 1324267 NIL IRRF2F (NIL T) -7 NIL NIL) (-541 1322411 1322449 1322525 "IRREDFFX" 1322620 NIL IRREDFFX (NIL T) -7 NIL NIL) (-540 1321026 1321285 1321584 "IROOT" 1322144 NIL IROOT (NIL T) -7 NIL NIL) (-539 1317664 1318715 1319405 "IR" 1320368 NIL IR (NIL T) -8 NIL NIL) (-538 1315277 1315772 1316338 "IR2" 1317142 NIL IR2 (NIL T T) -7 NIL NIL) (-537 1314353 1314466 1314686 "IR2F" 1315160 NIL IR2F (NIL T T) -7 NIL NIL) (-536 1314144 1314178 1314238 "IPRNTPK" 1314313 T IPRNTPK (NIL) -7 NIL NIL) (-535 1310698 1314033 1314102 "IPF" 1314107 NIL IPF (NIL NIL) -8 NIL NIL) (-534 1309015 1310623 1310680 "IPADIC" 1310685 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-533 1308514 1308572 1308761 "INVLAPLA" 1308951 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-532 1298163 1300516 1302902 "INTTR" 1306178 NIL INTTR (NIL T T) -7 NIL NIL) (-531 1294511 1295252 1296115 "INTTOOLS" 1297349 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-530 1294097 1294188 1294305 "INTSLPE" 1294414 T INTSLPE (NIL) -7 NIL NIL) (-529 1292047 1294020 1294079 "INTRVL" 1294084 NIL INTRVL (NIL T) -8 NIL NIL) (-528 1289654 1290166 1290740 "INTRF" 1291532 NIL INTRF (NIL T) -7 NIL NIL) (-527 1289069 1289166 1289307 "INTRET" 1289552 NIL INTRET (NIL T) -7 NIL NIL) (-526 1287071 1287460 1287929 "INTRAT" 1288677 NIL INTRAT (NIL T T) -7 NIL NIL) (-525 1284304 1284887 1285512 "INTPM" 1286556 NIL INTPM (NIL T T) -7 NIL NIL) (-524 1281013 1281612 1282356 "INTPAF" 1283690 NIL INTPAF (NIL T T T) -7 NIL NIL) (-523 1276256 1277202 1278237 "INTPACK" 1279998 T INTPACK (NIL) -7 NIL NIL) (-522 1273110 1275985 1276112 "INT" 1276149 T INT (NIL) -8 NIL NIL) (-521 1272362 1272514 1272722 "INTHERTR" 1272952 NIL INTHERTR (NIL T T) -7 NIL NIL) (-520 1271801 1271881 1272069 "INTHERAL" 1272276 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-519 1269647 1270090 1270547 "INTHEORY" 1271364 T INTHEORY (NIL) -7 NIL NIL) (-518 1260970 1262590 1264368 "INTG0" 1267999 NIL INTG0 (NIL T T T) -7 NIL NIL) (-517 1241543 1246333 1251143 "INTFTBL" 1256180 T INTFTBL (NIL) -8 NIL NIL) (-516 1240792 1240930 1241103 "INTFACT" 1241402 NIL INTFACT (NIL T) -7 NIL NIL) (-515 1238183 1238629 1239192 "INTEF" 1240346 NIL INTEF (NIL T T) -7 NIL NIL) (-514 1236644 1237393 1237422 "INTDOM" 1237723 T INTDOM (NIL) -9 NIL 1237930) (-513 1236013 1236187 1236429 "INTDOM-" 1236434 NIL INTDOM- (NIL T) -8 NIL NIL) (-512 1232505 1234437 1234492 "INTCAT" 1235291 NIL INTCAT (NIL T) -9 NIL 1235610) (-511 1231978 1232080 1232208 "INTBIT" 1232397 T INTBIT (NIL) -7 NIL NIL) (-510 1230653 1230807 1231120 "INTALG" 1231823 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-509 1230110 1230200 1230370 "INTAF" 1230557 NIL INTAF (NIL T T) -7 NIL NIL) (-508 1223564 1229920 1230060 "INTABL" 1230065 NIL INTABL (NIL T T T) -8 NIL NIL) (-507 1218514 1221243 1221272 "INS" 1222240 T INS (NIL) -9 NIL 1222921) (-506 1215754 1216525 1217499 "INS-" 1217572 NIL INS- (NIL T) -8 NIL NIL) (-505 1214533 1214760 1215057 "INPSIGN" 1215507 NIL INPSIGN (NIL T T) -7 NIL NIL) (-504 1213651 1213768 1213965 "INPRODPF" 1214413 NIL INPRODPF (NIL T T) -7 NIL NIL) (-503 1212545 1212662 1212899 "INPRODFF" 1213531 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-502 1211545 1211697 1211957 "INNMFACT" 1212381 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-501 1210742 1210839 1211027 "INMODGCD" 1211444 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-500 1209251 1209495 1209819 "INFSP" 1210487 NIL INFSP (NIL T T T) -7 NIL NIL) (-499 1208435 1208552 1208735 "INFPROD0" 1209131 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-498 1205445 1206604 1207095 "INFORM" 1207952 T INFORM (NIL) -8 NIL NIL) (-497 1205055 1205115 1205213 "INFORM1" 1205380 NIL INFORM1 (NIL T) -7 NIL NIL) (-496 1204578 1204667 1204781 "INFINITY" 1204961 T INFINITY (NIL) -7 NIL NIL) (-495 1203196 1203444 1203765 "INEP" 1204326 NIL INEP (NIL T T T) -7 NIL NIL) (-494 1202472 1203093 1203158 "INDE" 1203163 NIL INDE (NIL T) -8 NIL NIL) (-493 1202036 1202104 1202221 "INCRMAPS" 1202399 NIL INCRMAPS (NIL T) -7 NIL NIL) (-492 1197347 1198272 1199216 "INBFF" 1201124 NIL INBFF (NIL T) -7 NIL NIL) (-491 1193842 1197192 1197295 "IMATRIX" 1197300 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-490 1192554 1192677 1192992 "IMATQF" 1193698 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-489 1190774 1191001 1191338 "IMATLIN" 1192310 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-488 1185400 1190698 1190756 "ILIST" 1190761 NIL ILIST (NIL T NIL) -8 NIL NIL) (-487 1183353 1185260 1185373 "IIARRAY2" 1185378 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-486 1178721 1183264 1183328 "IFF" 1183333 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-485 1173764 1178013 1178201 "IFARRAY" 1178578 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-484 1172971 1173668 1173741 "IFAMON" 1173746 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-483 1172554 1172619 1172674 "IEVALAB" 1172881 NIL IEVALAB (NIL T T) -9 NIL NIL) (-482 1172229 1172297 1172457 "IEVALAB-" 1172462 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-481 1171887 1172143 1172206 "IDPO" 1172211 NIL IDPO (NIL T T) -8 NIL NIL) (-480 1171164 1171776 1171851 "IDPOAMS" 1171856 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-479 1170498 1171053 1171128 "IDPOAM" 1171133 NIL IDPOAM (NIL T T) -8 NIL NIL) (-478 1169583 1169833 1169887 "IDPC" 1170300 NIL IDPC (NIL T T) -9 NIL 1170449) (-477 1169079 1169475 1169548 "IDPAM" 1169553 NIL IDPAM (NIL T T) -8 NIL NIL) (-476 1168482 1168971 1169044 "IDPAG" 1169049 NIL IDPAG (NIL T T) -8 NIL NIL) (-475 1164737 1165585 1166480 "IDECOMP" 1167639 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-474 1157611 1158660 1159707 "IDEAL" 1163773 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-473 1156775 1156887 1157086 "ICDEN" 1157495 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-472 1155874 1156255 1156402 "ICARD" 1156648 T ICARD (NIL) -8 NIL NIL) (-471 1153946 1154259 1154662 "IBPTOOLS" 1155551 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-470 1149560 1153566 1153679 "IBITS" 1153865 NIL IBITS (NIL NIL) -8 NIL NIL) (-469 1146283 1146859 1147554 "IBATOOL" 1148977 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-468 1144063 1144524 1145057 "IBACHIN" 1145818 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-467 1141940 1143909 1144012 "IARRAY2" 1144017 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-466 1138093 1141866 1141923 "IARRAY1" 1141928 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-465 1132032 1136511 1136989 "IAN" 1137635 T IAN (NIL) -8 NIL NIL) (-464 1131543 1131600 1131773 "IALGFACT" 1131969 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-463 1131070 1131183 1131212 "HYPCAT" 1131419 T HYPCAT (NIL) -9 NIL NIL) (-462 1130608 1130725 1130911 "HYPCAT-" 1130916 NIL HYPCAT- (NIL T) -8 NIL NIL) (-461 1127287 1128618 1128660 "HOAGG" 1129641 NIL HOAGG (NIL T) -9 NIL 1130320) (-460 1125881 1126280 1126806 "HOAGG-" 1126811 NIL HOAGG- (NIL T T) -8 NIL NIL) (-459 1119712 1125322 1125488 "HEXADEC" 1125735 T HEXADEC (NIL) -8 NIL NIL) (-458 1118460 1118682 1118945 "HEUGCD" 1119489 NIL HEUGCD (NIL T) -7 NIL NIL) (-457 1117563 1118297 1118427 "HELLFDIV" 1118432 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-456 1115791 1117340 1117428 "HEAP" 1117507 NIL HEAP (NIL T) -8 NIL NIL) (-455 1109658 1115706 1115768 "HDP" 1115773 NIL HDP (NIL NIL T) -8 NIL NIL) (-454 1103370 1109295 1109446 "HDMP" 1109559 NIL HDMP (NIL NIL T) -8 NIL NIL) (-453 1102695 1102834 1102998 "HB" 1103226 T HB (NIL) -7 NIL NIL) (-452 1096192 1102541 1102645 "HASHTBL" 1102650 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-451 1093945 1095820 1095999 "HACKPI" 1096033 T HACKPI (NIL) -8 NIL NIL) (-450 1089641 1093799 1093911 "GTSET" 1093916 NIL GTSET (NIL T T T T) -8 NIL NIL) (-449 1083167 1089519 1089617 "GSTBL" 1089622 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-448 1075403 1082203 1082467 "GSERIES" 1082958 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-447 1074425 1074878 1074907 "GROUP" 1075168 T GROUP (NIL) -9 NIL 1075327) (-446 1073541 1073764 1074108 "GROUP-" 1074113 NIL GROUP- (NIL T) -8 NIL NIL) (-445 1071910 1072229 1072616 "GROEBSOL" 1073218 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-444 1070850 1071112 1071164 "GRMOD" 1071693 NIL GRMOD (NIL T T) -9 NIL 1071861) (-443 1070618 1070654 1070782 "GRMOD-" 1070787 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-442 1065946 1066972 1067972 "GRIMAGE" 1069638 T GRIMAGE (NIL) -8 NIL NIL) (-441 1064413 1064673 1064997 "GRDEF" 1065642 T GRDEF (NIL) -7 NIL NIL) (-440 1063857 1063973 1064114 "GRAY" 1064292 T GRAY (NIL) -7 NIL NIL) (-439 1063090 1063470 1063522 "GRALG" 1063675 NIL GRALG (NIL T T) -9 NIL 1063767) (-438 1062751 1062824 1062987 "GRALG-" 1062992 NIL GRALG- (NIL T T T) -8 NIL NIL) (-437 1059559 1062340 1062516 "GPOLSET" 1062658 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-436 1058915 1058972 1059229 "GOSPER" 1059496 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-435 1054674 1055353 1055879 "GMODPOL" 1058614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-434 1053679 1053863 1054101 "GHENSEL" 1054486 NIL GHENSEL (NIL T T) -7 NIL NIL) (-433 1047745 1048588 1049614 "GENUPS" 1052763 NIL GENUPS (NIL T T) -7 NIL NIL) (-432 1047442 1047493 1047582 "GENUFACT" 1047688 NIL GENUFACT (NIL T) -7 NIL NIL) (-431 1046854 1046931 1047096 "GENPGCD" 1047360 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-430 1046328 1046363 1046576 "GENMFACT" 1046813 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-429 1044896 1045151 1045458 "GENEEZ" 1046071 NIL GENEEZ (NIL T T) -7 NIL NIL) (-428 1038770 1044509 1044670 "GDMP" 1044819 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-427 1028152 1032541 1033647 "GCNAALG" 1037753 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-426 1026573 1027445 1027474 "GCDDOM" 1027729 T GCDDOM (NIL) -9 NIL 1027886) (-425 1026043 1026170 1026385 "GCDDOM-" 1026390 NIL GCDDOM- (NIL T) -8 NIL NIL) (-424 1024715 1024900 1025204 "GB" 1025822 NIL GB (NIL T T T T) -7 NIL NIL) (-423 1013335 1015661 1018053 "GBINTERN" 1022406 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-422 1011172 1011464 1011885 "GBF" 1013010 NIL GBF (NIL T T T T) -7 NIL NIL) (-421 1009953 1010118 1010385 "GBEUCLID" 1010988 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-420 1009302 1009427 1009576 "GAUSSFAC" 1009824 T GAUSSFAC (NIL) -7 NIL NIL) (-419 1007679 1007981 1008294 "GALUTIL" 1009021 NIL GALUTIL (NIL T) -7 NIL NIL) (-418 1005996 1006270 1006593 "GALPOLYU" 1007406 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-417 1003385 1003675 1004080 "GALFACTU" 1005693 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-416 995191 996690 998298 "GALFACT" 1001817 NIL GALFACT (NIL T) -7 NIL NIL) (-415 992578 993236 993265 "FVFUN" 994421 T FVFUN (NIL) -9 NIL 995141) (-414 991843 992025 992054 "FVC" 992345 T FVC (NIL) -9 NIL 992528) (-413 991485 991640 991721 "FUNCTION" 991795 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-412 989155 989706 990195 "FT" 991016 T FT (NIL) -8 NIL NIL) (-411 987973 988456 988659 "FTEM" 988972 T FTEM (NIL) -8 NIL NIL) (-410 986238 986526 986928 "FSUPFACT" 987665 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-409 984635 984924 985256 "FST" 985926 T FST (NIL) -8 NIL NIL) (-408 983810 983916 984110 "FSRED" 984517 NIL FSRED (NIL T T) -7 NIL NIL) (-407 982489 982744 983098 "FSPRMELT" 983525 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-406 979574 980012 980511 "FSPECF" 982052 NIL FSPECF (NIL T T) -7 NIL NIL) (-405 961947 970504 970545 "FS" 974383 NIL FS (NIL T) -9 NIL 976665) (-404 950597 953587 957643 "FS-" 957940 NIL FS- (NIL T T) -8 NIL NIL) (-403 950113 950167 950343 "FSINT" 950538 NIL FSINT (NIL T T) -7 NIL NIL) (-402 948394 949106 949409 "FSERIES" 949892 NIL FSERIES (NIL T T) -8 NIL NIL) (-401 947412 947528 947758 "FSCINT" 948274 NIL FSCINT (NIL T T) -7 NIL NIL) (-400 943646 946356 946398 "FSAGG" 946768 NIL FSAGG (NIL T) -9 NIL 947027) (-399 941408 942009 942805 "FSAGG-" 942900 NIL FSAGG- (NIL T T) -8 NIL NIL) (-398 940450 940593 940820 "FSAGG2" 941261 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-397 938109 938388 938941 "FS2UPS" 940168 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-396 937695 937738 937891 "FS2" 938060 NIL FS2 (NIL T T T T) -7 NIL NIL) (-395 936555 936726 937034 "FS2EXPXP" 937520 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-394 935981 936096 936248 "FRUTIL" 936435 NIL FRUTIL (NIL T) -7 NIL NIL) (-393 927402 931480 932836 "FR" 934657 NIL FR (NIL T) -8 NIL NIL) (-392 922478 925121 925162 "FRNAALG" 926558 NIL FRNAALG (NIL T) -9 NIL 927165) (-391 918157 919227 920502 "FRNAALG-" 921252 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-390 917795 917838 917965 "FRNAAF2" 918108 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-389 916160 916652 916946 "FRMOD" 917608 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-388 913883 914551 914867 "FRIDEAL" 915951 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-387 913082 913169 913456 "FRIDEAL2" 913790 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-386 912339 912747 912789 "FRETRCT" 912794 NIL FRETRCT (NIL T) -9 NIL 912965) (-385 911451 911682 912033 "FRETRCT-" 912038 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-384 908660 909880 909940 "FRAMALG" 910822 NIL FRAMALG (NIL T T) -9 NIL 911114) (-383 906793 907249 907879 "FRAMALG-" 908102 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-382 900695 906268 906544 "FRAC" 906549 NIL FRAC (NIL T) -8 NIL NIL) (-381 900331 900388 900495 "FRAC2" 900632 NIL FRAC2 (NIL T T) -7 NIL NIL) (-380 899967 900024 900131 "FR2" 900268 NIL FR2 (NIL T T) -7 NIL NIL) (-379 894640 897553 897582 "FPS" 898701 T FPS (NIL) -9 NIL 899257) (-378 894089 894198 894362 "FPS-" 894508 NIL FPS- (NIL T) -8 NIL NIL) (-377 891537 893234 893263 "FPC" 893488 T FPC (NIL) -9 NIL 893630) (-376 891330 891370 891467 "FPC-" 891472 NIL FPC- (NIL T) -8 NIL NIL) (-375 890208 890818 890860 "FPATMAB" 890865 NIL FPATMAB (NIL T) -9 NIL 891017) (-374 887908 888384 888810 "FPARFRAC" 889845 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-373 883303 883800 884482 "FORTRAN" 887340 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-372 881019 881519 882058 "FORT" 882784 T FORT (NIL) -7 NIL NIL) (-371 878694 879256 879285 "FORTFN" 880345 T FORTFN (NIL) -9 NIL 880969) (-370 878457 878507 878536 "FORTCAT" 878595 T FORTCAT (NIL) -9 NIL 878657) (-369 876517 877000 877399 "FORMULA" 878078 T FORMULA (NIL) -8 NIL NIL) (-368 876305 876335 876404 "FORMULA1" 876481 NIL FORMULA1 (NIL T) -7 NIL NIL) (-367 875828 875880 876053 "FORDER" 876247 NIL FORDER (NIL T T T T) -7 NIL NIL) (-366 874924 875088 875281 "FOP" 875655 T FOP (NIL) -7 NIL NIL) (-365 873532 874204 874378 "FNLA" 874806 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-364 872200 872589 872618 "FNCAT" 873190 T FNCAT (NIL) -9 NIL 873483) (-363 871766 872159 872187 "FNAME" 872192 T FNAME (NIL) -8 NIL NIL) (-362 870425 871398 871427 "FMTC" 871432 T FMTC (NIL) -9 NIL 871467) (-361 866743 867950 868578 "FMONOID" 869830 NIL FMONOID (NIL T) -8 NIL NIL) (-360 865963 866486 866634 "FM" 866639 NIL FM (NIL T T) -8 NIL NIL) (-359 863386 864032 864061 "FMFUN" 865205 T FMFUN (NIL) -9 NIL 865913) (-358 862654 862835 862864 "FMC" 863154 T FMC (NIL) -9 NIL 863336) (-357 859883 860717 860771 "FMCAT" 861953 NIL FMCAT (NIL T T) -9 NIL 862447) (-356 858778 859651 859750 "FM1" 859828 NIL FM1 (NIL T T) -8 NIL NIL) (-355 856552 856968 857462 "FLOATRP" 858329 NIL FLOATRP (NIL T) -7 NIL NIL) (-354 850038 854208 854838 "FLOAT" 855942 T FLOAT (NIL) -8 NIL NIL) (-353 847476 847976 848554 "FLOATCP" 849505 NIL FLOATCP (NIL T) -7 NIL NIL) (-352 846264 847112 847153 "FLINEXP" 847158 NIL FLINEXP (NIL T) -9 NIL 847251) (-351 845419 845654 845981 "FLINEXP-" 845986 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-350 844495 844639 844863 "FLASORT" 845271 NIL FLASORT (NIL T T) -7 NIL NIL) (-349 841713 842555 842608 "FLALG" 843835 NIL FLALG (NIL T T) -9 NIL 844302) (-348 835497 839199 839241 "FLAGG" 840503 NIL FLAGG (NIL T) -9 NIL 841155) (-347 834223 834562 835052 "FLAGG-" 835057 NIL FLAGG- (NIL T T) -8 NIL NIL) (-346 833265 833408 833635 "FLAGG2" 834076 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-345 830237 831255 831315 "FINRALG" 832443 NIL FINRALG (NIL T T) -9 NIL 832951) (-344 829397 829626 829965 "FINRALG-" 829970 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-343 828803 829016 829045 "FINITE" 829241 T FINITE (NIL) -9 NIL 829348) (-342 821262 823423 823464 "FINAALG" 827131 NIL FINAALG (NIL T) -9 NIL 828584) (-341 816603 817644 818788 "FINAALG-" 820167 NIL FINAALG- (NIL T T) -8 NIL NIL) (-340 815998 816358 816461 "FILE" 816533 NIL FILE (NIL T) -8 NIL NIL) (-339 814682 814994 815049 "FILECAT" 815733 NIL FILECAT (NIL T T) -9 NIL 815949) (-338 812544 814100 814129 "FIELD" 814169 T FIELD (NIL) -9 NIL 814249) (-337 811164 811549 812060 "FIELD-" 812065 NIL FIELD- (NIL T) -8 NIL NIL) (-336 808979 809801 810147 "FGROUP" 810851 NIL FGROUP (NIL T) -8 NIL NIL) (-335 808069 808233 808453 "FGLMICPK" 808811 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-334 803871 807994 808051 "FFX" 808056 NIL FFX (NIL T NIL) -8 NIL NIL) (-333 803472 803533 803668 "FFSLPE" 803804 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-332 799467 800244 801040 "FFPOLY" 802708 NIL FFPOLY (NIL T) -7 NIL NIL) (-331 798971 799007 799216 "FFPOLY2" 799425 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-330 794793 798890 798953 "FFP" 798958 NIL FFP (NIL T NIL) -8 NIL NIL) (-329 790161 794704 794768 "FF" 794773 NIL FF (NIL NIL NIL) -8 NIL NIL) (-328 785257 789504 789694 "FFNBX" 790015 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-327 780167 784392 784650 "FFNBP" 785111 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-326 774770 779451 779662 "FFNB" 780000 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-325 773602 773800 774115 "FFINTBAS" 774567 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-324 769825 772065 772094 "FFIELDC" 772714 T FFIELDC (NIL) -9 NIL 773090) (-323 768488 768858 769355 "FFIELDC-" 769360 NIL FFIELDC- (NIL T) -8 NIL NIL) (-322 768058 768103 768227 "FFHOM" 768430 NIL FFHOM (NIL T T T) -7 NIL NIL) (-321 765756 766240 766757 "FFF" 767573 NIL FFF (NIL T) -7 NIL NIL) (-320 761344 765498 765599 "FFCGX" 765699 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-319 756946 761076 761183 "FFCGP" 761287 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-318 752099 756673 756781 "FFCG" 756882 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-317 734044 743167 743254 "FFCAT" 748419 NIL FFCAT (NIL T T T) -9 NIL 749906) (-316 729242 730289 731603 "FFCAT-" 732833 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-315 728653 728696 728931 "FFCAT2" 729193 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-314 717853 721643 722860 "FEXPR" 727508 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-313 716852 717287 717329 "FEVALAB" 717413 NIL FEVALAB (NIL T) -9 NIL 717674) (-312 716011 716221 716559 "FEVALAB-" 716564 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-311 714604 715394 715597 "FDIV" 715910 NIL FDIV (NIL T T T T) -8 NIL NIL) (-310 711670 712385 712501 "FDIVCAT" 714069 NIL FDIVCAT (NIL T T T T) -9 NIL 714506) (-309 711432 711459 711629 "FDIVCAT-" 711634 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-308 710652 710739 711016 "FDIV2" 711339 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-307 709338 709597 709886 "FCPAK1" 710383 T FCPAK1 (NIL) -7 NIL NIL) (-306 708466 708838 708979 "FCOMP" 709229 NIL FCOMP (NIL T) -8 NIL NIL) (-305 692094 695509 699072 "FC" 704923 T FC (NIL) -8 NIL NIL) (-304 684689 688735 688776 "FAXF" 690578 NIL FAXF (NIL T) -9 NIL 691269) (-303 681968 682623 683448 "FAXF-" 683913 NIL FAXF- (NIL T T) -8 NIL NIL) (-302 677068 681344 681520 "FARRAY" 681825 NIL FARRAY (NIL T) -8 NIL NIL) (-301 672458 674529 674582 "FAMR" 675594 NIL FAMR (NIL T T) -9 NIL 676054) (-300 671349 671651 672085 "FAMR-" 672090 NIL FAMR- (NIL T T T) -8 NIL NIL) (-299 670545 671271 671324 "FAMONOID" 671329 NIL FAMONOID (NIL T) -8 NIL NIL) (-298 668377 669061 669115 "FAMONC" 670056 NIL FAMONC (NIL T T) -9 NIL 670441) (-297 667069 668131 668268 "FAGROUP" 668273 NIL FAGROUP (NIL T) -8 NIL NIL) (-296 664872 665191 665593 "FACUTIL" 666750 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-295 663971 664156 664378 "FACTFUNC" 664682 NIL FACTFUNC (NIL T) -7 NIL NIL) (-294 656294 663222 663434 "EXPUPXS" 663827 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-293 653777 654317 654903 "EXPRTUBE" 655728 T EXPRTUBE (NIL) -7 NIL NIL) (-292 649971 650563 651300 "EXPRODE" 653116 NIL EXPRODE (NIL T T) -7 NIL NIL) (-291 635130 648630 649056 "EXPR" 649577 NIL EXPR (NIL T) -8 NIL NIL) (-290 629558 630145 630957 "EXPR2UPS" 634428 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-289 629194 629251 629358 "EXPR2" 629495 NIL EXPR2 (NIL T T) -7 NIL NIL) (-288 620548 628331 628626 "EXPEXPAN" 629032 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-287 620375 620505 620534 "EXIT" 620539 T EXIT (NIL) -8 NIL NIL) (-286 620002 620064 620177 "EVALCYC" 620307 NIL EVALCYC (NIL T) -7 NIL NIL) (-285 619542 619660 619702 "EVALAB" 619872 NIL EVALAB (NIL T) -9 NIL 619976) (-284 619023 619145 619366 "EVALAB-" 619371 NIL EVALAB- (NIL T T) -8 NIL NIL) (-283 616485 617797 617826 "EUCDOM" 618381 T EUCDOM (NIL) -9 NIL 618731) (-282 614890 615332 615922 "EUCDOM-" 615927 NIL EUCDOM- (NIL T) -8 NIL NIL) (-281 602468 605216 607956 "ESTOOLS" 612170 T ESTOOLS (NIL) -7 NIL NIL) (-280 602104 602161 602268 "ESTOOLS2" 602405 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-279 601855 601897 601977 "ESTOOLS1" 602056 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-278 595792 597516 597545 "ES" 600309 T ES (NIL) -9 NIL 601715) (-277 590740 592026 593843 "ES-" 594007 NIL ES- (NIL T) -8 NIL NIL) (-276 587115 587875 588655 "ESCONT" 589980 T ESCONT (NIL) -7 NIL NIL) (-275 586860 586892 586974 "ESCONT1" 587077 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-274 586535 586585 586685 "ES2" 586804 NIL ES2 (NIL T T) -7 NIL NIL) (-273 586165 586223 586332 "ES1" 586471 NIL ES1 (NIL T T) -7 NIL NIL) (-272 585381 585510 585686 "ERROR" 586009 T ERROR (NIL) -7 NIL NIL) (-271 578884 585240 585331 "EQTBL" 585336 NIL EQTBL (NIL T T) -8 NIL NIL) (-270 571321 574202 575649 "EQ" 577470 NIL -3185 (NIL T) -8 NIL NIL) (-269 570953 571010 571119 "EQ2" 571258 NIL EQ2 (NIL T T) -7 NIL NIL) (-268 566245 567291 568384 "EP" 569892 NIL EP (NIL T) -7 NIL NIL) (-267 564828 565128 565445 "ENV" 565948 T ENV (NIL) -8 NIL NIL) (-266 563987 564551 564580 "ENTIRER" 564585 T ENTIRER (NIL) -9 NIL 564630) (-265 560443 561942 562312 "EMR" 563786 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-264 559586 559771 559826 "ELTAGG" 560206 NIL ELTAGG (NIL T T) -9 NIL 560417) (-263 559305 559367 559508 "ELTAGG-" 559513 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-262 559093 559122 559177 "ELTAB" 559261 NIL ELTAB (NIL T T) -9 NIL NIL) (-261 558219 558365 558564 "ELFUTS" 558944 NIL ELFUTS (NIL T T) -7 NIL NIL) (-260 557960 558016 558045 "ELEMFUN" 558150 T ELEMFUN (NIL) -9 NIL NIL) (-259 557830 557851 557919 "ELEMFUN-" 557924 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-258 552721 555930 555972 "ELAGG" 556912 NIL ELAGG (NIL T) -9 NIL 557375) (-257 551006 551440 552103 "ELAGG-" 552108 NIL ELAGG- (NIL T T) -8 NIL NIL) (-256 549662 549943 550238 "ELABEXPR" 550731 T ELABEXPR (NIL) -8 NIL NIL) (-255 542530 544329 545156 "EFUPXS" 548938 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-254 535980 537781 538591 "EFULS" 541806 NIL EFULS (NIL T T T) -8 NIL NIL) (-253 533411 533769 534247 "EFSTRUC" 535612 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-252 522483 524048 525608 "EF" 531926 NIL EF (NIL T T) -7 NIL NIL) (-251 521584 521968 522117 "EAB" 522354 T EAB (NIL) -8 NIL NIL) (-250 520797 521543 521571 "E04UCFA" 521576 T E04UCFA (NIL) -8 NIL NIL) (-249 520010 520756 520784 "E04NAFA" 520789 T E04NAFA (NIL) -8 NIL NIL) (-248 519223 519969 519997 "E04MBFA" 520002 T E04MBFA (NIL) -8 NIL NIL) (-247 518436 519182 519210 "E04JAFA" 519215 T E04JAFA (NIL) -8 NIL NIL) (-246 517651 518395 518423 "E04GCFA" 518428 T E04GCFA (NIL) -8 NIL NIL) (-245 516866 517610 517638 "E04FDFA" 517643 T E04FDFA (NIL) -8 NIL NIL) (-244 516079 516825 516853 "E04DGFA" 516858 T E04DGFA (NIL) -8 NIL NIL) (-243 510264 511609 512971 "E04AGNT" 514737 T E04AGNT (NIL) -7 NIL NIL) (-242 508990 509470 509511 "DVARCAT" 509986 NIL DVARCAT (NIL T) -9 NIL 510184) (-241 508194 508406 508720 "DVARCAT-" 508725 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-240 501056 507996 508123 "DSMP" 508128 NIL DSMP (NIL T T T) -8 NIL NIL) (-239 495866 497001 498069 "DROPT" 500008 T DROPT (NIL) -8 NIL NIL) (-238 495531 495590 495688 "DROPT1" 495801 NIL DROPT1 (NIL T) -7 NIL NIL) (-237 490646 491772 492909 "DROPT0" 494414 T DROPT0 (NIL) -7 NIL NIL) (-236 488991 489316 489702 "DRAWPT" 490280 T DRAWPT (NIL) -7 NIL NIL) (-235 483578 484501 485580 "DRAW" 487965 NIL DRAW (NIL T) -7 NIL NIL) (-234 483211 483264 483382 "DRAWHACK" 483519 NIL DRAWHACK (NIL T) -7 NIL NIL) (-233 481942 482211 482502 "DRAWCX" 482940 T DRAWCX (NIL) -7 NIL NIL) (-232 481460 481528 481678 "DRAWCURV" 481868 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-231 471932 473890 476005 "DRAWCFUN" 479365 T DRAWCFUN (NIL) -7 NIL NIL) (-230 468745 470627 470669 "DQAGG" 471298 NIL DQAGG (NIL T) -9 NIL 471571) (-229 457251 463989 464072 "DPOLCAT" 465910 NIL DPOLCAT (NIL T T T T) -9 NIL 466454) (-228 452091 453437 455394 "DPOLCAT-" 455399 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-227 446175 451953 452050 "DPMO" 452055 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-226 440162 445956 446122 "DPMM" 446127 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-225 439675 439773 439893 "DOMAIN" 440062 T DOMAIN (NIL) -8 NIL NIL) (-224 433387 439312 439463 "DMP" 439576 NIL DMP (NIL NIL T) -8 NIL NIL) (-223 432987 433043 433187 "DLP" 433325 NIL DLP (NIL T) -7 NIL NIL) (-222 426631 432088 432315 "DLIST" 432792 NIL DLIST (NIL T) -8 NIL NIL) (-221 423477 425486 425528 "DLAGG" 426078 NIL DLAGG (NIL T) -9 NIL 426307) (-220 422186 422878 422907 "DIVRING" 423057 T DIVRING (NIL) -9 NIL 423165) (-219 421174 421427 421820 "DIVRING-" 421825 NIL DIVRING- (NIL T) -8 NIL NIL) (-218 419276 419633 420039 "DISPLAY" 420788 T DISPLAY (NIL) -7 NIL NIL) (-217 413165 419190 419253 "DIRPROD" 419258 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-216 412013 412216 412481 "DIRPROD2" 412958 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-215 401643 407648 407702 "DIRPCAT" 408110 NIL DIRPCAT (NIL NIL T) -9 NIL 408937) (-214 398969 399611 400492 "DIRPCAT-" 400829 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-213 398256 398416 398602 "DIOSP" 398803 T DIOSP (NIL) -7 NIL NIL) (-212 394958 397168 397210 "DIOPS" 397644 NIL DIOPS (NIL T) -9 NIL 397873) (-211 394507 394621 394812 "DIOPS-" 394817 NIL DIOPS- (NIL T T) -8 NIL NIL) (-210 393378 394016 394045 "DIFRING" 394232 T DIFRING (NIL) -9 NIL 394341) (-209 393024 393101 393253 "DIFRING-" 393258 NIL DIFRING- (NIL T) -8 NIL NIL) (-208 390813 392095 392136 "DIFEXT" 392495 NIL DIFEXT (NIL T) -9 NIL 392788) (-207 389099 389527 390192 "DIFEXT-" 390197 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-206 386421 388631 388673 "DIAGG" 388678 NIL DIAGG (NIL T) -9 NIL 388698) (-205 385805 385962 386214 "DIAGG-" 386219 NIL DIAGG- (NIL T T) -8 NIL NIL) (-204 381270 384764 385041 "DHMATRIX" 385574 NIL DHMATRIX (NIL T) -8 NIL NIL) (-203 376882 377791 378801 "DFSFUN" 380280 T DFSFUN (NIL) -7 NIL NIL) (-202 371668 375596 375961 "DFLOAT" 376537 T DFLOAT (NIL) -8 NIL NIL) (-201 369901 370182 370577 "DFINTTLS" 371376 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-200 366934 367936 368334 "DERHAM" 369568 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-199 364783 366709 366798 "DEQUEUE" 366878 NIL DEQUEUE (NIL T) -8 NIL NIL) (-198 364001 364134 364329 "DEGRED" 364645 NIL DEGRED (NIL T T) -7 NIL NIL) (-197 360401 361146 361998 "DEFINTRF" 363229 NIL DEFINTRF (NIL T) -7 NIL NIL) (-196 357932 358401 358999 "DEFINTEF" 359920 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-195 351763 357373 357539 "DECIMAL" 357786 T DECIMAL (NIL) -8 NIL NIL) (-194 349275 349733 350239 "DDFACT" 351307 NIL DDFACT (NIL T T) -7 NIL NIL) (-193 348871 348914 349065 "DBLRESP" 349226 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-192 346581 346915 347284 "DBASE" 348629 NIL DBASE (NIL T) -8 NIL NIL) (-191 345716 346540 346568 "D03FAFA" 346573 T D03FAFA (NIL) -8 NIL NIL) (-190 344852 345675 345703 "D03EEFA" 345708 T D03EEFA (NIL) -8 NIL NIL) (-189 342802 343268 343757 "D03AGNT" 344383 T D03AGNT (NIL) -7 NIL NIL) (-188 342120 342761 342789 "D02EJFA" 342794 T D02EJFA (NIL) -8 NIL NIL) (-187 341438 342079 342107 "D02CJFA" 342112 T D02CJFA (NIL) -8 NIL NIL) (-186 340756 341397 341425 "D02BHFA" 341430 T D02BHFA (NIL) -8 NIL NIL) (-185 340074 340715 340743 "D02BBFA" 340748 T D02BBFA (NIL) -8 NIL NIL) (-184 333272 334860 336466 "D02AGNT" 338488 T D02AGNT (NIL) -7 NIL NIL) (-183 331041 331563 332109 "D01WGTS" 332746 T D01WGTS (NIL) -7 NIL NIL) (-182 330144 331000 331028 "D01TRNS" 331033 T D01TRNS (NIL) -8 NIL NIL) (-181 329247 330103 330131 "D01GBFA" 330136 T D01GBFA (NIL) -8 NIL NIL) (-180 328350 329206 329234 "D01FCFA" 329239 T D01FCFA (NIL) -8 NIL NIL) (-179 327453 328309 328337 "D01ASFA" 328342 T D01ASFA (NIL) -8 NIL NIL) (-178 326556 327412 327440 "D01AQFA" 327445 T D01AQFA (NIL) -8 NIL NIL) (-177 325659 326515 326543 "D01APFA" 326548 T D01APFA (NIL) -8 NIL NIL) (-176 324762 325618 325646 "D01ANFA" 325651 T D01ANFA (NIL) -8 NIL NIL) (-175 323865 324721 324749 "D01AMFA" 324754 T D01AMFA (NIL) -8 NIL NIL) (-174 322968 323824 323852 "D01ALFA" 323857 T D01ALFA (NIL) -8 NIL NIL) (-173 322071 322927 322955 "D01AKFA" 322960 T D01AKFA (NIL) -8 NIL NIL) (-172 321174 322030 322058 "D01AJFA" 322063 T D01AJFA (NIL) -8 NIL NIL) (-171 314478 316027 317586 "D01AGNT" 319635 T D01AGNT (NIL) -7 NIL NIL) (-170 313815 313943 314095 "CYCLOTOM" 314346 T CYCLOTOM (NIL) -7 NIL NIL) (-169 310550 311263 311990 "CYCLES" 313108 T CYCLES (NIL) -7 NIL NIL) (-168 309862 309996 310167 "CVMP" 310411 NIL CVMP (NIL T) -7 NIL NIL) (-167 307644 307901 308276 "CTRIGMNP" 309590 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-166 307249 307332 307437 "CTORCALL" 307559 T CTORCALL (NIL) -8 NIL NIL) (-165 306623 306722 306875 "CSTTOOLS" 307146 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-164 302422 303079 303837 "CRFP" 305935 NIL CRFP (NIL T T) -7 NIL NIL) (-163 301469 301654 301882 "CRAPACK" 302226 NIL CRAPACK (NIL T) -7 NIL NIL) (-162 300853 300954 301158 "CPMATCH" 301345 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-161 300578 300606 300712 "CPIMA" 300819 NIL CPIMA (NIL T T T) -7 NIL NIL) (-160 296942 297614 298332 "COORDSYS" 299913 NIL COORDSYS (NIL T) -7 NIL NIL) (-159 296326 296455 296605 "CONTOUR" 296812 T CONTOUR (NIL) -8 NIL NIL) (-158 292187 294329 294821 "CONTFRAC" 295866 NIL CONTFRAC (NIL T) -8 NIL NIL) (-157 291340 291904 291933 "COMRING" 291938 T COMRING (NIL) -9 NIL 291989) (-156 290421 290698 290882 "COMPPROP" 291176 T COMPPROP (NIL) -8 NIL NIL) (-155 290082 290117 290245 "COMPLPAT" 290380 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-154 280063 289891 290000 "COMPLEX" 290005 NIL COMPLEX (NIL T) -8 NIL NIL) (-153 279699 279756 279863 "COMPLEX2" 280000 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-152 279417 279452 279550 "COMPFACT" 279658 NIL COMPFACT (NIL T T) -7 NIL NIL) (-151 263751 274045 274086 "COMPCAT" 275088 NIL COMPCAT (NIL T) -9 NIL 276481) (-150 253266 256190 259817 "COMPCAT-" 260173 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-149 252997 253025 253127 "COMMUPC" 253232 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-148 252792 252825 252884 "COMMONOP" 252958 T COMMONOP (NIL) -7 NIL NIL) (-147 252375 252543 252630 "COMM" 252725 T COMM (NIL) -8 NIL NIL) (-146 251623 251817 251846 "COMBOPC" 252184 T COMBOPC (NIL) -9 NIL 252359) (-145 250519 250729 250971 "COMBINAT" 251413 NIL COMBINAT (NIL T) -7 NIL NIL) (-144 246717 247290 247930 "COMBF" 249941 NIL COMBF (NIL T T) -7 NIL NIL) (-143 245503 245833 246068 "COLOR" 246502 T COLOR (NIL) -8 NIL NIL) (-142 245143 245190 245315 "CMPLXRT" 245450 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-141 240645 241673 242753 "CLIP" 244083 T CLIP (NIL) -7 NIL NIL) (-140 238983 239753 239991 "CLIF" 240473 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-139 235205 237129 237171 "CLAGG" 238100 NIL CLAGG (NIL T) -9 NIL 238636) (-138 233627 234084 234667 "CLAGG-" 234672 NIL CLAGG- (NIL T T) -8 NIL NIL) (-137 233171 233256 233396 "CINTSLPE" 233536 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-136 230672 231143 231691 "CHVAR" 232699 NIL CHVAR (NIL T T T) -7 NIL NIL) (-135 229894 230458 230487 "CHARZ" 230492 T CHARZ (NIL) -9 NIL 230506) (-134 229648 229688 229766 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(-12 (-5 *3 (-1032)) (-5 *2 (-108)) (-5 *1 (-758))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-108) *4)) (|has| *1 (-6 -4238)) (-4 *1 (-461 *4)) - (-4 *4 (-1120)) (-5 *2 (-108))))) -(((*1 *1 *2) (-12 (-5 *2 (-803)) (-5 *1 (-239)))) - ((*1 *1 *2) (-12 (-5 *2 (-354)) (-5 *1 (-239))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-588 (-777 (-202)))) (-5 *4 (-202)) (-5 *2 (-588 *4)) - (-5 *1 (-243))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-588 *6)) (-4 *1 (-903 *3 *4 *5 *6)) (-4 *3 (-971)) - (-4 *4 (-730)) (-4 *5 (-784)) (-4 *6 (-985 *3 *4 *5)) - (-4 *3 (-514))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *3 (-708)) (-4 *4 (-283)) (-4 *6 (-1142 *4)) - (-5 *2 (-1166 (-588 *6))) (-5 *1 (-429 *4 *6)) (-5 *5 (-588 *6))))) + (-12 (-5 *3 (-202)) (-5 *4 (-522)) (-5 *2 (-960)) (-5 *1 (-696))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-708)) (-5 *3 (-872 *4)) (-4 *1 (-1046 *4)) + (-4 *4 (-971)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-708)) (-5 *4 (-872 (-202))) (-5 *2 (-1171)) + (-5 *1 (-1168))))) +(((*1 *2 *2) (-12 (-5 *2 (-108)) (-5 *1 (-855))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1085)) (|:| |fn| (-291 (-202))) - (|:| -2386 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| -2321 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (-5 *2 (-2 @@ -6205,7 +5902,7 @@ (-3 (|:| |str| (-1066 (-202))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2386 + (|:| -2321 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -6213,99 +5910,86 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-517))))) -(((*1 *1 *2 *3) - (-12 (-5 *3 (-393 *2)) (-4 *2 (-283)) (-5 *1 (-843 *2)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-382 (-881 *5))) (-5 *4 (-1085)) - (-4 *5 (-13 (-283) (-135))) (-5 *2 (-51)) (-5 *1 (-844 *5)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-393 (-881 *6))) (-5 *5 (-1085)) (-5 *3 (-881 *6)) - (-4 *6 (-13 (-283) 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(-522))) (-5 *1 (-859))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-426))) (-5 *1 (-1112 *3 *2)) - (-4 *2 (-13 (-405 *3) (-1106)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-522)) (-5 *2 (-588 (-588 (-202)))) (-5 *1 (-1117))))) -(((*1 *2 *2 *3) - (-12 (-4 *3 (-514)) (-4 *4 (-348 *3)) (-4 *5 (-348 *3)) - (-5 *1 (-1111 *3 *4 *5 *2)) (-4 *2 (-626 *3 *4 *5))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-442)) (-5 *4 (-850)) (-5 *2 (-1171)) (-5 *1 (-1167))))) -(((*1 *2) (-12 (-5 *2 (-1171)) (-5 *1 (-697))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-522)) (-5 *6 (-1 (-1171) (-1166 *5) (-1166 *5) (-354))) + (-5 *3 (-1166 (-354))) (-5 *5 (-354)) (-5 *2 (-1171)) + (-5 *1 (-725)))) + ((*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) + (-12 (-5 *4 (-522)) (-5 *6 (-1 (-1171) (-1166 *5) (-1166 *5) (-354))) + (-5 *3 (-1166 (-354))) (-5 *5 (-354)) (-5 *2 (-1171)) + (-5 *1 (-725))))) +(((*1 *2 *3 *2) + (-12 + (-5 *2 + (-588 + (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-708)) (|:| |poli| *3) + (|:| |polj| *3)))) + (-4 *5 (-730)) (-4 *3 (-878 *4 *5 *6)) (-4 *4 (-426)) (-4 *6 (-784)) + (-5 *1 (-423 *4 *5 *6 *3))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1188 *4 *2)) (-4 *1 (-349 *4 *2)) (-4 *4 (-784)) (-4 *2 (-157)))) @@ -6465,22 +6084,28 @@ ((*1 *2 *1 *3) (-12 (-4 *2 (-971)) (-5 *1 (-1187 *2 *3)) (-4 *3 (-780))))) (((*1 *2 *1) - (-12 (-5 *2 (-588 (-2 (|:| |gen| *3) (|:| -3266 (-522))))) - (-5 *1 (-336 *3)) (-4 *3 (-1014)))) - ((*1 *2 *1) - (-12 (-5 *2 (-588 (-2 (|:| |gen| *3) (|:| -3266 (-708))))) - (-5 *1 (-361 *3)) (-4 *3 (-1014)))) - ((*1 *2 *1) - (-12 (-5 *2 (-588 (-2 (|:| -1916 *3) (|:| -1400 (-522))))) - (-5 *1 (-393 *3)) (-4 *3 (-514)))) - ((*1 *2 *1) - (-12 (-5 *2 (-588 (-2 (|:| |gen| *3) (|:| -3266 (-708))))) - (-5 *1 (-756 *3)) (-4 *3 (-784))))) -(((*1 *2 *3) (-12 (-5 *3 (-1166 *1)) (-4 *1 (-342 *2)) (-4 *2 (-157)))) - ((*1 *2) (-12 (-4 *2 (-157)) (-5 *1 (-391 *3 *2)) (-4 *3 (-392 *2)))) - ((*1 *2) (-12 (-4 *1 (-392 *2)) (-4 *2 (-157))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-910 *2)) (-4 *2 (-1106))))) -(((*1 *2 *2) 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(-522)))))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-338) (-782))) (-5 *1 (-164 *3 *2)) - (-4 *2 (-1142 (-154 *3)))))) -(((*1 *2 *3 *4) - (-12 (-4 *7 (-426)) (-4 *5 (-730)) (-4 *6 (-784)) (-4 *7 (-514)) - (-4 *8 (-878 *7 *5 *6)) - (-5 *2 (-2 (|:| -1400 (-708)) (|:| -2977 *3) (|:| |radicand| *3))) - (-5 *1 (-882 *5 *6 *7 *8 *3)) (-5 *4 (-708)) - (-4 *3 - (-13 (-338) - (-10 -8 (-15 -2805 (*8 $)) (-15 -2816 (*8 $)) (-15 -2190 ($ *8)))))))) -(((*1 *2 *1) - (-12 (-4 *3 (-338)) (-4 *4 (-730)) (-4 *5 (-784)) (-5 *2 (-588 *6)) - (-5 *1 (-474 *3 *4 *5 *6)) (-4 *6 (-878 *3 *4 *5)))) - ((*1 *2 *1) - (-12 (-5 *2 (-588 (-834 *3))) (-5 *1 (-833 *3)) (-4 *3 (-1014))))) -(((*1 *2 *3) - (-12 (-4 *4 (-514)) (-4 *5 (-730)) (-4 *6 (-784)) - (-4 *7 (-985 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-588 *7)) (|:| |badPols| (-588 *7)))) - (-5 *1 (-904 *4 *5 *6 *7)) (-5 *3 (-588 *7))))) + (-2 + (|:| -2644 + (-2 (|:| |var| (-1085)) (|:| |fn| (-291 (-202))) + (|:| -2321 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| |relerr| (-202)))) + (|:| -3149 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1066 (-202))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2321 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-517))))) +(((*1 *2 *2) (-12 (-5 *2 (-202)) (-5 *1 (-203)))) + ((*1 *2 *2) (-12 (-5 *2 (-154 (-202))) (-5 *1 (-203))))) +(((*1 *2 *1) (-12 (-4 *1 (-512 *2)) (-4 *2 (-13 (-379) (-1106)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-850)) (-5 *1 (-140 *3 *4 *5)) (-14 *3 *2) + (-4 *4 (-338)) (-14 *5 (-920 *3 *4))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-270 (-770 *3))) - (-4 *5 (-13 (-426) (-784) (-962 (-522)) (-584 (-522)))) - (-5 *2 (-770 *3)) (-5 *1 (-581 *5 *3)) - (-4 *3 (-13 (-27) (-1106) (-405 *5))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-270 (-770 (-881 *5)))) (-4 *5 (-426)) - (-5 *2 (-770 (-382 (-881 *5)))) (-5 *1 (-582 *5)) - (-5 *3 (-382 (-881 *5))))) + (-12 (-5 *3 (-202)) (-5 *4 (-522)) (-5 *2 (-960)) (-5 *1 (-696))))) +(((*1 *2 *3 *4 *4 *5 *6) + (-12 (-5 *3 (-588 (-588 (-872 (-202))))) (-5 *4 (-803)) + (-5 *5 (-850)) (-5 *6 (-588 (-239))) (-5 *2 (-442)) (-5 *1 (-1170)))) + ((*1 *2 *3) + (-12 (-5 *3 (-588 (-588 (-872 (-202))))) (-5 *2 (-442)) + (-5 *1 (-1170)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-270 (-382 (-881 *5)))) (-5 *3 (-382 (-881 *5))) - (-4 *5 (-426)) (-5 *2 (-770 *3)) (-5 *1 (-582 *5))))) + (-12 (-5 *3 (-588 (-588 (-872 (-202))))) (-5 *4 (-588 (-239))) + (-5 *2 (-442)) (-5 *1 (-1170))))) +(((*1 *1 *2) (-12 (-5 *2 (-522)) (-5 *1 (-792))))) +(((*1 *2 *1 *3 *3 *4) + (-12 (-5 *3 (-1 (-792) (-792) (-792))) (-5 *4 (-522)) (-5 *2 (-792)) + (-5 *1 (-591 *5 *6 *7)) (-4 *5 (-1014)) (-4 *6 (-23)) (-14 *7 *6))) + ((*1 *2 *1 *2) + (-12 (-5 *2 (-792)) (-5 *1 (-788 *3 *4 *5)) (-4 *3 (-971)) + (-14 *4 (-94 *3)) (-14 *5 (-1 *3 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-202)) (-5 *1 (-792)))) + ((*1 *1 *2) (-12 (-5 *2 (-1068)) (-5 *1 (-792)))) + ((*1 *1 *2) (-12 (-5 *2 (-1085)) (-5 *1 (-792)))) + ((*1 *1 *2) (-12 (-5 *2 (-522)) (-5 *1 (-792)))) + ((*1 *2 *1 *2) (-12 (-5 *2 (-792)) (-5 *1 (-1081 *3)) (-4 *3 (-971))))) +(((*1 *1 *1) + (-12 (-5 *1 (-547 *2)) (-4 *2 (-37 (-382 (-522)))) (-4 *2 (-971))))) (((*1 *1 *1) (-4 *1 (-507)))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-808 (-1 (-202) (-202)))) (-5 *4 (-1009 (-354))) @@ -6644,91 +6283,101 @@ (-12 (-5 *3 (-811 *5)) (-5 *4 (-1007 (-354))) (-4 *5 (-13 (-563 (-498)) (-1014))) (-5 *2 (-1045 (-202))) 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*6 *7 *3 *4)) (-4 *4 (-990 *5 *6 *7 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 (-588 *5) *6)) + (-4 *5 (-13 (-338) (-135) (-962 (-382 (-522))))) (-4 *6 (-1142 *5)) + (-5 *2 (-588 (-2 (|:| -2855 *5) (|:| -3277 *3)))) + (-5 *1 (-746 *5 *6 *3 *7)) (-4 *3 (-598 *6)) + (-4 *7 (-598 (-382 *6)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-405 *3) (-928))))) @@ -6886,6 +6639,9 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-382 (-522)))) (-4 *4 (-1126 *3)) (-5 *1 (-255 *3 *4 *2 *5)) (-4 *2 (-1149 *3 *4)) (-4 *5 (-910 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-314 *2 *3 *4)) (-14 *2 (-588 (-1085))) + (-14 *3 (-588 (-1085))) (-4 *4 (-362)))) ((*1 *1 *1) (-4 *1 (-463))) ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) @@ -6893,31 +6649,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *1 *1) - (-12 (-5 *1 (-547 *2)) (-4 *2 (-37 (-382 (-522)))) (-4 *2 (-971))))) -(((*1 *2 *2) (-12 (-5 *1 (-540 *2)) (-4 *2 (-507))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-522)) (-5 *5 (-628 (-202))) (-5 *4 (-202)) - (-5 *2 (-960)) (-5 *1 (-690))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1014)) (-4 *3 (-829 *5)) (-5 *2 (-1166 *3)) - (-5 *1 (-630 *5 *3 *6 *4)) (-4 *6 (-348 *3)) - (-4 *4 (-13 (-348 *5) (-10 -7 (-6 -4238))))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-588 *5)) (-5 *4 (-522)) (-4 *5 (-782)) (-4 *5 (-338)) - (-5 *2 (-708)) (-5 *1 (-874 *5 *6)) (-4 *6 (-1142 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-1046 *3)) (-4 *3 (-971)) (-5 *2 (-108))))) -(((*1 *2 *2) (-12 (-5 *2 (-522)) (-5 *1 (-519))))) -(((*1 *2 *3) (-12 (-5 *3 (-202)) (-5 *2 (-291 (-354))) (-5 *1 (-281))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) - (-4 *2 (-13 (-405 *3) (-928)))))) (((*1 *1 *2 *3) (-12 (-5 *2 (-110)) (-5 *3 (-588 *1)) (-4 *1 (-278)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-278)) (-5 *2 (-110)))) ((*1 *1 *2) (-12 (-5 *2 (-1085)) (-5 *1 (-561 *3)) (-4 *3 (-784)))) ((*1 *1 *2 *3 *4) (-12 (-5 *2 (-110)) (-5 *3 (-588 *5)) (-5 *4 (-708)) (-4 *5 (-784)) (-5 *1 (-561 *5))))) +(((*1 *2 *2) (|partial| -12 (-5 *2 (-291 (-202))) (-5 *1 (-243))))) +(((*1 *2 *2) + (-12 (-5 *2 (-588 (-2 (|:| |val| (-588 *6)) (|:| -1974 *7)))) + (-4 *6 (-985 *3 *4 *5)) (-4 *7 (-990 *3 *4 *5 *6)) (-4 *3 (-426)) + (-4 *4 (-730)) (-4 *5 (-784)) (-5 *1 (-915 *3 *4 *5 *6 *7)))) + ((*1 *2 *2) + (-12 (-5 *2 (-588 (-2 (|:| |val| (-588 *6)) (|:| -1974 *7)))) + (-4 *6 (-985 *3 *4 *5)) (-4 *7 (-990 *3 *4 *5 *6)) (-4 *3 (-426)) + (-4 *4 (-730)) (-4 *5 (-784)) (-5 *1 (-1021 *3 *4 *5 *6 *7))))) +(((*1 *1 *1) (|partial| -4 *1 (-133))) ((*1 *1 *1) (-4 *1 (-324))) + ((*1 *1 *1) (|partial| -12 (-4 *1 (-133)) (-4 *1 (-838))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-990 *4 *5 *6 *3)) (-4 *4 (-426)) (-4 *5 (-730)) + (-4 *6 (-784)) (-4 *3 (-985 *4 *5 *6)) (-5 *2 (-108))))) +(((*1 *2 *1) + (-12 (-4 *3 (-971)) (-4 *4 (-1014)) (-5 *2 (-588 *1)) + (-4 *1 (-357 *3 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-588 (-673 *3 *4))) (-5 *1 (-673 *3 *4)) (-4 *3 (-971)) + (-4 *4 (-664)))) + ((*1 *2 *1) + (-12 (-4 *3 (-971)) (-4 *4 (-730)) (-4 *5 (-784)) (-5 *2 (-588 *1)) + (-4 *1 (-878 *3 *4 *5))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014)) + (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-108))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-921 *2)) (-4 *2 (-1120))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-405 *3) (-928))))) @@ -6937,40 +6701,38 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) +(((*1 *2 *2 *3 *2) + (-12 (-5 *2 (-628 *3)) (-4 *3 (-971)) (-5 *1 (-629 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-132))))) (((*1 *1 *1 *1) (-5 *1 (-792)))) -(((*1 *2 *3 *4 *5 *5 *5 *5 *6 *4 *4 *4 *4 *4 *5 *4 *5 *5 *4) - (-12 (-5 *3 (-1068)) (-5 *4 (-522)) (-5 *5 (-628 (-202))) - (-5 *6 (-202)) (-5 *2 (-960)) (-5 *1 (-690))))) -(((*1 *2 *3) - (-12 (-5 *3 (-588 (-522))) (-5 *2 (-833 (-522))) (-5 *1 (-846)))) - ((*1 *2) (-12 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(-108)))) - ((*1 *2 *3) - (-12 (-4 *1 (-317 *3 *4 *5)) (-4 *3 (-1124)) (-4 *4 (-1142 *3)) - (-4 *5 (-1142 (-382 *4))) (-5 *2 (-108))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-338)) (-5 *1 (-825 *2 *3)) + (-4 *2 (-1142 *3))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-1014)) (-4 *2 (-829 *5)) (-5 *1 (-630 *5 *2 *3 *4)) + (-4 *3 (-348 *2)) (-4 *4 (-13 (-348 *5) (-10 -7 (-6 -4238))))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1 *4 (-522))) (-5 *5 (-1 (-1066 *4))) (-4 *4 (-338)) + (-4 *4 (-971)) (-5 *2 (-1066 *4)) (-5 *1 (-1070 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-1018)) (-5 *1 (-51))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *3 *4 *3 *5 *5 *3) + (-12 (-5 *3 (-522)) (-5 *4 (-108)) (-5 *5 (-628 (-202))) + (-5 *2 (-960)) (-5 *1 (-693))))) +(((*1 *2 *3 *1 *4) + (-12 (-5 *3 (-1050 *5 *6)) (-5 *4 (-1 (-108) *6 *6)) + (-4 *5 (-13 (-1014) (-33))) (-4 *6 (-13 (-1014) (-33))) + (-5 *2 (-108)) (-5 *1 (-1051 *5 *6))))) +(((*1 *2) (-12 (-5 *2 (-777 (-522))) (-5 *1 (-496)))) + ((*1 *1) (-12 (-5 *1 (-777 *2)) (-4 *2 (-1014))))) +(((*1 *2 *1) + (-12 (-4 *1 (-298 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-124)) + (-5 *2 (-588 (-2 (|:| |gen| *3) (|:| -3357 *4)))))) + ((*1 *2 *1) + (-12 (-5 *2 (-588 (-2 (|:| -3112 *3) (|:| -2623 *4)))) + (-5 *1 (-673 *3 *4)) (-4 *3 (-971)) (-4 *4 (-664)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1144 *3 *4)) (-4 *3 (-971)) (-4 *4 (-729)) + (-5 *2 (-1066 (-2 (|:| |k| *4) (|:| |c| *3))))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-405 *3) (-928))))) @@ -6990,25 +6752,26 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *2 *1) (-12 (-5 *1 (-843 *2)) (-4 *2 (-283))))) -(((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-588 (-561 *2))) (-5 *4 (-1085)) - (-4 *2 (-13 (-27) (-1106) (-405 *5))) - (-4 *5 (-13 (-514) (-784) (-962 (-522)) (-584 (-522)))) - (-5 *1 (-253 *5 *2))))) -(((*1 *2 *3 *1) - (-12 (-4 *4 (-426)) (-4 *5 (-730)) (-4 *6 (-784)) - (-4 *3 (-985 *4 *5 *6)) (-5 *2 (-588 *1)) - (-4 *1 (-990 *4 *5 *6 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-588 (-522))) (-5 *2 (-1087 (-382 (-522)))) - (-5 *1 (-169))))) -(((*1 *2) (-12 (-5 *2 (-1171)) (-5 *1 (-517))))) -(((*1 *1 *2) (-12 (-5 *2 (-588 *3)) (-4 *3 (-1014)) (-4 *1 (-832 *3))))) -(((*1 *2) - (-12 (-4 *4 (-157)) (-5 *2 (-108)) (-5 *1 (-341 *3 *4)) - (-4 *3 (-342 *4)))) - ((*1 *2) (-12 (-4 *1 (-342 *3)) (-4 *3 (-157)) (-5 *2 (-108))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-202)) (-5 *4 (-522)) (-5 *2 (-960)) (-5 *1 (-696))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-626 *2 *3 *4)) (-4 *2 (-971)) (-4 *3 (-348 *2)) + (-4 *4 (-348 *2))))) +(((*1 *2 *3) (-12 (-5 *3 (-1166 *1)) (-4 *1 (-342 *2)) (-4 *2 (-157)))) + ((*1 *2) (-12 (-4 *2 (-157)) (-5 *1 (-391 *3 *2)) (-4 *3 (-392 *2)))) + ((*1 *2) (-12 (-4 *1 (-392 *2)) (-4 *2 (-157))))) +(((*1 *1 *2 *1) (-12 (-5 *1 (-588 *2)) (-4 *2 (-1120)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-1066 *2)) (-4 *2 (-1120))))) +(((*1 *2 *3) (-12 (-5 *3 (-850)) (-5 *2 (-833 (-522))) (-5 *1 (-846)))) + ((*1 *2 *3) + (-12 (-5 *3 (-588 (-522))) (-5 *2 (-833 (-522))) (-5 *1 (-846))))) +(((*1 *2 *2) (-12 (-5 *2 (-588 (-628 (-291 (-522))))) (-5 *1 (-956))))) +(((*1 *2 *3 *2) + (-12 (-4 *2 (-13 (-338) (-782))) (-5 *1 (-164 *2 *3)) + (-4 *3 (-1142 (-154 *2))))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-338) (-782))) (-5 *1 (-164 *2 *3)) + (-4 *3 (-1142 (-154 *2)))))) (((*1 *2 *1) (-12 (-5 *2 (-1085)) (-5 *1 (-104)))) ((*1 *2 *1) (-12 (-5 *2 (-1085)) (-5 *1 (-110)))) ((*1 *2 *1) @@ -7019,13 +6782,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-1085)) (-5 *1 (-893)))) ((*1 *2 *1) (-12 (-5 *2 (-1085)) (-5 *1 (-992 *3)) (-14 *3 *2))) ((*1 *1 *1) (-5 *1 (-1085)))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-834 *4)) (-4 *4 (-1014)) (-5 *2 (-588 (-708))) - (-5 *1 (-833 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-522)) (-5 *1 (-519))))) +(((*1 *2 *3) + (-12 (-5 *3 (-588 *4)) (-4 *4 (-782)) (-4 *4 (-338)) (-5 *2 (-708)) + (-5 *1 (-874 *4 *5)) (-4 *5 (-1142 *4))))) (((*1 *2) (-12 (-5 *2 (-777 (-522))) (-5 *1 (-496)))) ((*1 *1) (-12 (-5 *1 (-777 *2)) (-4 *2 (-1014))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-230 *2)) (-4 *2 (-1120))))) -(((*1 *2 *2) +(((*1 *1 *1) (-4 *1 (-91))) + ((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-405 *3) (-928))))) ((*1 *2 *2) @@ -7034,43 +6798,46 @@ ((*1 *2 *2) (-12 (-4 *3 (-37 (-382 (-522)))) (-4 *4 (-1126 *3)) (-5 *1 (-255 *3 *4 *2 *5)) (-4 *2 (-1149 *3 *4)) (-4 *5 (-910 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-314 *2 *3 *4)) (-14 *2 (-588 (-1085))) - (-14 *3 (-588 (-1085))) (-4 *4 (-362)))) - ((*1 *1 *1) (-4 *1 (-463))) ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1071 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-108)) (-5 *1 (-1116 *3)) (-4 *3 (-901))))) -(((*1 *2 *3) (-12 (-5 *3 (-850)) (-5 *2 (-1068)) (-5 *1 (-723))))) -(((*1 *2 *3 *4 *5 *5 *5 *6 *4 *4 *4 *5 *4 *5 *7) - (-12 (-5 *3 (-1068)) (-5 *5 (-628 (-202))) (-5 *6 (-202)) - (-5 *7 (-628 (-522))) (-5 *4 (-522)) (-5 *2 (-960)) (-5 *1 (-690))))) -(((*1 *2 *2) - (-12 (-4 *3 (-514)) (-4 *3 (-157)) (-4 *4 (-348 *3)) - (-4 *5 (-348 *3)) (-5 *1 (-627 *3 *4 *5 *2)) - (-4 *2 (-626 *3 *4 *5))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014)) - (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-108))))) -(((*1 *2) - (-12 (-4 *4 (-157)) (-5 *2 (-108)) (-5 *1 (-341 *3 *4)) - (-4 *3 (-342 *4)))) - ((*1 *2) (-12 (-4 *1 (-342 *3)) (-4 *3 (-157)) (-5 *2 (-108))))) +(((*1 *2 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-522)) (-5 *4 (-628 (-202))) (-5 *2 (-960)) + (-5 *1 (-692))))) +(((*1 *2) (-12 (-5 *2 (-108)) (-5 *1 (-441)))) + ((*1 *2 *2) (-12 (-5 *2 (-108)) (-5 *1 (-441))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-405 *3) (-928)))))) +(((*1 *2 *1) (-12 (-4 *1 (-514)) (-5 *2 (-108))))) (((*1 *2 *3) - (-12 (-5 *2 (-1066 (-522))) (-5 *1 (-1070 *4)) (-4 *4 (-971)) - (-5 *3 (-522))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-512 *3)) (-4 *3 (-13 (-379) (-1106))) (-5 *2 (-108))))) + (-12 (-5 *3 (-202)) (-5 *2 (-108)) (-5 *1 (-275 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-1009 (-777 (-202)))) (-5 *3 (-202)) (-5 *2 (-108)) + (-5 *1 (-281)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-338)) (-4 *4 (-730)) (-4 *5 (-784)) (-5 *2 (-108)) + (-5 *1 (-474 *3 *4 *5 *6)) (-4 *6 (-878 *3 *4 *5))))) +(((*1 *2 *3) (-12 (-5 *3 (-872 *2)) (-5 *1 (-909 *2)) (-4 *2 (-971))))) +(((*1 *2 *2 *3) + (-12 (-4 *3 (-283)) (-5 *1 (-429 *3 *2)) (-4 *2 (-1142 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-283)) (-5 *1 (-434 *3 *2)) (-4 *2 (-1142 *3)))) + ((*1 *2 *2 *3) + (-12 (-4 *3 (-283)) (-14 *4 *3) (-14 *5 (-1 *3 *3 (-708))) + (-5 *1 (-501 *3 *2 *4 *5)) (-4 *2 (-1142 *3))))) (((*1 *2) (-12 (-5 *2 (-588 *3)) (-5 *1 (-1000 *3)) (-4 *3 (-125))))) -(((*1 *2) (-12 (-5 *2 (-777 (-522))) (-5 *1 (-496)))) - ((*1 *1) (-12 (-5 *1 (-777 *2)) (-4 *2 (-1014))))) +(((*1 *2 *1) + (-12 + (-5 *2 + (-588 + (-2 (|:| |scalar| (-382 (-522))) (|:| |coeff| (-1081 *3)) + (|:| |logand| (-1081 *3))))) + (-5 *1 (-539 *3)) (-4 *3 (-338))))) (((*1 *1 *1) (-4 *1 (-91))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) @@ -7087,83 +6854,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-872 (-202))) (-5 *4 (-803)) (-5 *5 (-850)) - (-5 *2 (-1171)) (-5 *1 (-442)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-872 (-202))) (-5 *2 (-1171)) (-5 *1 (-442)))) - ((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-588 (-872 (-202)))) (-5 *4 (-803)) (-5 *5 (-850)) - (-5 *2 (-1171)) (-5 *1 (-442))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-426) (-135))) (-5 *2 (-393 *3)) - (-5 *1 (-95 *4 *3)) (-4 *3 (-1142 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-588 *3)) (-4 *3 (-1142 *5)) (-4 *5 (-13 (-426) (-135))) - (-5 *2 (-393 *3)) (-5 *1 (-95 *5 *3))))) -(((*1 *2) - (-12 (-5 *2 (-108)) (-5 *1 (-1098 *3 *4)) (-4 *3 (-1014)) - (-4 *4 (-1014))))) -(((*1 *1 *1) (-4 *1 (-131))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-514))) 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*1) + (-12 (-4 *3 (-514)) (-4 *3 (-971)) (-4 *4 (-730)) (-4 *5 (-784)) + (-5 *2 (-2 (|:| -2308 *1) (|:| |coef1| *1))) + (-4 *1 (-985 *3 *4 *5))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-1 (-154 (-202)) (-154 (-202)))) (-5 *4 (-1009 (-202))) + (-5 *2 (-1168)) (-5 *1 (-233))))) (((*1 *2 *3) - (-12 (-5 *3 (-628 *4)) (-4 *4 (-338)) (-5 *2 (-1081 *4)) - (-5 *1 (-495 *4 *5 *6)) (-4 *5 (-338)) (-4 *6 (-13 (-338) (-782)))))) -(((*1 *2 *1) (-12 (-4 *1 (-1059 *3)) (-4 *3 (-1120)) (-5 *2 (-108))))) -(((*1 *1 *2) - (-12 (-5 *2 (-588 (-588 *3))) (-4 *3 (-1014)) (-5 *1 (-834 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) - (-4 *2 (-13 (-405 *3) (-928)))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-756 *3)) (-4 *3 (-784)) (-5 *1 (-613 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-588 *6)) (-5 *4 (-1085)) (-4 *6 (-405 *5)) - (-4 *5 (-784)) (-5 *2 (-588 (-561 *6))) (-5 *1 (-531 *5 *6))))) + (-12 (-5 *3 (-1139 *5 *4)) (-4 *4 (-426)) (-4 *4 (-757)) + (-14 *5 (-1085)) (-5 *2 (-522)) (-5 *1 (-1028 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-1171)) (-5 *1 (-759))))) +(((*1 *2 *1) + (-12 (-5 *2 (-588 (-1107 *3))) (-5 *1 (-1107 *3)) (-4 *3 (-1014))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-1054)) (-5 *2 (-129)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1054)) (-5 *2 (-132))))) +(((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-522)) (-5 *1 (-969))))) (((*1 *2) (-12 (-5 *2 (-770 (-522))) (-5 *1 (-496)))) ((*1 *1) (-12 (-5 *1 (-770 *2)) (-4 *2 (-1014))))) (((*1 *1 *1) (-4 *1 (-91))) @@ -7182,34 +6896,50 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-628 *6)) (-5 *5 (-1 (-393 (-1081 *6)) (-1081 *6))) - (-4 *6 (-338)) - (-5 *2 - (-588 - (-2 (|:| |outval| *7) (|:| |outmult| (-522)) - (|:| |outvect| (-588 (-628 *7)))))) - (-5 *1 (-495 *6 *7 *4)) (-4 *7 (-338)) (-4 *4 (-13 (-338) (-782)))))) -(((*1 *2 *2) (-12 (-5 *2 (-588 *3)) (-4 *3 (-782)) (-5 *1 (-279 *3))))) (((*1 *2 *1) - (-12 (-4 *1 (-1164 *2)) (-4 *2 (-1120)) (-4 *2 (-928)) - 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(-750 *6 *7)) (-5 *4 (-1166 *6))))) +(((*1 *1 *1) (-12 (-4 *1 (-151 *2)) (-4 *2 (-157)))) + ((*1 *1 *1 *1) (-4 *1 (-447))) + ((*1 *1 *1) (-12 (-4 *1 (-734 *2)) (-4 *2 (-157)))) + ((*1 *2 *2) (-12 (-5 *2 (-588 (-522))) (-5 *1 (-812)))) + ((*1 *1 *1) (-5 *1 (-898))) + ((*1 *1 *1) (-12 (-4 *1 (-923 *2)) (-4 *2 (-157))))) +(((*1 *2 *1) + (-12 (-4 *1 (-339 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1014))))) +(((*1 *2) (-12 (-5 *2 (-588 (-1068))) (-5 *1 (-1169))))) (((*1 *2) (-12 (-4 *2 (-13 (-405 *3) (-928))) (-5 *1 (-252 *3 *2)) (-4 *3 (-13 (-784) (-514))))) @@ -7217,8 +6947,12 @@ (-12 (-5 *1 (-314 *2 *3 *4)) (-14 *2 (-588 (-1085))) (-14 *3 (-588 (-1085))) (-4 *4 (-362)))) ((*1 *1) (-5 *1 (-451))) ((*1 *1) (-4 *1 (-1106)))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-1085)) (-5 *3 (-588 (-893))) (-5 *1 (-104))))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-1054)) (-5 *2 (-129)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1054)) (-5 *2 (-132))))) +(((*1 *2 *1) + (-12 (-5 *2 (-108)) (-5 *1 (-1074 *3 *4)) (-14 *3 (-850)) + (-4 *4 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(-5 *2 (-1171)) (-5 *1 (-305))))) +(((*1 *2 *3) + (-12 (-5 *3 (-588 (-202))) (-5 *2 (-1166 (-637))) (-5 *1 (-281))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-426)) (-4 *4 (-784)) (-4 *5 (-730)) (-5 *2 (-108)) (-5 *1 (-914 *3 *4 *5 *6)) @@ -7260,21 +6986,54 @@ ((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-1050 *3 *4)) (-4 *3 (-13 (-1014) (-33))) (-4 *4 (-13 (-1014) (-33)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-588 *2)) (-4 *2 (-1142 *4)) (-5 *1 (-501 *4 *2 *5 *6)) - (-4 *4 (-283)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-708)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1068)) (-5 *1 (-1102)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-1068)) (-5 *1 (-1102))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1166 *1)) (-4 *1 (-342 *4)) (-4 *4 (-157)) - (-5 *2 (-628 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-392 *3)) (-4 *3 (-157)) (-5 *2 (-628 *3))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-522)) (-5 *1 (-393 *2)) (-4 *2 (-514))))) -(((*1 *2 *3 *4 *2 *2 *5) - (|partial| -12 (-5 *2 (-777 *4)) (-5 *3 (-561 *4)) (-5 *5 (-108)) - (-4 *4 (-13 (-1106) (-29 *6))) - (-4 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(-730)) + (-4 *4 (-784)) (-4 *2 (-426)))) + ((*1 *2 *3 *1) + (-12 (-4 *4 (-426)) (-4 *5 (-730)) (-4 *6 (-784)) + (-4 *3 (-985 *4 *5 *6)) + (-5 *2 (-588 (-2 (|:| |val| *3) (|:| -1974 *1)))) + (-4 *1 (-990 *4 *5 *6 *3)))) + ((*1 *1 *1) (-4 *1 (-1124))) + ((*1 *2 *2) + (-12 (-4 *3 (-514)) (-5 *1 (-1145 *3 *2)) + (-4 *2 (-13 (-1142 *3) (-514) (-10 -8 (-15 -2308 ($ $ $)))))))) +(((*1 *2 *1) + (-12 (-4 *1 (-55 *3 *4 *5)) (-4 *3 (-1120)) (-4 *4 (-348 *3)) + (-4 *5 (-348 *3)) (-5 *2 (-708)))) + ((*1 *2 *1) + (-12 (-4 *1 (-974 *3 *4 *5 *6 *7)) (-4 *5 (-971)) + (-4 *6 (-215 *4 *5)) (-4 *7 (-215 *3 *5)) (-5 *2 (-708))))) (((*1 *2 *1) (-12 (-5 *2 (-1037 (-522) (-561 (-47)))) (-5 *1 (-47)))) ((*1 *2 *1) (-12 (-4 *3 (-919 *2)) (-4 *4 (-1142 *3)) (-4 *2 (-283)) @@ -7335,6 +7100,8 @@ (-12 (-4 *4 (-157)) (-4 *2 (|SubsetCategory| (-664) *4)) (-5 *1 (-604 *3 *4 *2)) (-4 *3 (-655 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-919 *2)) (-4 *2 (-514))))) +(((*1 *2) (-12 (-5 *2 (-803)) (-5 *1 (-1169)))) + ((*1 *2 *2) (-12 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(-4 *1 (-555 *3 *2)) (-4 *3 (-1014)) (-4 *3 (-784)) (-4 *2 (-1120)))) @@ -10184,31 +10564,48 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-708)) (-4 *1 (-1154 *3)) (-4 *3 (-1120)))) ((*1 *2 *1) (-12 (-4 *1 (-1154 *2)) (-4 *2 (-1120))))) -(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) - (-12 (-5 *3 (-850)) (-5 *4 (-202)) (-5 *5 (-522)) (-5 *6 (-803)) - (-5 *2 (-1171)) (-5 *1 (-1167))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-3 - (|:| |noa| - (-2 (|:| |fn| (-291 (-202))) (|:| -3802 (-588 (-202))) - (|:| |lb| (-588 (-777 (-202)))) - (|:| |cf| (-588 (-291 (-202)))) - (|:| |ub| (-588 (-777 (-202)))))) - (|:| |lsa| - (-2 (|:| |lfn| (-588 (-291 (-202)))) - (|:| -3802 (-588 (-202))))))) - (-5 *2 (-588 (-1068))) (-5 *1 (-243))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-426)) (-4 *5 (-730)) (-4 *6 (-784)) - (-4 *7 (-985 *4 *5 *6)) (-5 *2 (-108)) - (-5 *1 (-915 *4 *5 *6 *7 *3)) (-4 *3 (-990 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-426)) (-4 *5 (-730)) (-4 *6 (-784)) - (-4 *7 (-985 *4 *5 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"void"))) (-5 *3 (-588 (-881 (-522)))) (-5 *4 (-108)) (-5 *1 (-412)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-5 *3 (-588 (-1085))) (-5 *4 (-108)) (-5 *1 (-412)))) ((*1 *2 *1) (-12 (-5 *2 (-1066 *3)) (-5 *1 (-552 *3)) (-4 *3 (-1120)))) @@ -10787,23 +11187,23 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-651 *2 *3 *4)) (-4 *2 (-784)) (-4 *3 (-1014)) (-14 *4 - (-1 (-108) (-2 (|:| -2717 *2) (|:| -1400 *3)) - (-2 (|:| -2717 *2) (|:| -1400 *3)))))) + (-1 (-108) (-2 (|:| -2882 *2) (|:| -3858 *3)) + (-2 (|:| -2882 *2) (|:| -3858 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *1 (-802 *2 *3)) (-4 *2 (-1120)) (-4 *3 (-1120)))) ((*1 *1 *2) - (-12 (-5 *2 (-588 (-2 (|:| -2530 (-1085)) (|:| -3048 *4)))) + (-12 (-5 *2 (-588 (-2 (|:| -2644 (-1085)) (|:| -3149 *4)))) (-4 *4 (-1014)) (-5 *1 (-818 *3 *4)) (-4 *3 (-1014)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-588 *5)) (-4 *5 (-13 (-1014) (-33))) (-5 *2 (-588 (-1050 *3 *5))) (-5 *1 (-1050 *3 *5)) (-4 *3 (-13 (-1014) (-33))))) ((*1 *2 *3) - (-12 (-5 *3 (-588 (-2 (|:| |val| *4) (|:| -1886 *5)))) + (-12 (-5 *3 (-588 (-2 (|:| |val| *4) (|:| -1974 *5)))) (-4 *4 (-13 (-1014) (-33))) (-4 *5 (-13 (-1014) (-33))) (-5 *2 (-588 (-1050 *4 *5))) (-5 *1 (-1050 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1886 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1974 *4))) (-4 *3 (-13 (-1014) (-33))) (-4 *4 (-13 (-1014) (-33))) (-5 *1 (-1050 *3 *4)))) ((*1 *1 *2 *3) @@ -10826,44 +11226,55 @@ (-4 *4 (-13 (-1014) (-33))) (-5 *1 (-1051 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1075 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-354)) (-5 *2 (-1171)) (-5 *1 (-1168))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-708)) (-4 *1 (-678 *4 *5)) (-4 *4 (-971)) - (-4 *5 (-784)) (-5 *2 (-881 *4)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-708)) (-4 *1 (-678 *4 *5)) (-4 *4 (-971)) - (-4 *5 (-784)) (-5 *2 (-881 *4)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-708)) (-4 *1 (-1157 *4)) (-4 *4 (-971)) - (-5 *2 (-881 *4)))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-588 + (-2 + (|:| -2644 + (-2 (|:| |xinit| (-202)) (|:| |xend| (-202)) + (|:| |fn| (-1166 (-291 (-202)))) + (|:| |yinit| (-588 (-202))) (|:| |intvals| (-588 (-202))) + (|:| |g| (-291 (-202))) (|:| |abserr| (-202)) + (|:| |relerr| (-202)))) + (|:| -3149 + (-2 (|:| |stiffness| (-354)) (|:| |stability| (-354)) + (|:| |expense| (-354)) (|:| |accuracy| (-354)) + (|:| |intermediateResults| (-354))))))) + (-5 *1 (-740))))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-522)) (-5 *4 (-628 (-202))) (-5 *2 (-960)) + (-5 *1 (-685))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1068)) (-5 *4 (-522)) (-5 *5 (-628 (-154 (-202)))) + (-5 *2 (-960)) (-5 *1 (-692))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-522)) (-4 *1 (-55 *4 *5 *2)) (-4 *4 (-1120)) + (-4 *5 (-348 *4)) (-4 *2 (-348 *4)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (-708)) (-4 *1 (-1157 *4)) (-4 *4 (-971)) - (-5 *2 (-881 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-990 *3 *4 *5 *6)) (-4 *3 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(-1166 *3)) (-4 *3 (-338)) (-14 *6 (-1166 (-628 *3))) @@ -10871,69 +11282,69 @@ ((*1 *1 *2) (-12 (-5 *2 (-1037 (-522) (-561 (-47)))) (-5 *1 (-47)))) ((*1 *2 *3) (-12 (-5 *2 (-51)) (-5 *1 (-50 *3)) (-4 *3 (-1120)))) ((*1 *1 *2) - (-12 (-5 *2 (-1166 (-314 (-2201 'JINT 'X 'ELAM) (-2201) (-637)))) + (-12 (-5 *2 (-1166 (-314 (-2227 'JINT 'X 'ELAM) (-2227) (-637)))) (-5 *1 (-59 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-1166 (-314 (-2201) (-2201 'XC) (-637)))) + (-12 (-5 *2 (-1166 (-314 (-2227) (-2227 'XC) (-637)))) (-5 *1 (-61 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-314 (-2201 'X) (-2201) (-637))) (-5 *1 (-62 *3)) + (-12 (-5 *2 (-314 (-2227 'X) (-2227) (-637))) (-5 *1 (-62 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-628 (-314 (-2201) (-2201 'X 'HESS) (-637)))) + (-12 (-5 *2 (-628 (-314 (-2227) (-2227 'X 'HESS) (-637)))) (-5 *1 (-63 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-314 (-2201) (-2201 'XC) (-637))) (-5 *1 (-64 *3)) + (-12 (-5 *2 (-314 (-2227) 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(-12 (-5 *2 (-628 (-314 (-2201 'X) (-2201) (-637)))) (-5 *1 (-82 *3)) + (-12 (-5 *2 (-628 (-314 (-2227 'X) (-2227) (-637)))) (-5 *1 (-82 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-1166 (-314 (-2201 'X) (-2201) (-637)))) + (-12 (-5 *2 (-1166 (-314 (-2227 'X) (-2227) (-637)))) (-5 *1 (-83 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-1166 (-314 (-2201 'X) (-2201 '-1352) (-637)))) + (-12 (-5 *2 (-1166 (-314 (-2227 'X) (-2227 '-1330) (-637)))) (-5 *1 (-84 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-628 (-314 (-2201 'XL 'XR 'ELAM) (-2201) (-637)))) + (-12 (-5 *2 (-628 (-314 (-2227 'XL 'XR 'ELAM) (-2227) (-637)))) (-5 *1 (-85 *3)) (-14 *3 (-1085)))) ((*1 *1 *2) - (-12 (-5 *2 (-314 (-2201 'X) (-2201 '-1352) (-637))) (-5 *1 (-87 *3)) + (-12 (-5 *2 (-314 (-2227 'X) (-2227 '-1330) (-637))) (-5 *1 (-87 *3)) (-14 *3 (-1085)))) ((*1 *2 *1) (-12 (-5 *2 (-930 2)) (-5 *1 (-103)))) ((*1 *2 *1) (-12 (-5 *2 (-382 (-522))) (-5 *1 (-103)))) @@ -10956,8 +11367,8 @@ (-12 (-5 *2 (-588 *3)) (-4 *3 (-13 (-784) - (-10 -8 (-15 -2545 ((-1068) $ (-1085))) (-15 -1678 ((-1171) $)) - (-15 -2664 ((-1171) $))))) + (-10 -8 (-15 -2683 ((-1068) $ (-1085))) (-15 -1757 ((-1171) $)) + (-15 -2113 ((-1171) $))))) (-5 *1 (-192 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-930 10)) (-5 *1 (-195)))) ((*1 *2 *1) (-12 (-5 *2 (-382 (-522))) (-5 *1 (-195)))) @@ -10998,14 +11409,14 @@ ((*1 *1 *2) (-12 (-4 *1 (-349 *2 *3)) (-4 *2 (-784)) (-4 *3 (-157)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2033 (-588 (-305))))) + (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2077 (-588 (-305))))) (-4 *1 (-358)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-4 *1 (-358)))) ((*1 *1 *2) (-12 (-5 *2 (-588 (-305))) (-4 *1 (-358)))) ((*1 *1 *2) (-12 (-5 *2 (-628 (-637))) (-4 *1 (-358)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2033 (-588 (-305))))) + (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2077 (-588 (-305))))) (-4 *1 (-359)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-4 *1 (-359)))) ((*1 *1 *2) (-12 (-5 *2 (-588 (-305))) (-4 *1 (-359)))) @@ -11015,71 +11426,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-792)) (-5 *1 (-369)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2033 (-588 (-305))))) + (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2077 (-588 (-305))))) (-4 *1 (-371)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-4 *1 (-371)))) ((*1 *1 *2) (-12 (-5 *2 (-588 (-305))) (-4 *1 (-371)))) ((*1 *1 *2) (-12 (-5 *2 (-270 (-291 (-154 (-354))))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-270 (-291 (-354)))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-270 (-291 (-522)))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-291 (-154 (-354)))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-291 (-354))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-291 (-522))) (-5 *1 (-373 *3 *4 *5 *6)) - (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *3 (-1085)) (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-270 (-291 (-632)))) (-5 *1 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(|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-5 *1 (-373 *3 *4 *5 *6)) (-14 *3 (-1085)) - (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1367 "void"))) + (-14 *4 (-3 (|:| |fst| (-409)) (|:| -1350 "void"))) (-14 *5 (-588 (-1085))) (-14 *6 (-1089)))) ((*1 *1 *2) (-12 (-5 *2 (-306 *4)) (-4 *4 (-13 (-784) (-21))) @@ -11107,14 +11518,14 @@ ((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-412)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2033 (-588 (-305))))) + (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2077 (-588 (-305))))) (-4 *1 (-414)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-4 *1 (-414)))) ((*1 *1 *2) (-12 (-5 *2 (-588 (-305))) (-4 *1 (-414)))) ((*1 *1 *2) (-12 (-5 *2 (-1166 (-637))) (-4 *1 (-414)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2033 (-588 (-305))))) + (-5 *2 (-2 (|:| |localSymbols| (-1089)) (|:| -2077 (-588 (-305))))) (-4 *1 (-415)))) ((*1 *1 *2) (-12 (-5 *2 (-305)) (-4 *1 (-415)))) ((*1 *1 *2) (-12 (-5 *2 (-588 (-305))) (-4 *1 (-415)))) @@ -11179,18 +11590,18 @@ ((*1 *1 *2) (-12 (-4 *3 (-971)) (-5 *1 (-650 *3 *2)) (-4 *2 (-1142 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -2717 *3) (|:| -1400 *4))) + (-12 (-5 *2 (-2 (|:| -2882 *3) (|:| -3858 *4))) (-5 *1 (-651 *3 *4 *5)) (-4 *3 (-784)) (-4 *4 (-1014)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -2717 *3) (|:| -1400 *4))) (-4 *3 (-784)) + (-12 (-5 *2 (-2 (|:| -2882 *3) (|:| -3858 *4))) (-4 *3 (-784)) (-4 *4 (-1014)) (-5 *1 (-651 *3 *4 *5)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-157)) (-5 *1 (-653 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-588 (-2 (|:| -2977 *3) (|:| -2518 *4)))) (-4 *3 (-971)) + (-12 (-5 *2 (-588 (-2 (|:| -3112 *3) (|:| -2623 *4)))) (-4 *3 (-971)) (-4 *4 (-664)) (-5 *1 (-673 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-522)) (-4 *1 (-701)))) ((*1 *1 *2) @@ -11199,25 +11610,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1085)) (|:| |fn| (-291 (-202))) - (|:| -2386 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| -2321 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (|:| |mdnia| (-2 (|:| |fn| (-291 (-202))) - (|:| -2386 (-588 (-1009 (-777 (-202))))) + (|:| -2321 (-588 (-1009 (-777 (-202))))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))))) (-5 *1 (-706)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-291 (-202))) - (|:| -2386 (-588 (-1009 (-777 (-202))))) (|:| |abserr| (-202)) + (|:| -2321 (-588 (-1009 (-777 (-202))))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (-5 *1 (-706)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1085)) (|:| |fn| (-291 (-202))) - (|:| -2386 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| -2321 (-1009 (-777 (-202)))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (-5 *1 (-706)))) ((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-706)))) @@ -11243,23 +11654,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-291 (-202))) (|:| -3802 (-588 (-202))) + (-2 (|:| |fn| (-291 (-202))) (|:| -3937 (-588 (-202))) (|:| |lb| (-588 (-777 (-202)))) (|:| |cf| (-588 (-291 (-202)))) (|:| |ub| (-588 (-777 (-202)))))) (|:| |lsa| (-2 (|:| |lfn| (-588 (-291 (-202)))) - (|:| -3802 (-588 (-202))))))) + (|:| -3937 (-588 (-202))))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-588 (-291 (-202)))) (|:| -3802 (-588 (-202))))) + (-2 (|:| |lfn| (-588 (-291 (-202)))) (|:| -3937 (-588 (-202))))) (-5 *1 (-775)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-291 (-202))) (|:| -3802 (-588 (-202))) + (-2 (|:| |fn| (-291 (-202))) (|:| -3937 (-588 (-202))) (|:| |lb| (-588 (-777 (-202)))) (|:| |cf| (-588 (-291 (-202)))) (|:| |ub| (-588 (-777 (-202)))))) (-5 *1 (-775)))) @@ -11418,75 +11829,9 @@ (-12 (-5 *2 (-606 *3 *4)) (-4 *3 (-784)) (-4 *4 (-157)) (-5 *1 (-1184 *3 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-1187 *3 *2)) (-4 *3 (-971)) (-4 *2 (-780))))) -(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-409))))) -(((*1 *2 *3 *2) - 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*3 (-1166 (-291 *5))) + (-5 *4 (-522)) (-4 *5 (-13 (-514) (-784))) (-5 *1 (-1042 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1081 *5)) (-4 *5 (-338)) (-5 *2 (-588 *6)) + (-5 *1 (-495 *5 *6 *4)) (-4 *6 (-338)) (-4 *4 (-13 (-338) (-782)))))) +(((*1 *2 *1) (-12 (-4 *1 (-364)) (-5 *2 (-1068))))) +(((*1 *2 *3) (-12 (-5 *2 (-588 (-522))) (-5 *1 (-519)) (-5 *3 (-522))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-758)) (-5 *4 (-51)) (-5 *2 (-1171)) (-5 *1 (-768))))) (((*1 *2 *1) (-12 (-4 *1 (-151 *2)) (-4 *2 (-157)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-514) (-784) (-962 (-522)))) (-5 *2 (-291 *4)) @@ -12681,40 +12880,93 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-426) (-784) (-962 (-522)) (-584 (-522)))) (-5 *1 (-1110 *3 *2)) (-4 *2 (-13 (-27) (-1106) (-405 *3)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1068)) (-5 *3 (-588 (-239))) (-5 *1 (-237)))) - ((*1 *1 *2) (-12 (-5 *2 (-1068)) (-5 *1 (-239))))) -(((*1 *2 *2) - (-12 (-5 *2 (-872 *3)) (-4 *3 (-13 (-338) (-1106) (-928))) - (-5 *1 (-160 *3))))) (((*1 *2 *1 *3) - (-12 (-5 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(-722 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-291 *5)) (-5 *4 (-850)) (-4 *5 (-514)) + (-4 *5 (-784)) (-4 *5 (-563 *2)) (-5 *2 (-354)) + (-5 *1 (-722 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-382 (-881 *3))) (-5 *1 (-427 *3 *4 *5 *6)) + (-4 *3 (-514)) (-4 *3 (-157)) (-14 *4 (-850)) + (-14 *5 (-588 (-1085))) (-14 *6 (-1166 (-628 *3)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1114 *3 *4 *5 *6)) (-4 *3 (-514)) (-4 *4 (-730)) + (-4 *5 (-784)) (-4 *6 (-985 *3 *4 *5)) (-5 *2 (-588 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-51))))) (((*1 *2 *2 *3 *2) (-12 (-5 *2 (-1068)) (-5 *3 (-522)) (-5 *1 (-218)))) ((*1 *2 *2 *3 *4) (-12 (-5 *2 (-588 (-1068))) (-5 *3 (-522)) (-5 *4 (-1068)) @@ -13023,77 +13270,106 @@ ((*1 *1 *1) (-5 *1 (-792))) ((*1 *1 *1 *2) (-12 (-5 *2 (-522)) (-5 *1 (-792)))) ((*1 *2 *1) (-12 (-4 *1 (-1144 *2 *3)) (-4 *3 (-729)) (-4 *2 (-971))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) - (-4 *2 (-13 (-405 *3) (-928)))))) (((*1 *2 *3) - (-12 (-5 *3 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"Internal singularities not yet evaluated"))) + (|:| -2321 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-517)))) + ((*1 *2 *1) + (-12 (-4 *1 (-555 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1120)) + (-5 *2 (-588 *4))))) +(((*1 *1 *1 *2) + (-12 (-4 *1 (-55 *2 *3 *4)) (-4 *2 (-1120)) (-4 *3 (-348 *2)) + (-4 *4 (-348 *2)))) + ((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4239)) (-4 *1 (-555 *3 *2)) (-4 *3 (-1014)) + (-4 *2 (-1120))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) + (-4 *2 (-13 (-405 *3) (-928)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-547 *2)) (-4 *2 (-37 (-382 (-522)))) (-4 *2 (-971))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *2 *2)) (-4 *2 (-1157 *4)) (-5 *1 (-1159 *4 *2)) + (-4 *4 (-37 (-382 (-522))))))) +(((*1 *1 *1 *1) (-4 *1 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*2 (-708)) (-5 *1 (-126))))) +(((*1 *2 *3) + (|partial| -12 (-5 *2 (-522)) (-5 *1 (-1103 *3)) (-4 *3 (-971))))) (((*1 *1 *1) (-4 *1 (-34))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-784) (-514))) (-5 *1 (-252 *3 *2)) @@ -13931,34 +13895,31 @@ ((*1 *2 *2) (-12 (-5 *2 (-1066 *3)) (-4 *3 (-37 (-382 (-522)))) (-5 *1 (-1072 *3))))) -(((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4238)) (-4 *1 (-555 *4 *3)) (-4 *4 (-1014)) - (-4 *3 (-1120)) (-4 *3 (-1014)) (-5 *2 (-108))))) -(((*1 *2 *2) - (-12 - (-5 *2 - (-2 (|:| |fn| (-291 (-202))) (|:| -3802 (-588 (-202))) - (|:| |lb| (-588 (-777 (-202)))) (|:| |cf| (-588 (-291 (-202)))) - (|:| |ub| (-588 (-777 (-202)))))) - (-5 *1 (-243))))) -(((*1 *1 *2) (-12 (-5 *2 (-588 (-792))) (-5 *1 (-792))))) (((*1 *2) - (-12 - (-5 *2 - (-1166 (-588 (-2 (|:| -3435 (-839 *3)) (|:| -2717 (-1032)))))) - (-5 *1 (-326 *3 *4)) (-14 *3 (-850)) (-14 *4 (-850)))) - ((*1 *2) - (-12 (-5 *2 (-1166 (-588 (-2 (|:| -3435 *3) (|:| -2717 (-1032)))))) - (-5 *1 (-327 *3 *4)) (-4 *3 (-324)) (-14 *4 (-3 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\ No newline at end of file |