diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-12-05 07:38:09 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-12-05 07:38:09 +0000 |
| commit | dd55b5ac1701d057ec49a45bfbc790f628757b52 (patch) | |
| tree | 3315c4e42e463924750f565f2e4e5da1a7b1683c /src/share/algebra | |
| parent | b18855381e61c452349e46e79e9b83ebd1a94dee (diff) | |
| download | open-axiom-dd55b5ac1701d057ec49a45bfbc790f628757b52.tar.gz | |
r12404@gauss: gdr | 2008-12-04 21:21:54 -0600
Branch for fixing CoercibleFrom changes.
r12405@gauss: gdr | 2008-12-05 01:34:50 -0600
* algebra/fs2ups.spad.pamphlet
(FunctionSpaceToUnivariatePowerSeries): Revert previous
requirement change on parameter.
* algebra/manip.spad.pamphlet (PolynomialRoots): Likewise.
* algebra/rf.spad.pamphlet (PolynomialCategoryQuotientFunctions):
Likewise.
* algebra/sum.spad.pamphlet (GosperSummationMethod): Likewise.
* share/algebra: Update databases.
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 874 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1494 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1313 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8870 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27458 |
5 files changed, 20011 insertions, 19998 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 9c8912b2..92a64920 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2272506 . 3436193628) +(2273396 . 3437447581) (-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."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4366 . T) (-4364 . T) (-4363 . T) ((-4371 "*") . T) (-4362 . T) (-4367 . T) (-4361 . T) (-4284 . T)) +((-4366 . T) (-4364 . T) (-4363 . T) ((-4371 "*") . T) (-4362 . T) (-4367 . T) (-4361 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3219) +(-32 R -3105) ((|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 -1020) (QUOTE (-553))))) @@ -66,7 +66,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4369))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-4284 . T)) +NIL NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,25 +74,25 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-37 S R) -((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) +((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) NIL NIL (-38 R) -((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) +((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) ((-4363 . T) (-4364 . T) (-4366 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3219 UP UPUP -4304) +(-40 -3105 UP UPUP -2326) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4362 |has| (-401 |#2|) (-357)) (-4367 |has| (-401 |#2|) (-357)) (-4361 |has| (-401 |#2|) (-357)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-4028 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-4028 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-4028 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4028 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) -(-41 R -3219) +((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-3988 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-3988 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-3988 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -626) (QUOTE (-553)))) (-3988 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) +(-41 R -3105) ((|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 (-445))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -424) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4369 . T) (-4370 . T)) -((-4028 (-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|))))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|))))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3219) +(-54 |Base| R -3105) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -154,7 +154,7 @@ NIL NIL (-56 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-57 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -163,64 +163,64 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-59 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) -(-60 -4292) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +(-60 -4298) ((|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 -(-61 -4292) +(-61 -4298) ((|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 -(-62 -4292) +(-62 -4298) ((|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 -(-63 -4292) +(-63 -4298) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-64 -4292) -((|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."))) +(-64 -4298) +((|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}"))) NIL NIL -(-65 -4292) +(-65 -4298) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-66 -4292) +(-66 -4298) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -4292) +(-67 -4298) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -4292) +(-68 -4298) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-69 -4292) +(-69 -4298) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-70 -4292) +(-70 -4298) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-71 -4292) +(-71 -4298) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-72 -4292) +(-72 -4298) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-73 -4292) +(-73 -4298) ((|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 @@ -232,55 +232,55 @@ 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 -(-76 -4292) +(-76 -4298) ((|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 -(-77 -4292) +(-77 -4298) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -4292) +(-78 -4298) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -4292) +(-79 -4298) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -4292) -((|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."))) +(-80 -4298) +((|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}"))) NIL NIL -(-81 -4292) +(-81 -4298) ((|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 -(-82 -4292) +(-82 -4298) ((|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 -(-83 -4292) +(-83 -4298) ((|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 -(-84 -4292) +(-84 -4298) ((|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 -(-85 -4292) +(-85 -4298) ((|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 -(-86 -4292) +(-86 -4298) ((|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 -(-87 -4292) +(-87 -4298) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -4292) +(-88 -4298) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -291,13 +291,13 @@ NIL (-90 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-91 S) -((|constructor| (NIL "This is the category of Spad abstract syntax trees.")) (|coerce| (($ (|Syntax|)) "\\spad{coerce(s)} parses syntax object \\spad{`s'} as a Spad construct."))) +((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL NIL (-92) -((|constructor| (NIL "This is the category of Spad abstract syntax trees.")) (|coerce| (($ (|Syntax|)) "\\spad{coerce(s)} parses syntax object \\spad{`s'} as a Spad construct."))) +((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL NIL (-93 S) @@ -339,7 +339,7 @@ NIL (-102 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-103 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -354,12 +354,12 @@ NIL NIL (-106 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-107) -((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-4028 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) +((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-3988 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) (-108) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -384,7 +384,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-114 -3219 UP) +(-114 -3105 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 @@ -395,14 +395,14 @@ NIL (-116 |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}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-115 |#1|) (QUOTE (-891))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-144))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-115 |#1|) (QUOTE (-1004))) (|HasCategory| (-115 |#1|) (QUOTE (-806))) (-4028 (|HasCategory| (-115 |#1|) (QUOTE (-806))) (|HasCategory| (-115 |#1|) (QUOTE (-833)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (QUOTE (-1130))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (QUOTE (-228))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -115) (|devaluate| |#1|)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (QUOTE (-301))) (|HasCategory| (-115 |#1|) (QUOTE (-538))) (|HasCategory| (-115 |#1|) (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-891)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))))) +((|HasCategory| (-115 |#1|) (QUOTE (-891))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-144))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-115 |#1|) (QUOTE (-1004))) (|HasCategory| (-115 |#1|) (QUOTE (-806))) (-3988 (|HasCategory| (-115 |#1|) (QUOTE (-806))) (|HasCategory| (-115 |#1|) (QUOTE (-833)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (QUOTE (-1130))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-115 |#1|) (QUOTE (-228))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -115) (|devaluate| |#1|)) (LIST (QUOTE -115) (|devaluate| |#1|)))) (|HasCategory| (-115 |#1|) (QUOTE (-301))) (|HasCategory| (-115 |#1|) (QUOTE (-538))) (|HasCategory| (-115 |#1|) (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-115 |#1|) (QUOTE (-891)))) (|HasCategory| (-115 |#1|) (QUOTE (-142))))) (-117 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4370))) (-118 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-4284 . T)) +NIL NIL (-119 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."))) @@ -411,14 +411,14 @@ NIL (-120 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"))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-121 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-122) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-123 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -426,22 +426,22 @@ NIL NIL (-124 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-126 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."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-127) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it has it is not as rigid as PrimitiveArray Byte is. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`c'}. The array can then store up to \\spad{`c'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128)))))) (-4028 (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-128) (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-128) (QUOTE (-1079)))) (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-128) (QUOTE (-1079))) (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128)))))) (-3988 (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128))))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-128) (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-128) (QUOTE (-1079)))) (|HasCategory| (-128) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-128) (QUOTE (-1079))) (|HasCategory| (-128) (LIST (QUOTE -303) (QUOTE (-128)))))) (-128) -((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} views \\spad{`c'} a a byte. In particular \\spad{`c'} is supposed to have a numerical value less than 256.") (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) +((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL NIL (-129) @@ -460,11 +460,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4371 "*") . T)) NIL -(-133 |minix| -2073 S T$) +(-133 |minix| -2026 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-134 |minix| -2073 R) +(-134 |minix| -2026 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -483,7 +483,7 @@ NIL (-138) ((|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}."))) ((-4369 . T) (-4359 . T) (-4370 . T)) -((-4028 (-12 (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-141) (QUOTE (-362))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-139 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 @@ -508,7 +508,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4366 . T)) NIL -(-145 -3219 UP UPUP) +(-145 -3105 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 @@ -522,7 +522,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasAttribute| |#1| (QUOTE -4369))) (-148 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."))) -((-4284 . T)) +NIL NIL (-149 |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."))) @@ -548,7 +548,7 @@ 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 -(-155 R -3219) +(-155 R -3105) ((|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 @@ -582,7 +582,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-538))) (|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (QUOTE (-1040))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasAttribute| |#2| (QUOTE -4365)) (|HasAttribute| |#2| (QUOTE -4368)) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-833)))) (-163 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| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4362 -4028 (|has| |#1| (-545)) (-12 (|has| |#1| (-301)) (|has| |#1| (-891)))) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4365 |has| |#1| (-6 -4365)) (-4368 |has| |#1| (-6 -4368)) (-4284 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4362 -3988 (|has| |#1| (-545)) (-12 (|has| |#1| (-301)) (|has| |#1| (-891)))) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4365 |has| |#1| (-6 -4365)) (-4368 |has| |#1| (-6 -4368)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-164 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."))) @@ -594,8 +594,8 @@ NIL NIL (-166 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}."))) -((-4362 -4028 (|has| |#1| (-545)) (-12 (|has| |#1| (-301)) (|has| |#1| (-891)))) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4365 |has| |#1| (-6 -4365)) (-4368 |has| |#1| (-6 -4368)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-343)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-228))) (-12 (|HasCategory| |#1| 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(QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (QUOTE (-1040))) (-12 (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-228))) (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasAttribute| |#1| (QUOTE -4365)) (|HasAttribute| |#1| (QUOTE -4368)) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155))))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-343))))) (-167 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 @@ -660,7 +660,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|arity| (((|SingleInteger|) $) "\\spad{arity(ctor)} returns the arity of the constructor `ctor'. \\indented{2}{A negative value means that the \\spad{ctor} takes a variable} \\indented{2}{length argument list,{} \\spadignore{e.g.} Mapping,{} Record,{} etc.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")) (|name| (((|Identifier|) $) "\\spad{name(ctor)} returns the name of the constructor `ctor'."))) NIL NIL -(-183 R -3219) +(-183 R -3105) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -765,26 +765,26 @@ NIL NIL NIL (-209 S) -((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|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}"))) +((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-210 -3219 UP UPUP R) +(-210 -3105 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 -(-211 -3219 FP) +(-211 -3105 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 (-212) -((|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|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-4028 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) +((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-3988 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) (-213) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-214 R -3219) +(-214 R -3105) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -799,18 +799,18 @@ NIL (-217 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-218 |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}."))) ((-4366 . T)) NIL -(-219 R -3219) +(-219 R -3105) ((|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 (-220) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4312 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4327 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-221) ((|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)}.}"))) @@ -819,14 +819,14 @@ NIL (-222 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}"))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-223 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 (-224 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."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-225 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}."))) @@ -850,28 +850,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4369))) (-230 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}."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-231) ((|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 -(-232 S -2073 R) +(-232 S -2026 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 (-357))) (|HasCategory| |#3| (QUOTE (-779))) (|HasCategory| |#3| (QUOTE (-831))) (|HasAttribute| |#3| (QUOTE -4366)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-712))) (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1031))) (|HasCategory| |#3| (QUOTE (-1079)))) -(-233 -2073 R) +(-233 -2026 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"))) -((-4363 |has| |#2| (-1031)) (-4364 |has| |#2| (-1031)) (-4366 |has| |#2| (-6 -4366)) ((-4371 "*") |has| |#2| (-169)) (-4369 . T) (-4284 . T)) +((-4363 |has| |#2| (-1031)) (-4364 |has| |#2| (-1031)) (-4366 |has| |#2| (-6 -4366)) ((-4371 "*") |has| |#2| (-169)) (-4369 . T)) NIL -(-234 -2073 A B) +(-234 -2026 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-235 -2073 R) +(-235 -2026 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4363 |has| |#2| (-1031)) (-4364 |has| |#2| (-1031)) (-4366 |has| |#2| (-6 -4366)) ((-4371 "*") |has| |#2| (-169)) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-129))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-712))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (LIST 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(-845)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))))) (-236) ((|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 @@ -886,12 +886,12 @@ NIL NIL (-239 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."))) -((-4284 . T)) +NIL NIL (-240 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}"))) +((|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}"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-241 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 @@ -899,19 +899,19 @@ NIL (-242 |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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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 @@ -922,7 +922,7 @@ NIL NIL (-248 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}."))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-249) ((|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."))) @@ -963,7 +963,7 @@ NIL (-258 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"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#3| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#3| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#3| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#3| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-259 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 @@ -1008,11 +1008,11 @@ 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 -(-270 R -3219) +(-270 R -3105) ((|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 -(-271 R -3219) +(-271 R -3105) ((|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 @@ -1034,7 +1034,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079)))) (-276 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}."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-277 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}."))) @@ -1060,7 +1060,7 @@ 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 -(-283 S R |Mod| -3233 -3858 |exactQuo|) +(-283 S R |Mod| -3668 -3160 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL @@ -1082,21 +1082,21 @@ NIL NIL (-288 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4366 -4028 (|has| |#1| (-1031)) (|has| |#1| (-466))) (-4363 |has| |#1| (-1031)) (-4364 |has| |#1| (-1031))) -((|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-1031)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-4028 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712)))) (|HasCategory| |#1| (QUOTE (-466))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1079)))) (-4028 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-296))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-466)))) (-4028 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712)))) (-4028 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1031)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25)))) +((-4366 -3988 (|has| |#1| (-1031)) (|has| |#1| (-466))) (-4363 |has| |#1| (-1031)) (-4364 |has| |#1| (-1031))) +((|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-1031)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1031)))) (-3988 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712)))) (|HasCategory| |#1| (QUOTE (-466))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1079)))) (-3988 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1091)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-296))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-466)))) (-3988 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712)))) (-3988 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1031)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-169)))) (-289 |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."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) (-290) ((|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 -(-291 -3219 S) +(-291 -3105 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 -(-292 E -3219) +(-292 E -3105) ((|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 @@ -1144,7 +1144,7 @@ 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 -(-304 -3219) +(-304 -3105) ((|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 @@ -1159,7 +1159,7 @@ NIL (-307 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))}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-1004))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-806))) (-4028 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-806))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-833)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-1130))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-228))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-538))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-833))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| $ (QUOTE (-142)))) (-4028 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| $ (QUOTE (-142)))))) +((|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-1004))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-806))) (-3988 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-806))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-833)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-1130))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-228))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1224) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-538))) (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-833))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| $ (QUOTE (-142)))) (-3988 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-142))) (-12 (|HasCategory| (-1224 |#1| |#2| |#3| |#4|) (QUOTE (-891))) (|HasCategory| $ (QUOTE (-142)))))) (-308 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 @@ -1170,9 +1170,9 @@ NIL NIL (-310 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."))) -((-4366 -4028 (-3791 (|has| |#1| (-1031)) (|has| |#1| (-626 (-553)))) (-12 (|has| |#1| (-545)) (-4028 (-3791 (|has| |#1| (-1031)) (|has| |#1| (-626 (-553)))) (|has| |#1| (-1031)) (|has| |#1| (-466)))) (|has| |#1| (-1031)) (|has| |#1| (-466))) (-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) ((-4371 "*") |has| |#1| (-545)) (-4362 |has| |#1| (-545)) (-4367 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(QUOTE (-1031)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1091)))) (-3988 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))))) (-3988 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1091)))) (-3988 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))))) (-3988 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1031)))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| $ (QUOTE (-1031))) (|HasCategory| $ (LIST (QUOTE -1020) (QUOTE (-553))))) +(-311 R -3105) ((|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 @@ -1183,7 +1183,7 @@ NIL (-313 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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-314 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 @@ -1215,17 +1215,17 @@ NIL (-321 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."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) -(-322 S -3219) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) +(-322 S -3105) ((|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 (-362)))) -(-323 -3219) +(-323 -3105) ((|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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-324) -((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) +((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) NIL NIL (-325 E) @@ -1240,15 +1240,15 @@ 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 -(-328 S -3219 UP UPUP R) +(-328 S -3105 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 -(-329 -3219 UP UPUP R) +(-329 -3105 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 -(-330 -3219 UP UPUP R) +(-330 -3105 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 @@ -1268,26 +1268,26 @@ 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 -(-335 S -3219 UP UPUP) +(-335 S -3105 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-357)))) -(-336 -3219 UP UPUP) +(-336 -3105 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4362 |has| (-401 |#2|) (-357)) (-4367 |has| (-401 |#2|) (-357)) (-4361 |has| (-401 |#2|) (-357)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-337 |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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) +((-3988 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) (-338 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-339 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-340 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 @@ -1304,31 +1304,31 @@ 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL -(-344 R UP -3219) +(-344 R UP -3105) ((|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 (-345 |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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) +((-3988 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) (-346 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-347 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-348 |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}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) +((-3988 (|HasCategory| (-892 |#1|) (QUOTE (-142))) (|HasCategory| (-892 |#1|) (QUOTE (-362)))) (|HasCategory| (-892 |#1|) (QUOTE (-144))) (|HasCategory| (-892 |#1|) (QUOTE (-362))) (|HasCategory| (-892 |#1|) (QUOTE (-142)))) (-349 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) -(-350 -3219 GF) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +(-350 -3105 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 @@ -1336,14 +1336,14 @@ 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 -(-352 -3219 FP FPP) +(-352 -3105 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 (-353 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}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) +((-3988 (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-142)))) (-354 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 @@ -1398,7 +1398,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079)))) (-367 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4369 . T) (-4284 . T)) +((-4369 . T)) NIL (-368 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1421,8 +1421,8 @@ NIL NIL NIL (-373) -((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4352 . T) (-4360 . T) (-4312 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((|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}.")) (|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}."))) +((-4352 . T) (-4360 . T) (-4327 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-374 |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}."))) @@ -1438,11 +1438,11 @@ NIL NIL (-377) ((|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}."))) -((-4284 . T)) +NIL NIL (-378) ((|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.}"))) -((-4284 . T)) +NIL NIL (-379 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."))) @@ -1461,7 +1461,7 @@ NIL NIL NIL (-383) -((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,{}pref,{}e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,{}n,{}e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used.")) (|coerce| (((|String|) $) "\\spad{coerce(fn)} produces a string for a file name according to operating system-dependent conventions.") (($ (|String|)) "\\spad{coerce(s)} converts a string to a file name according to operating system-dependent conventions."))) +((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,{}pref,{}e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,{}n,{}e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used."))) NIL NIL (-384 |n| |class| R) @@ -1472,7 +1472,7 @@ 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 -(-386 -3219 UP UPUP R) +(-386 -3105 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 @@ -1481,32 +1481,32 @@ NIL NIL NIL (-388) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL (-389) ((|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."))) -((-4284 . T)) +NIL NIL (-390) ((|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.}"))) -((-4284 . T)) +NIL NIL (-391) ((|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 -(-392 -4292 |returnType| -3674 |symbols|) +(-392 -4298 |returnType| -4112 |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 -(-393 -3219 UP) +(-393 -3105 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-394 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-4284 . T)) +NIL NIL (-395 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1522,7 +1522,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4352)) (|HasAttribute| |#1| (QUOTE -4360))) (-398) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-4312 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4327 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-399 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."))) @@ -1535,7 +1535,7 @@ NIL (-401 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."))) ((-4356 -12 (|has| |#1| (-6 -4367)) (|has| |#1| (-445)) (|has| |#1| (-6 -4356))) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-806))) (-4028 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#1| (QUOTE (-833)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1130))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814))))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-538))) (-12 (|HasAttribute| |#1| (QUOTE -4367)) (|HasAttribute| |#1| (QUOTE -4356)) (|HasCategory| |#1| (QUOTE (-445)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-806))) (-3988 (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#1| (QUOTE (-833)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814))))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-814)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-538))) (-12 (|HasAttribute| |#1| (QUOTE -4367)) (|HasAttribute| |#1| (QUOTE -4356)) (|HasCategory| |#1| (QUOTE (-445)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-402 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1556,11 +1556,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-407 R -3219 UP A) +(-407 R -3105 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4366 . T)) NIL -(-408 R -3219 UP A |ibasis|) +(-408 R -3105 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 -1020) (|devaluate| |#2|)))) @@ -1579,7 +1579,7 @@ NIL (-412 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."))) ((-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-1196))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-445)))) +((|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-1196))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-445)))) (-413 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 @@ -1593,7 +1593,7 @@ NIL NIL NIL (-416 R FE |Expon| UPS TRAN |x|) -((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) +((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) NIL NIL (-417 S A R B) @@ -1606,9 +1606,9 @@ NIL ((|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-362)))) (-419 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4369 . T) (-4359 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4359 . T) (-4370 . T)) NIL -(-420 R -3219) +(-420 R -3105) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1616,7 +1616,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4356 -12 (|has| |#1| (-6 -4356)) (|has| |#2| (-6 -4356))) (-4363 . T) (-4364 . T) (-4366 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4356)) (|HasAttribute| |#2| (QUOTE -4356)))) -(-422 R -3219) +(-422 R -3105) ((|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 @@ -1626,17 +1626,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (-424 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}."))) -((-4366 -4028 (|has| |#1| (-1031)) (|has| |#1| (-466))) (-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) ((-4371 "*") |has| |#1| (-545)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-545)) (-4361 |has| |#1| (-545)) (-4284 . T)) +((-4366 -3988 (|has| |#1| (-1031)) (|has| |#1| (-466))) (-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) ((-4371 "*") |has| |#1| (-545)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-545)) (-4361 |has| |#1| (-545))) NIL -(-425 R -3219) +(-425 R -3105) ((|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 -(-426 R -3219) +(-426 R -3105) ((|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)))) -(-427 R -3219) +(-427 R -3105) ((|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 @@ -1644,7 +1644,7 @@ 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 -(-429 R -3219 UP) +(-429 R -3105 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 -1020) (QUOTE (-48))))) @@ -1653,7 +1653,7 @@ NIL NIL NIL (-431) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL NIL (-432 |f|) @@ -1662,17 +1662,17 @@ NIL NIL (-433) ((|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}."))) -((-4284 . T)) +NIL NIL (-434) ((|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.}"))) -((-4284 . T)) +NIL NIL (-435 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 -(-436 R UP -3219) +(-436 R UP -3105) ((|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 @@ -1719,7 +1719,7 @@ NIL (-447 |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"))) (((-4371 "*") |has| |#2| (-169)) (-4362 |has| |#2| (-545)) (-4367 |has| |#2| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#2| (QUOTE (-891))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357))) (-4028 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) +((|HasCategory| |#2| (QUOTE (-891))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) (-448 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 @@ -1784,7 +1784,7 @@ 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 -(-464 |lv| -3219 R) +(-464 |lv| -3105 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 @@ -1799,11 +1799,11 @@ NIL (-467 |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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-468 |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."))) ((-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-833))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-833))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079)))) (-469 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)}"))) ((-4370 . T) (-4369 . T)) @@ -1819,7 +1819,7 @@ NIL (-472 |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."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) (-473) ((|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 @@ -1827,11 +1827,11 @@ NIL (-474 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(-845)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))))) (-476) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1839,8 +1839,8 @@ NIL (-477 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) -(-478 -3219 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +(-478 -3105 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 @@ -1849,16 +1849,16 @@ NIL NIL NIL (-480) -((|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|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-4028 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) +((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-3988 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) (-481 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 -4369)) (|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (-482 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-4284 . T)) +NIL NIL (-483 S) ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) @@ -1876,7 +1876,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-487 -3219 UP |AlExt| |AlPol|) +(-487 -3105 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 @@ -1887,16 +1887,16 @@ NIL (-489 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-490 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-491 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-492 R UP -3219) +(-492 R UP -3105) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1916,7 +1916,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-497 -3219 |Expon| |VarSet| |DPoly|) +(-497 -3105 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-1155))))) @@ -1967,7 +1967,7 @@ NIL (-509 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-510) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1975,15 +1975,15 @@ NIL (-511 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((-4028 (|HasCategory| (-570 |#1|) (QUOTE (-142))) (|HasCategory| (-570 |#1|) (QUOTE (-362)))) (|HasCategory| (-570 |#1|) (QUOTE (-144))) (|HasCategory| (-570 |#1|) (QUOTE (-362))) (|HasCategory| (-570 |#1|) (QUOTE (-142)))) +((-3988 (|HasCategory| (-570 |#1|) (QUOTE (-142))) (|HasCategory| (-570 |#1|) (QUOTE (-362)))) (|HasCategory| (-570 |#1|) (QUOTE (-144))) (|HasCategory| (-570 |#1|) (QUOTE (-362))) (|HasCategory| (-570 |#1|) (QUOTE (-142)))) (-512 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-513 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-514 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -1995,7 +1995,7 @@ NIL (-516 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-517) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2028,7 +2028,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-525 K -3219 |Par|) +(-525 K -3105 |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 @@ -2052,7 +2052,7 @@ 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 -(-531 K -3219 |Par|) +(-531 K -3105 |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 @@ -2087,12 +2087,12 @@ NIL (-539 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) -(-540 R -3219) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +(-540 R -3105) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-541 R0 -3219 UP UPUP R) +(-541 R0 -3105 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 @@ -2102,7 +2102,7 @@ NIL NIL (-543 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."))) -((-4312 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4327 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-544 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."))) @@ -2112,7 +2112,7 @@ 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."))) ((-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL -(-546 R -3219) +(-546 R -3105) ((|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 @@ -2124,7 +2124,7 @@ 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 -(-549 R -3219 L) +(-549 R -3105 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 -641) (|devaluate| |#2|)))) @@ -2132,11 +2132,11 @@ 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 -(-551 -3219 UP UPUP R) +(-551 -3105 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-552 -3219 UP) +(-552 -3105 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 @@ -2148,15 +2148,15 @@ 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 -(-555 R -3219 L) +(-555 R -3105 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 -641) (|devaluate| |#2|)))) -(-556 R -3219) +(-556 R -3105) ((|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 -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-1118)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-616))))) -(-557 -3219 UP) +(-557 -3105 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 @@ -2164,27 +2164,27 @@ 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 -(-559 -3219) +(-559 -3105) ((|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 (-560 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."))) -((-4312 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4327 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-561) ((|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 -(-562 R -3219) +(-562 R -3105) ((|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 -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-616))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155))))) (-12 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-545)))) -(-563 -3219 UP) +(-563 -3105 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 -(-564 R -3219) +(-564 R -3105) ((|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 @@ -2216,15 +2216,15 @@ 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 -(-572 R -3219) +(-572 R -3105) ((|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 -(-573 E -3219) +(-573 E -3105) ((|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 -(-574 -3219) +(-574 -3105) ((|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}."))) ((-4364 . T) (-4363 . T)) ((|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-1155))))) @@ -2255,7 +2255,7 @@ NIL (-581 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-4028 (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079)))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-3988 (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079)))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-582 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 @@ -2263,7 +2263,7 @@ NIL (-583 |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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-553)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-553)) (|devaluate| |#1|)))) (|HasCategory| (-553) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-553)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-553)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-553)) (|devaluate| |#1|)))) (|HasCategory| (-553) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-553)))))) (-584 |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.}"))) ((-4364 |has| |#1| (-545)) (-4363 |has| |#1| (-545)) ((-4371 "*") |has| |#1| (-545)) (-4362 |has| |#1| (-545)) (-4366 . T)) @@ -2276,7 +2276,7 @@ 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 -(-587 R -3219 FG) +(-587 R -3105 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 @@ -2287,17 +2287,17 @@ NIL (-589 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-590 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 -4370)) (|HasCategory| |#2| (QUOTE (-833))) (|HasAttribute| |#1| (QUOTE -4369)) (|HasCategory| |#3| (QUOTE (-1079)))) (-591 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-4284 . T)) +NIL NIL (-592) -((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) +((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) NIL NIL (-593) @@ -2306,19 +2306,19 @@ NIL NIL (-594 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)."))) -((-4366 -4028 (-3791 (|has| |#2| (-361 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-545)))) (-4364 . T) (-4363 . T)) -((-4028 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) +((-4366 -3988 (-3726 (|has| |#2| (-361 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-545)))) (-4364 . T) (-4363 . T)) +((-3988 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-595 |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."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| (-1137) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| (-1137) (QUOTE (-833))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -600) (QUOTE (-845))))) (-596 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 (-597 |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}."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-598 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"))) @@ -2336,12 +2336,12 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-602 -3219 UP) +(-602 -3105 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 (-603 S) -((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B}. In symbols \\indented{3}{A has CoercibleFrom \\spad{B}\\space{3}\\spad{<=>}\\space{2}\\spad{B} has CoercibleTo A}")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'."))) +((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL (-604) @@ -2349,7 +2349,7 @@ NIL NIL NIL (-605 S) -((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain \\spad{B}. In symbols \\indented{3}{A has ConvertibleFrom \\spad{B}\\space{3}\\spad{<=>}\\space{2}\\spad{B} has ConvertibleTo A}")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) +((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL (-606 S R) @@ -2364,7 +2364,7 @@ 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}."))) ((-4363 . T) (-4364 . T) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-831)))) -(-609 R -3219) +(-609 R -3105) ((|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 @@ -2396,18 +2396,18 @@ 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 -(-617 R -3219) +(-617 R -3105) ((|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 -(-618 |lv| -3219) +(-618 |lv| -3105) ((|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 (-619) ((|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."))) ((-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3359) (QUOTE (-52))))))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-1137) (QUOTE (-833))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3256) (QUOTE (-52))))))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-1137) (QUOTE (-833))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (QUOTE (-1079)))) (-620 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2418,8 +2418,8 @@ NIL NIL (-622 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4366 -4028 (-3791 (|has| |#2| (-361 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-545)))) (-4364 . T) (-4363 . T)) -((-4028 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) +((-4366 -3988 (-3726 (|has| |#2| (-361 |#1|)) (|has| |#1| (-545))) (-12 (|has| |#2| (-411 |#1|)) (|has| |#1| (-545)))) (-4364 . T) (-4363 . T)) +((-3988 (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -411) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -361) (|devaluate| |#1|)))) (-623 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 @@ -2431,7 +2431,7 @@ NIL (-625 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 -((-4106 (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-357)))) +((-2826 (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-357)))) (-626 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4366 . T)) @@ -2451,7 +2451,7 @@ NIL (-630 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-631 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2459,7 +2459,7 @@ NIL (-632 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-633 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2474,9 +2474,9 @@ NIL ((|HasAttribute| |#1| (QUOTE -4370))) (-636 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})}."))) -((-4284 . T)) NIL -(-637 R -3219 L) +NIL +(-637 R -3105 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 @@ -2496,11 +2496,11 @@ 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}."))) ((-4363 . T) (-4364 . T) (-4366 . T)) NIL -(-642 -3219 UP) +(-642 -3105 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)))) -(-643 A -4311) +(-643 A -1725) ((|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}}"))) ((-4363 . T) (-4364 . T) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) @@ -2534,13 +2534,13 @@ NIL NIL (-651 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}."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL -(-652 -3219) +(-652 -3105) ((|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 -(-653 -3219 |Row| |Col| M) +(-653 -3105 |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 @@ -2551,7 +2551,7 @@ NIL (-655 |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."))) ((-4366 . T) (-4369 . T) (-4363 . T) (-4364 . T)) -((|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-4028 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-545))) (-4028 (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-169)))) +((|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-545))) (-3988 (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-169)))) (-656) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2566,12 +2566,12 @@ NIL NIL (-659 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-4284 . T)) +NIL NIL (-660 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 -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-661) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2618,7 +2618,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-545)))) (-672 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"))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-673 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."))) @@ -2627,7 +2627,7 @@ NIL (-674 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."))) ((-4369 . T) (-4370 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-545))) (|HasAttribute| |#1| (QUOTE (-4371 "*"))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-675 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 @@ -2636,7 +2636,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-677 S -3219 FLAF FLAS) +(-677 S -3105 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 @@ -2647,10 +2647,10 @@ NIL (-679) ((|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"))) ((-4362 . T) (-4367 |has| (-684) (-357)) (-4361 |has| (-684) (-357)) (-4368 |has| (-684) (-6 -4368)) (-4365 |has| (-684) (-6 -4365)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-684) (QUOTE (-144))) (|HasCategory| (-684) (QUOTE (-142))) (|HasCategory| (-684) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-684) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-684) (QUOTE (-362))) (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-684) (QUOTE (-228))) (-4028 (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-343)))) (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (LIST (QUOTE -280) (QUOTE (-684)) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -303) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-684) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-684) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-684) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (-4028 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-343)))) (|HasCategory| (-684) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-684) (QUOTE (-1004))) (|HasCategory| (-684) (QUOTE (-1177))) (-12 (|HasCategory| (-684) (QUOTE (-984))) (|HasCategory| (-684) (QUOTE (-1177)))) (-4028 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-357))) (-12 (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (QUOTE (-891))))) (-4028 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (-12 (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-891)))) (-12 (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (QUOTE (-891))))) (|HasCategory| (-684) (QUOTE (-538))) (-12 (|HasCategory| (-684) (QUOTE (-1040))) (|HasCategory| (-684) (QUOTE (-1177)))) (|HasCategory| (-684) (QUOTE (-1040))) (-4028 (|HasCategory| (-684) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-684) (QUOTE (-357)))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891))) (-4028 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-357)))) (-4028 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-545)))) (-12 (|HasCategory| (-684) (QUOTE (-228))) (|HasCategory| (-684) (QUOTE (-357)))) (-12 (|HasCategory| (-684) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-684) (QUOTE (-357)))) (|HasCategory| (-684) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-684) (QUOTE (-833))) (|HasCategory| (-684) (QUOTE (-545))) (|HasAttribute| (-684) (QUOTE -4368)) (|HasAttribute| (-684) (QUOTE -4365)) (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-142)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-343))))) +((|HasCategory| (-684) (QUOTE (-144))) (|HasCategory| (-684) (QUOTE (-142))) (|HasCategory| (-684) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-684) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-684) (QUOTE (-362))) (|HasCategory| (-684) (QUOTE (-357))) (-3988 (|HasCategory| (-684) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-684) (QUOTE (-357)))) (|HasCategory| (-684) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-684) (QUOTE (-228))) (-3988 (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-343)))) (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (LIST (QUOTE -280) (QUOTE (-684)) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -303) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-684)))) (|HasCategory| (-684) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-684) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-684) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-684) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (-3988 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-343)))) (|HasCategory| (-684) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-684) (QUOTE (-1004))) (|HasCategory| (-684) (QUOTE (-1177))) (-12 (|HasCategory| (-684) (QUOTE (-984))) (|HasCategory| (-684) (QUOTE (-1177)))) (-3988 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-357))) (-12 (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (QUOTE (-891))))) (-3988 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (-12 (|HasCategory| (-684) (QUOTE (-357))) (|HasCategory| (-684) (QUOTE (-891)))) (-12 (|HasCategory| (-684) (QUOTE (-343))) (|HasCategory| (-684) (QUOTE (-891))))) (|HasCategory| (-684) (QUOTE (-538))) (-12 (|HasCategory| (-684) (QUOTE (-1040))) (|HasCategory| (-684) (QUOTE (-1177)))) (|HasCategory| (-684) (QUOTE (-1040))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891))) (-3988 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-357)))) (-3988 (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-545)))) (-12 (|HasCategory| (-684) (QUOTE (-228))) (|HasCategory| (-684) (QUOTE (-357)))) (-12 (|HasCategory| (-684) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-684) (QUOTE (-357)))) (|HasCategory| (-684) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-684) (QUOTE (-833))) (|HasCategory| (-684) (QUOTE (-545))) (|HasAttribute| (-684) (QUOTE -4368)) (|HasAttribute| (-684) (QUOTE -4365)) (-12 (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-142)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-684) (QUOTE (-301))) (|HasCategory| (-684) (QUOTE (-891)))) (|HasCategory| (-684) (QUOTE (-343))))) (-680 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}."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-681 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}."))) @@ -2660,13 +2660,13 @@ 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 -(-683 OV E -3219 PG) +(-683 OV E -3105 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 (-684) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-4312 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4327 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-685 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."))) @@ -2681,7 +2681,7 @@ NIL NIL NIL (-688 S) -((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s} viewed as an element of \\%."))) +((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set."))) NIL NIL (-689 S) @@ -2696,7 +2696,7 @@ 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 -(-692 S -1766 I) +(-692 S -1780 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 @@ -2716,23 +2716,23 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-697 R |Mod| -3233 -3858 |exactQuo|) +(-697 R |Mod| -3668 -3160 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-698 R |Rep|) -((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) +((|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")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4365 |has| |#1| (-357)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-343))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-699 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| $) "\\spad{exponent(x)} \\undocumented"))) +((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-700 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144)))) -(-701 R |Mod| -3233 -3858 |exactQuo|) +(-701 R |Mod| -3668 -3160 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4366 . T)) NIL @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4364 . T) (-4363 . T)) NIL -(-704 -3219) +(-704 -3105) ((|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]]}."))) ((-4366 . T)) NIL @@ -2780,7 +2780,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-713 -3219 UP) +(-713 -3105 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 @@ -2799,7 +2799,7 @@ NIL (-717 |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."))) (((-4371 "*") |has| |#2| (-169)) (-4362 |has| |#2| (-545)) (-4367 |has| |#2| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#2| (QUOTE (-891))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357))) (-4028 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) +((|HasCategory| |#2| (QUOTE (-891))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-847 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) (-718 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2818,7 +2818,7 @@ NIL ((-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-833)))) (-722 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4359 . T) (-4370 . T) (-4284 . T)) +((-4359 . T) (-4370 . T)) NIL (-723 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|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}."))) @@ -2932,11 +2932,11 @@ 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 -(-751 -3219) +(-751 -3105) ((|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 -(-752 P -3219) +(-752 P -3105) ((|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 @@ -2944,12 +2944,12 @@ NIL NIL NIL NIL -(-754 UP -3219) +(-754 UP -3105) ((|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 (-755) -((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) +((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL (-756 R) @@ -2960,7 +2960,7 @@ 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."))) (((-4371 "*") . T)) NIL -(-758 R -3219) +(-758 R -3105) ((|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 @@ -2980,7 +2980,7 @@ 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 -(-763 -3219 |ExtF| |SUEx| |ExtP| |n|) +(-763 -3105 |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 @@ -2995,7 +2995,7 @@ NIL (-766 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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . 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(|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-1155)))) (-2826 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-553))))) (-2826 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-1155)))) (-2826 (|HasCategory| |#1| (LIST (QUOTE -974) (QUOTE (-553))))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-767 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 @@ -3003,14 +3003,14 @@ NIL (-768 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)}"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4365 |has| |#1| (-357)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-769 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-770 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.}"))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-771 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}."))) @@ -3064,23 +3064,23 @@ 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4363 . T) (-4364 . T) (-4366 . T)) NIL -(-784 -4028 R OS S) +(-784 -3988 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-785 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-4028 (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (-3988 (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-981 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (-786) ((|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 -(-787 R -3219 L) +(-787 R -3105 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 -(-788 R -3219) +(-788 R -3105) ((|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 @@ -3088,7 +3088,7 @@ 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 -(-790 R -3219) +(-790 R -3105) ((|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 @@ -3096,52 +3096,52 @@ 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 -(-792 -3219 UP UPUP R) +(-792 -3105 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 -(-793 -3219 UP L LQ) +(-793 -3105 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 (-794) -((|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{}"))) +((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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 -(-795 -3219 UP L LQ) +(-795 -3105 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 -(-796 -3219 UP) +(-796 -3105 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 -(-797 -3219 L UP A LO) +(-797 -3105 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 -(-798 -3219 UP) +(-798 -3105 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)))) -(-799 -3219 LO) +(-799 -3105 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}.") 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-804 (-1155)) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-803 |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."))) +((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4371 "*") |has| |#2| (-357)) (-4362 |has| |#2| (-357)) (-4367 |has| |#2| (-357)) (-4361 |has| |#2| (-357)) (-4366 . T) (-4364 . T) (-4363 . T)) ((|HasCategory| |#2| (QUOTE (-357)))) (-804 S) @@ -3194,7 +3194,7 @@ NIL NIL (-816 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4369 . T) (-4359 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4359 . T) (-4370 . T)) NIL (-817) ((|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."))) @@ -3207,7 +3207,7 @@ NIL (-819 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."))) ((-4366 |has| |#1| (-831))) -((|HasCategory| |#1| (QUOTE (-831))) (-4028 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-538))) (-4028 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-831))) (-3988 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-3988 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-21)))) (-820 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) (-4366 . T)) @@ -3225,7 +3225,7 @@ NIL NIL NIL (-824) -((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) +((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL (-825 R S) @@ -3235,12 +3235,12 @@ NIL (-826 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."))) ((-4366 |has| |#1| (-831))) -((|HasCategory| |#1| (QUOTE (-831))) (-4028 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-538))) (-4028 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-831))) (-3988 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-3988 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-538))) (|HasCategory| |#1| (QUOTE (-21)))) (-827) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-828 -2073 S) +(-828 -2026 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 @@ -3276,12 +3276,12 @@ 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 (-357))) (|HasCategory| |#1| (QUOTE (-545)))) -(-837 R |sigma| -2695) +(-837 R |sigma| -2245) ((|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."))) ((-4363 . T) (-4364 . T) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-357)))) -(-838 |x| R |sigma| -2695) -((|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."))) +(-838 |x| R |sigma| -2245) +((|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}."))) ((-4363 . T) (-4364 . T) (-4366 . T)) ((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-357)))) (-839 R) @@ -3321,7 +3321,7 @@ NIL NIL NIL (-848 R |vl| |wl| |wtlevel|) -((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) +((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) ((-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) (-849 R PS UP) @@ -3343,15 +3343,15 @@ NIL (-853 |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)."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-852 |#1|) (QUOTE (-891))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-852 |#1|) (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-144))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-852 |#1|) (QUOTE (-1004))) (|HasCategory| (-852 |#1|) (QUOTE (-806))) (-4028 (|HasCategory| (-852 |#1|) (QUOTE (-806))) (|HasCategory| (-852 |#1|) (QUOTE (-833)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (QUOTE (-1130))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (QUOTE (-228))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -852) (|devaluate| |#1|)) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (QUOTE (-301))) (|HasCategory| (-852 |#1|) (QUOTE (-538))) (|HasCategory| (-852 |#1|) (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-891)))) (|HasCategory| (-852 |#1|) (QUOTE (-142))))) +((|HasCategory| (-852 |#1|) (QUOTE (-891))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-852 |#1|) (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-144))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-852 |#1|) (QUOTE (-1004))) (|HasCategory| (-852 |#1|) (QUOTE (-806))) (-3988 (|HasCategory| (-852 |#1|) (QUOTE (-806))) (|HasCategory| (-852 |#1|) (QUOTE (-833)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (QUOTE (-1130))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-852 |#1|) (QUOTE (-228))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -507) (QUOTE (-1155)) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -852) (|devaluate| |#1|)) (LIST (QUOTE -852) (|devaluate| |#1|)))) (|HasCategory| (-852 |#1|) (QUOTE (-301))) (|HasCategory| (-852 |#1|) (QUOTE (-538))) (|HasCategory| (-852 |#1|) (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-852 |#1|) (QUOTE (-891)))) (|HasCategory| (-852 |#1|) (QUOTE (-142))))) (-854 |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)}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-806))) (-4028 (|HasCategory| |#2| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-538))) (|HasCategory| |#2| (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) +((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-806))) (-3988 (|HasCategory| |#2| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-833)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-538))) (|HasCategory| |#2| (QUOTE (-833))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) (-855 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 (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))))) (-856) ((|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 @@ -3407,7 +3407,7 @@ NIL (-869 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-4106 (|HasCategory| |#2| (QUOTE (-1031)))) (-4106 (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))))) (-12 (|HasCategory| |#2| (QUOTE (-1031))) (-4106 (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155))))) +((-12 (-2826 (|HasCategory| |#2| (QUOTE (-1031)))) (-2826 (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))))) (-12 (|HasCategory| |#2| (QUOTE (-1031))) (-2826 (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155))))) (-870 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 @@ -3416,7 +3416,7 @@ 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 -(-872 R -1766) +(-872 R -1780) ((|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 @@ -3440,7 +3440,7 @@ 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 -(-878 UP -3219) +(-878 UP -3105) ((|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 @@ -3449,7 +3449,7 @@ NIL NIL NIL (-880) -((|retract| (((|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{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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{coerce(x)} \\undocumented{}"))) +((|retract| (((|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|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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{coerce(x)} \\undocumented{}"))) NIL NIL (-881 A S) @@ -3461,9 +3461,9 @@ NIL ((-4366 . T)) NIL (-883 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"))) +((|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}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-884 |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 @@ -3479,7 +3479,7 @@ NIL (-887 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."))) ((-4366 . T)) -((-4028 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-833)))) +((-3988 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-833)))) (-888 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 @@ -3500,7 +3500,7 @@ 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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) ((|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-142))) (|HasCategory| $ (QUOTE (-362)))) -(-893 R0 -3219 UP UPUP R) +(-893 R0 -3105 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 @@ -3528,7 +3528,7 @@ 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 -(-900 -3219) +(-900 -3105) ((|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 @@ -3544,11 +3544,11 @@ 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}."))) (((-4371 "*") . T)) NIL -(-904 -3219 P) +(-904 -3105 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-905 |xx| -3219) +(-905 |xx| -3105) ((|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 @@ -3572,7 +3572,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-911 R -3219) +(-911 R -3105) ((|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 @@ -3584,7 +3584,7 @@ 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 -(-914 S R -3219) +(-914 S R -3105) ((|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 @@ -3604,11 +3604,11 @@ 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 -868) (|devaluate| |#1|)))) -(-919 R -3219 -1766) +(-919 R -3105 -1780) ((|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 -(-920 -1766) +(-920 -1780) ((|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 @@ -3631,7 +3631,7 @@ NIL (-925 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-926 |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 @@ -3656,7 +3656,7 @@ 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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) NIL -(-932 E V R P -3219) +(-932 E V R P -3105) ((|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 @@ -3667,9 +3667,9 @@ NIL (-934 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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) -(-935 E V R P -3219) -((|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"))) +((|HasCategory| |#1| (QUOTE (-891))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1155) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +(-935 E V R P -3105) +((|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)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-445)))) (-936) @@ -3691,12 +3691,12 @@ NIL (-940 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-941) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-942 -3219) +(-942 -3105) ((|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 @@ -3711,11 +3711,11 @@ NIL (-945 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}"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-129)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-129)))) (|HasAttribute| |#1| (QUOTE -4367))) (-946 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"))) ((-4366 -12 (|has| |#2| (-466)) (|has| |#1| (-466)))) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-833))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-12 (|HasCategory| |#1| (QUOTE (-712))) 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(|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-833))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-12 (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#2| (QUOTE (-712))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-362)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-466)))) (-12 (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#2| (QUOTE (-712)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779))))) (-12 (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#2| (QUOTE (-712)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-129))) (|HasCategory| |#2| (QUOTE (-129)))) (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-833))))) (-947) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3730,7 +3730,7 @@ NIL NIL (-950 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-951 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}}"))) @@ -3741,7 +3741,7 @@ NIL NIL NIL (-953) -((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) +((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) NIL NIL (-954 S |Coef| |Expon| |Var|) @@ -3762,7 +3762,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-545)))) (-958 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."))) -((-4369 . T) (-4284 . T)) +((-4369 . T)) NIL (-959 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."))) @@ -3777,8 +3777,8 @@ NIL NIL NIL (-962 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}."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((|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")) (|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}."))) +((-4370 . T) (-4369 . T)) NIL (-963 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3796,7 +3796,7 @@ 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 -(-967 K R UP -3219) +(-967 K R UP -3105) ((|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 @@ -3826,7 +3826,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-538))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-806))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-1130)))) (-974 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}."))) -((-4284 . T) (-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-975 |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}."))) @@ -3838,7 +3838,7 @@ NIL NIL (-977 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."))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-978 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}."))) @@ -3855,11 +3855,11 @@ NIL (-981 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.}"))) ((-4362 |has| |#1| (-284)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-538))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357))))) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -507) (QUOTE (-1155)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-1040))) (|HasCategory| |#1| (QUOTE (-538)))) (-982 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}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-983 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3868,14 +3868,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-985 -3219 UP UPUP |radicnd| |n|) +(-985 -3105 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4362 |has| (-401 |#2|) (-357)) (-4367 |has| (-401 |#2|) (-357)) (-4361 |has| (-401 |#2|) (-357)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-4028 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-4028 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-4028 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4028 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) +((|HasCategory| (-401 |#2|) (QUOTE (-142))) (|HasCategory| (-401 |#2|) (QUOTE (-144))) (|HasCategory| (-401 |#2|) (QUOTE (-343))) (-3988 (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (|HasCategory| (-401 |#2|) (QUOTE (-357))) (|HasCategory| (-401 |#2|) (QUOTE (-362))) (-3988 (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (QUOTE (-343)))) (-3988 (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-343))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -626) (QUOTE (-553)))) (-3988 (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 |#2|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| (-401 |#2|) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-401 |#2|) (QUOTE (-357)))) (-12 (|HasCategory| (-401 |#2|) (QUOTE (-228))) (|HasCategory| (-401 |#2|) (QUOTE (-357))))) (-986 |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|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|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."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-4028 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) +((|HasCategory| (-553) (QUOTE (-891))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-1155)))) (|HasCategory| (-553) (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-144))) (|HasCategory| (-553) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-1004))) (|HasCategory| (-553) (QUOTE (-806))) (-3988 (|HasCategory| (-553) (QUOTE (-806))) (|HasCategory| (-553) (QUOTE (-833)))) (|HasCategory| (-553) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-1130))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| (-553) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| (-553) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| (-553) (QUOTE (-228))) (|HasCategory| (-553) (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| (-553) (LIST (QUOTE -507) (QUOTE (-1155)) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -303) (QUOTE (-553)))) (|HasCategory| (-553) (LIST (QUOTE -280) (QUOTE (-553)) (QUOTE (-553)))) (|HasCategory| (-553) (QUOTE (-301))) (|HasCategory| (-553) (QUOTE (-538))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-553) (LIST (QUOTE -626) (QUOTE (-553)))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| (-553) (QUOTE (-891)))) (|HasCategory| (-553) (QUOTE (-142))))) (-987) ((|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 @@ -3898,7 +3898,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#2| (QUOTE (-1079)))) (-992 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}."))) -((-4284 . T)) +NIL NIL (-993 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3908,19 +3908,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4362 . T) (-4367 . T) (-4361 . T) (-4364 . T) (-4363 . T) ((-4371 "*") . T) (-4366 . T)) NIL -(-995 R -3219) +(-995 R -3105) ((|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 -(-996 R -3219) +(-996 R -3105) ((|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 -(-997 -3219 UP) +(-997 -3105 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 -(-998 -3219 UP) +(-998 -3105 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 @@ -3955,8 +3955,8 @@ NIL (-1006 |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"))) ((-4362 . T) (-4367 . T) (-4361 . T) (-4364 . T) (-4363 . T) ((-4371 "*") . T) (-4366 . T)) -((-4028 (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (QUOTE (-553))))) -(-1007 -3219 L) +((-3988 (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-401 (-553)) (LIST (QUOTE -1020) (QUOTE (-553))))) +(-1007 -3105 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 @@ -3992,14 +3992,14 @@ 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 -(-1016 -3219 |Expon| |VarSet| |FPol| |LFPol|) +(-1016 -3105 |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"))) (((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1017) ((|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.}"))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3359) (QUOTE (-52))))))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-1155) (QUOTE (-833))) (|HasCategory| (-52) (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3256) (QUOTE (-52))))))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-1155) (QUOTE (-833))) (|HasCategory| (-52) (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845))))) (-1018) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4049,14 +4049,14 @@ NIL NIL NIL (-1030 S) -((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|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."))) +((|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\"}.")) (|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."))) NIL NIL (-1031) -((|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."))) +((|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\"}.")) (|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."))) ((-4366 . T)) NIL -(-1032 |xx| -3219) +(-1032 |xx| -3105) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4066,12 +4066,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-301))) (|HasCategory| |#4| (QUOTE (-357))) (|HasCategory| |#4| (QUOTE (-545))) (|HasCategory| |#4| (QUOTE (-169)))) (-1034 |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"))) -((-4369 . T) (-4284 . T) (-4364 . T) (-4363 . T)) +((-4369 . T) (-4364 . T) (-4363 . T)) NIL (-1035 |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}."))) +((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4369 . T) (-4364 . T) (-4363 . T)) -((-4028 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-357)))) (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) +((-3988 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-357)))) (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-169))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-845))))) (-1036 |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 @@ -4097,13 +4097,13 @@ NIL NIL NIL (-1042) -((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) +((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) ((-4357 . T) (-4361 . T) (-4356 . T) (-4367 . T) (-4368 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1043) ((|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}"))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3359) (QUOTE (-52))))))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (QUOTE (-1079))) (|HasCategory| (-1155) (QUOTE (-833))) (|HasCategory| (-52) (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 (-1155)) (|:| -3359 (-52))) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (QUOTE (-1155))) (LIST (QUOTE |:|) (QUOTE -3256) (QUOTE (-52))))))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-52) (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| (-52) (QUOTE (-1079))) (|HasCategory| (-52) (LIST (QUOTE -303) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (QUOTE (-1079))) (|HasCategory| (-1155) (QUOTE (-833))) (|HasCategory| (-52) (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-52) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (LIST (QUOTE -600) (QUOTE (-845))))) (-1044 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 @@ -4134,7 +4134,7 @@ NIL NIL (-1051 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}."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1052 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."))) @@ -4148,11 +4148,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1055 |Base| R -3219) +(-1055 |Base| R -3105) ((|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 -(-1056 |Base| R -3219) +(-1056 |Base| R -3105) ((|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 @@ -4167,7 +4167,7 @@ NIL (-1059 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."))) ((-4362 |has| |#1| (-357)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-343)))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155))))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357)))) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))))) +((|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-343))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-343)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-362))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (QUOTE (-343)))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155))))) (-12 (|HasCategory| |#1| (QUOTE (-343))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155))))) (-12 (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (QUOTE (-357))))) (-1060 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 @@ -4195,7 +4195,7 @@ NIL (-1066 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"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1067 (-1155)) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-228))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-1067 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 @@ -4217,8 +4217,8 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-1079)))) (-1072 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."))) -((-4284 . T)) +((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|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."))) +NIL NIL (-1073 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -4226,7 +4226,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-1079)))) (-1074 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]}."))) -((-4284 . T)) +NIL NIL (-1075) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) @@ -4238,7 +4238,7 @@ NIL NIL (-1077 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4359 . T) (-4284 . T)) +((-4359 . T)) NIL (-1078 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}."))) @@ -4255,9 +4255,9 @@ NIL (-1081 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)}}"))) ((-4369 . T) (-4359 . T) (-4370 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1082 |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|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) +((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|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.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL (-1083) @@ -4282,7 +4282,7 @@ NIL NIL (-1088 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.}"))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1089) ((|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."))) @@ -4299,7 +4299,7 @@ NIL (-1092 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4363 |has| |#3| (-1031)) (-4364 |has| |#3| (-1031)) (-4366 |has| |#3| (-6 -4366)) ((-4371 "*") |has| |#3| (-169)) (-4369 . 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(|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-228))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-357))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-712))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-779))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-831))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-1031))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553)))))) (|HasCategory| (-553) (QUOTE (-833))) (-12 (|HasCategory| |#3| (QUOTE (-1031))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (QUOTE (-228))) (|HasCategory| |#3| (QUOTE (-1031)))) (-12 (|HasCategory| |#3| (QUOTE (-1031))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-1155))))) (-3988 (|HasCategory| |#3| (QUOTE (-1031))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553)))))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -1020) (QUOTE (-553))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#3| (QUOTE (-1079)))) (|HasAttribute| |#3| (QUOTE -4366)) (|HasCategory| |#3| (QUOTE (-129))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))))) (-1093 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4308,7 +4308,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1095 R -3219) +(-1095 R -3105) ((|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 @@ -4330,7 +4330,7 @@ NIL NIL (-1100 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4369 . T) (-4370 . T) (-4284 . T)) +((-4369 . T) (-4370 . T)) NIL (-1101 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4338,7 +4338,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-357))) (|HasAttribute| |#3| (QUOTE (-4371 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) (-1102 |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."))) -((-4284 . T) (-4369 . T) (-4363 . T) (-4364 . T) (-4366 . T)) +((-4369 . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1103 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}."))) @@ -4347,16 +4347,16 @@ NIL (-1104 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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-891))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) +((|HasCategory| |#1| (QUOTE (-891))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-1105 |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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-357)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-357)))) (-1106 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}"))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL -(-1107 UP -3219) +(-1107 UP -3105) ((|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 @@ -4394,7 +4394,7 @@ NIL NIL (-1116) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) -((-4284 . T)) +NIL NIL (-1117) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) @@ -4411,18 +4411,18 @@ NIL (-1120 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1119) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079))) (-4028 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1119) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079))))) (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1119) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079))) (-3988 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1119) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1119 |#1| |#2|) (QUOTE (-1079))))) (|HasCategory| (-1119 |#1| |#2|) (LIST (QUOTE -600) (QUOTE (-845))))) (-1121 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4366 . T) (-4358 |has| |#2| (-6 (-4371 "*"))) (-4369 . T) (-4363 . T) (-4364 . T)) -((|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-4028 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-357))) (-4028 (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-169)))) +((|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (-12 (|HasCategory| |#2| (QUOTE (-228))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-357))) (-3988 (|HasAttribute| |#2| (QUOTE (-4371 "*"))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-169)))) (-1122 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1123) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1124 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4435,19 +4435,19 @@ NIL (-1126 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-1127 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 (-1128 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})}."))) -((-4284 . T)) +NIL NIL (-1129 |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."))) ((-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-833))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-833))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079)))) (-1130) ((|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 @@ -4469,21 +4469,21 @@ NIL NIL NIL (-1135 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."))) +((|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}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4370 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-1136) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1137) NIL ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141))))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (|HasCategory| (-141) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| (-141) (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| (-141) (QUOTE (-1079))) (|HasCategory| (-141) (LIST (QUOTE -303) (QUOTE (-141)))))) (-1138 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#1|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (QUOTE (-1079))) (|HasCategory| (-1137) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (QUOTE (-1137))) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#1|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (QUOTE (-1079))) (|HasCategory| (-1137) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (LIST (QUOTE -600) (QUOTE (-845))))) (-1139 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 @@ -4514,9 +4514,9 @@ NIL NIL (-1146 |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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(QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#1| (QUOTE (-228))) (|HasAttribute| |#1| (QUOTE -4367)) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-891)))) (|HasCategory| |#1| (QUOTE (-142))))) (-1152 |Coef| |var| |cen|) -((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) +((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-1153 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|)))) (|HasCategory| (-757) (QUOTE (-1091))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|)))) (|HasCategory| (-757) (QUOTE (-1091))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-1154) ((|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 NIL (-1155) -((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) +((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL (-1156 R) @@ -4559,7 +4559,7 @@ NIL (-1157 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-6 -4367)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| (-953) (QUOTE (-129))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasAttribute| |#1| (QUOTE -4367))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-3988 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-445))) (-12 (|HasCategory| (-953) (QUOTE (-129))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasAttribute| |#1| (QUOTE -4367))) (-1158) ((|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 @@ -4591,7 +4591,7 @@ NIL (-1165 |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}"))) ((-4369 . T) (-4370 . T)) -((-12 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2669) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3359) (|devaluate| |#2|)))))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-4028 (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2578) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3256) (|devaluate| |#2|)))))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-1079)))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -601) (QUOTE (-529)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#2| (QUOTE (-1079))) (-3988 (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#2| (LIST (QUOTE -600) (QUOTE (-845)))) (|HasCategory| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (LIST (QUOTE -600) (QUOTE (-845))))) (-1166 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 @@ -4602,7 +4602,7 @@ NIL NIL (-1168 |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})}."))) -((-4370 . T) (-4284 . T)) +((-4370 . T)) NIL (-1169 |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."))) @@ -4617,7 +4617,7 @@ NIL NIL NIL (-1172) -((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) +((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL (-1173) @@ -4643,7 +4643,7 @@ NIL (-1178 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4370 . T) (-4369 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1079))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (-1179 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4652,7 +4652,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1181 R -3219) +(-1181 R -3105) ((|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 @@ -4660,7 +4660,7 @@ 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 -(-1183 R -3219) +(-1183 R -3105) ((|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 -601) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -868) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -868) (|devaluate| |#1|))))) @@ -4670,12 +4670,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-362)))) (-1185 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1186 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4364 . T) (-4363 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-357)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-142))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-357)))) (-1187 |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 @@ -4685,10 +4685,10 @@ NIL NIL NIL (-1189 S) -((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) +((|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"))) NIL ((|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) -(-1190 -3219) +(-1190 -3105) ((|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 @@ -4698,7 +4698,7 @@ NIL NIL (-1192) ((|constructor| (NIL "The fundamental Type."))) -((-4284 . T)) +NIL NIL (-1193 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}.}"))) @@ -4725,21 +4725,21 @@ NIL (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1199 S |Coef| UTS) -((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) +((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-357)))) (-1200 |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)}."))) -(((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4284 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) +((|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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|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)}."))) +(((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1201 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4773,9 +4773,9 @@ NIL NIL NIL (-1211 |x| R) -((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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T)) -((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-4028 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (-4028 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-4028 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) +((|HasCategory| |#2| (QUOTE (-891))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-169))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-545)))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-373)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-373))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -868) (QUOTE (-553)))) (|HasCategory| |#2| (LIST (QUOTE -868) (QUOTE (-553))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-373)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -874) (QUOTE (-553)))))) (-12 (|HasCategory| (-1061) (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-529))))) (|HasCategory| |#2| (QUOTE (-833))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (QUOTE (-553)))) (-3988 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| |#2| (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (-3988 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-445))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-357))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasCategory| |#2| (QUOTE (-228))) (|HasAttribute| |#2| (QUOTE -4367)) (|HasCategory| |#2| (QUOTE (-445))) (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (-3988 (-12 (|HasCategory| $ (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-891)))) (|HasCategory| |#2| (QUOTE (-142))))) (-1212 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4791,7 +4791,7 @@ NIL (-1215 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 -882) (QUOTE (-1155)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1091))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3212) (LIST (|devaluate| |#2|) (QUOTE (-1155)))))) +((|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1091))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3110) (LIST (|devaluate| |#2|) (QUOTE (-1155)))))) (-1216 |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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) @@ -4809,32 +4809,32 @@ NIL (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1220 S |Coef| ULS) -((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) +((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL (-1221 |Coef| ULS) -((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) +((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1222 |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)}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) +((|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-1223 |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."))) +((|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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4367 |has| |#1| (-357)) (-4361 |has| |#1| (-357)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-4028 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-169))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553))) (|devaluate| |#1|)))) (|HasCategory| (-401 (-553)) (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-3988 (|HasCategory| |#1| (QUOTE (-357))) (|HasCategory| |#1| (QUOTE (-545)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -401) (QUOTE (-553)))))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-1224 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))}."))) (((-4371 "*") |has| (-1223 |#2| |#3| |#4|) (-169)) (-4362 |has| (-1223 |#2| |#3| |#4|) (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-357))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-445))) (-4028 (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-545)))) +((|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-142))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-169))) (-3988 (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553)))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| (-1223 |#2| |#3| |#4|) (LIST (QUOTE -1020) (QUOTE (-553)))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-357))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-445))) (|HasCategory| (-1223 |#2| |#3| |#4|) (QUOTE (-545)))) (-1225 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4370))) (-1226 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-4284 . T)) +NIL NIL (-1227 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4843,7 +4843,7 @@ NIL (-1228 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-553)))) (|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasSignature| |#2| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1619) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1155))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#2| (QUOTE (-941))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasSignature| |#2| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3406) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1155))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#2| (QUOTE (-357)))) (-1229 |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."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) @@ -4851,18 +4851,18 @@ NIL (-1230 |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}."))) (((-4371 "*") |has| |#1| (-169)) (-4362 |has| |#1| (-545)) (-4363 . T) (-4364 . T) (-4366 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-4028 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|)))) (|HasCategory| (-757) (QUOTE (-1091))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasSignature| |#1| (LIST (QUOTE -3212) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasCategory| |#1| (QUOTE (-357))) (-4028 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -1619) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3611) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasCategory| |#1| (QUOTE (-545))) (-3988 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-142))) (|HasCategory| |#1| (QUOTE (-144))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-1155)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-757)) (|devaluate| |#1|)))) (|HasCategory| (-757) (QUOTE (-1091))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasSignature| |#1| (LIST (QUOTE -3110) (LIST (|devaluate| |#1|) (QUOTE (-1155)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-757))))) (|HasCategory| |#1| (QUOTE (-357))) (-3988 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-941))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -401) (QUOTE (-553))))) (|HasSignature| |#1| (LIST (QUOTE -3406) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1155))))) (|HasSignature| |#1| (LIST (QUOTE -3506) (LIST (LIST (QUOTE -630) (QUOTE (-1155))) (|devaluate| |#1|))))))) (-1231 |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 -(-1232 -3219 UP L UTS) +(-1232 -3105 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-545)))) (-1233) ((|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."))) -((-4284 . T)) +NIL NIL (-1234 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4874,7 +4874,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-984))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-712))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1236 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4370 . T) (-4369 . T) (-4284 . T)) +((-4370 . T) (-4369 . T)) NIL (-1237 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4883,7 +4883,7 @@ NIL (-1238 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4370 . T) (-4369 . T)) -((-4028 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-4028 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-4028 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) +((-3988 (-12 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-3988 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845))))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-529)))) (-3988 (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-553) (QUOTE (-833))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-712))) (|HasCategory| |#1| (QUOTE (-1031))) (-12 (|HasCategory| |#1| (QUOTE (-984))) (|HasCategory| |#1| (QUOTE (-1031)))) (|HasCategory| |#1| (LIST (QUOTE -600) (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))))) (-1239) ((|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 @@ -4901,7 +4901,7 @@ NIL NIL NIL (-1243) -((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) +((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL (-1244 A S) @@ -4916,7 +4916,7 @@ 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 -(-1247 K R UP -3219) +(-1247 K R UP -3105) ((|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 @@ -4929,7 +4929,7 @@ NIL NIL NIL (-1250 R |VarSet| E P |vl| |wl| |wtlevel|) -((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) +((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) ((-4364 |has| |#1| (-169)) (-4363 |has| |#1| (-169)) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357)))) (-1251 R E V P) @@ -4937,7 +4937,7 @@ NIL ((-4370 . T) (-4369 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1079))) (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-529)))) (|HasCategory| |#4| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -600) (QUOTE (-845))))) (-1252 R) -((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) +((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) ((-4363 . T) (-4364 . T) (-4366 . T)) NIL (-1253 |vl| R) @@ -4952,11 +4952,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4362 |has| |#2| (-6 -4362)) (-4364 . T) (-4363 . T) (-4366 . T)) NIL -(-1256 S -3219) +(-1256 S -3105) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-142))) (|HasCategory| |#2| (QUOTE (-144)))) -(-1257 -3219) +(-1257 -3105) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4361 . T) (-4367 . T) (-4362 . T) ((-4371 "*") . T) (-4363 . T) (-4364 . T) (-4366 . T)) NIL @@ -4973,7 +4973,7 @@ NIL ((-4362 |has| |#1| (-6 -4362)) (-4364 . T) (-4363 . T) (-4366 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasAttribute| |#1| (QUOTE -4362))) (-1261 R E) -((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) +((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) ((-4366 . T) (-4367 |has| |#1| (-6 -4367)) (-4362 |has| |#1| (-6 -4362)) (-4364 . T) (-4363 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-357))) (|HasAttribute| |#1| (QUOTE -4366)) (|HasAttribute| |#1| (QUOTE -4367)) (|HasAttribute| |#1| (QUOTE -4362))) (-1262 |VarSet| R) @@ -5012,4 +5012,4 @@ NIL NIL NIL NIL -((-3 NIL 2272486 2272491 2272496 2272501) (-2 NIL 2272466 2272471 2272476 2272481) (-1 NIL 2272446 2272451 2272456 2272461) (0 NIL 2272426 2272431 2272436 2272441) (-1266 "ZMOD.spad" 2272235 2272248 2272364 2272421) (-1265 "ZLINDEP.spad" 2271279 2271290 2272225 2272230) (-1264 "ZDSOLVE.spad" 2261128 2261150 2271269 2271274) (-1263 "YSTREAM.spad" 2260621 2260632 2261118 2261123) (-1262 "XRPOLY.spad" 2259841 2259861 2260477 2260546) (-1261 "XPR.spad" 2257570 2257583 2259559 2259658) (-1260 "XPOLY.spad" 2257125 2257136 2257426 2257495) (-1259 "XPOLYC.spad" 2256442 2256458 2257051 2257120) (-1258 "XPBWPOLY.spad" 2254879 2254899 2256222 2256291) (-1257 "XF.spad" 2253340 2253355 2254781 2254874) (-1256 "XF.spad" 2251781 2251798 2253224 2253229) (-1255 "XFALG.spad" 2248805 2248821 2251707 2251776) (-1254 "XEXPPKG.spad" 2248056 2248082 2248795 2248800) (-1253 "XDPOLY.spad" 2247670 2247686 2247912 2247981) (-1252 "XALG.spad" 2247268 2247279 2247626 2247665) (-1251 "WUTSET.spad" 2243107 2243124 2246914 2246941) (-1250 "WP.spad" 2242121 2242165 2242965 2243032) (-1249 "WHILEAST.spad" 2241919 2241928 2242111 2242116) (-1248 "WHEREAST.spad" 2241590 2241599 2241909 2241914) (-1247 "WFFINTBS.spad" 2239153 2239175 2241580 2241585) (-1246 "WEIER.spad" 2237367 2237378 2239143 2239148) (-1245 "VSPACE.spad" 2237040 2237051 2237335 2237362) (-1244 "VSPACE.spad" 2236733 2236746 2237030 2237035) (-1243 "VOID.spad" 2236323 2236332 2236723 2236728) (-1242 "VIEW.spad" 2233945 2233954 2236313 2236318) (-1241 "VIEWDEF.spad" 2229142 2229151 2233935 2233940) (-1240 "VIEW3D.spad" 2212977 2212986 2229132 2229137) (-1239 "VIEW2D.spad" 2200714 2200723 2212967 2212972) (-1238 "VECTOR.spad" 2199389 2199400 2199640 2199667) (-1237 "VECTOR2.spad" 2198016 2198029 2199379 2199384) (-1236 "VECTCAT.spad" 2195904 2195915 2197972 2198011) (-1235 "VECTCAT.spad" 2193612 2193625 2195682 2195687) (-1234 "VARIABLE.spad" 2193392 2193407 2193602 2193607) (-1233 "UTYPE.spad" 2193026 2193035 2193372 2193387) (-1232 "UTSODETL.spad" 2192319 2192343 2192982 2192987) (-1231 "UTSODE.spad" 2190507 2190527 2192309 2192314) (-1230 "UTS.spad" 2185296 2185324 2188974 2189071) (-1229 "UTSCAT.spad" 2182747 2182763 2185194 2185291) (-1228 "UTSCAT.spad" 2179842 2179860 2182291 2182296) (-1227 "UTS2.spad" 2179435 2179470 2179832 2179837) (-1226 "URAGG.spad" 2174057 2174068 2179415 2179430) (-1225 "URAGG.spad" 2168653 2168666 2174013 2174018) (-1224 "UPXSSING.spad" 2166296 2166322 2167734 2167867) (-1223 "UPXS.spad" 2163323 2163351 2164428 2164577) (-1222 "UPXSCONS.spad" 2161080 2161100 2161455 2161604) (-1221 "UPXSCCA.spad" 2159538 2159558 2160926 2161075) (-1220 "UPXSCCA.spad" 2158138 2158160 2159528 2159533) (-1219 "UPXSCAT.spad" 2156719 2156735 2157984 2158133) (-1218 "UPXS2.spad" 2156260 2156313 2156709 2156714) (-1217 "UPSQFREE.spad" 2154672 2154686 2156250 2156255) (-1216 "UPSCAT.spad" 2152265 2152289 2154570 2154667) (-1215 "UPSCAT.spad" 2149564 2149590 2151871 2151876) (-1214 "UPOLYC.spad" 2144542 2144553 2149406 2149559) (-1213 "UPOLYC.spad" 2139412 2139425 2144278 2144283) (-1212 "UPOLYC2.spad" 2138881 2138900 2139402 2139407) (-1211 "UP.spad" 2135923 2135938 2136431 2136584) (-1210 "UPMP.spad" 2134813 2134826 2135913 2135918) (-1209 "UPDIVP.spad" 2134376 2134390 2134803 2134808) (-1208 "UPDECOMP.spad" 2132613 2132627 2134366 2134371) (-1207 "UPCDEN.spad" 2131820 2131836 2132603 2132608) (-1206 "UP2.spad" 2131182 2131203 2131810 2131815) (-1205 "UNISEG.spad" 2130535 2130546 2131101 2131106) (-1204 "UNISEG2.spad" 2130028 2130041 2130491 2130496) (-1203 "UNIFACT.spad" 2129129 2129141 2130018 2130023) (-1202 "ULS.spad" 2119681 2119709 2120774 2121203) (-1201 "ULSCONS.spad" 2113718 2113738 2114090 2114239) (-1200 "ULSCCAT.spad" 2111315 2111335 2113538 2113713) (-1199 "ULSCCAT.spad" 2109046 2109068 2111271 2111276) (-1198 "ULSCAT.spad" 2107262 2107278 2108892 2109041) (-1197 "ULS2.spad" 2106774 2106827 2107252 2107257) (-1196 "UFD.spad" 2105839 2105848 2106700 2106769) (-1195 "UFD.spad" 2104966 2104977 2105829 2105834) (-1194 "UDVO.spad" 2103813 2103822 2104956 2104961) (-1193 "UDPO.spad" 2101240 2101251 2103769 2103774) (-1192 "TYPE.spad" 2101162 2101171 2101220 2101235) (-1191 "TYPEAST.spad" 2101081 2101090 2101152 2101157) (-1190 "TWOFACT.spad" 2099731 2099746 2101071 2101076) (-1189 "TUPLE.spad" 2099117 2099128 2099630 2099635) (-1188 "TUBETOOL.spad" 2095954 2095963 2099107 2099112) (-1187 "TUBE.spad" 2094595 2094612 2095944 2095949) (-1186 "TS.spad" 2093184 2093200 2094160 2094257) (-1185 "TSETCAT.spad" 2080299 2080316 2093140 2093179) (-1184 "TSETCAT.spad" 2067412 2067431 2080255 2080260) (-1183 "TRMANIP.spad" 2061778 2061795 2067118 2067123) (-1182 "TRIMAT.spad" 2060737 2060762 2061768 2061773) (-1181 "TRIGMNIP.spad" 2059254 2059271 2060727 2060732) (-1180 "TRIGCAT.spad" 2058766 2058775 2059244 2059249) (-1179 "TRIGCAT.spad" 2058276 2058287 2058756 2058761) (-1178 "TREE.spad" 2056847 2056858 2057883 2057910) (-1177 "TRANFUN.spad" 2056678 2056687 2056837 2056842) (-1176 "TRANFUN.spad" 2056507 2056518 2056668 2056673) (-1175 "TOPSP.spad" 2056181 2056190 2056497 2056502) (-1174 "TOOLSIGN.spad" 2055844 2055855 2056171 2056176) (-1173 "TEXTFILE.spad" 2054401 2054410 2055834 2055839) (-1172 "TEX.spad" 2051418 2051427 2054391 2054396) (-1171 "TEX1.spad" 2050974 2050985 2051408 2051413) (-1170 "TEMUTL.spad" 2050529 2050538 2050964 2050969) (-1169 "TBCMPPK.spad" 2048622 2048645 2050519 2050524) (-1168 "TBAGG.spad" 2047646 2047669 2048590 2048617) (-1167 "TBAGG.spad" 2046690 2046715 2047636 2047641) (-1166 "TANEXP.spad" 2046066 2046077 2046680 2046685) (-1165 "TABLE.spad" 2044477 2044500 2044747 2044774) (-1164 "TABLEAU.spad" 2043958 2043969 2044467 2044472) (-1163 "TABLBUMP.spad" 2040741 2040752 2043948 2043953) (-1162 "SYSTEM.spad" 2040015 2040024 2040731 2040736) (-1161 "SYSSOLP.spad" 2037488 2037499 2040005 2040010) (-1160 "SYNTAX.spad" 2033758 2033767 2037478 2037483) (-1159 "SYMTAB.spad" 2031814 2031823 2033748 2033753) (-1158 "SYMS.spad" 2027799 2027808 2031804 2031809) (-1157 "SYMPOLY.spad" 2026806 2026817 2026888 2027015) (-1156 "SYMFUNC.spad" 2026281 2026292 2026796 2026801) (-1155 "SYMBOL.spad" 2023617 2023626 2026271 2026276) (-1154 "SWITCH.spad" 2020374 2020383 2023607 2023612) (-1153 "SUTS.spad" 2017273 2017301 2018841 2018938) (-1152 "SUPXS.spad" 2014287 2014315 2015405 2015554) (-1151 "SUP.spad" 2011056 2011067 2011837 2011990) (-1150 "SUPFRACF.spad" 2010161 2010179 2011046 2011051) (-1149 "SUP2.spad" 2009551 2009564 2010151 2010156) (-1148 "SUMRF.spad" 2008517 2008528 2009541 2009546) (-1147 "SUMFS.spad" 2008150 2008167 2008507 2008512) (-1146 "SULS.spad" 1998689 1998717 1999795 2000224) (-1145 "SUCHTAST.spad" 1998458 1998467 1998679 1998684) (-1144 "SUCH.spad" 1998138 1998153 1998448 1998453) (-1143 "SUBSPACE.spad" 1990145 1990160 1998128 1998133) (-1142 "SUBRESP.spad" 1989305 1989319 1990101 1990106) (-1141 "STTF.spad" 1985404 1985420 1989295 1989300) (-1140 "STTFNC.spad" 1981872 1981888 1985394 1985399) (-1139 "STTAYLOR.spad" 1974270 1974281 1981753 1981758) (-1138 "STRTBL.spad" 1972775 1972792 1972924 1972951) (-1137 "STRING.spad" 1972184 1972193 1972198 1972225) (-1136 "STRICAT.spad" 1971960 1971969 1972140 1972179) (-1135 "STREAM.spad" 1968728 1968739 1971485 1971500) (-1134 "STREAM3.spad" 1968273 1968288 1968718 1968723) (-1133 "STREAM2.spad" 1967341 1967354 1968263 1968268) (-1132 "STREAM1.spad" 1967045 1967056 1967331 1967336) (-1131 "STINPROD.spad" 1965951 1965967 1967035 1967040) (-1130 "STEP.spad" 1965152 1965161 1965941 1965946) (-1129 "STBL.spad" 1963678 1963706 1963845 1963860) (-1128 "STAGG.spad" 1962743 1962754 1963658 1963673) (-1127 "STAGG.spad" 1961816 1961829 1962733 1962738) (-1126 "STACK.spad" 1961167 1961178 1961423 1961450) (-1125 "SREGSET.spad" 1958871 1958888 1960813 1960840) (-1124 "SRDCMPK.spad" 1957416 1957436 1958861 1958866) (-1123 "SRAGG.spad" 1952501 1952510 1957372 1957411) (-1122 "SRAGG.spad" 1947618 1947629 1952491 1952496) (-1121 "SQMATRIX.spad" 1945234 1945252 1946150 1946237) (-1120 "SPLTREE.spad" 1939786 1939799 1944670 1944697) (-1119 "SPLNODE.spad" 1936374 1936387 1939776 1939781) (-1118 "SPFCAT.spad" 1935151 1935160 1936364 1936369) (-1117 "SPECOUT.spad" 1933701 1933710 1935141 1935146) (-1116 "SPADXPT.spad" 1925830 1925839 1933681 1933696) (-1115 "spad-parser.spad" 1925295 1925304 1925820 1925825) (-1114 "SPADAST.spad" 1924996 1925005 1925285 1925290) (-1113 "SPACEC.spad" 1909009 1909020 1924986 1924991) (-1112 "SPACE3.spad" 1908785 1908796 1908999 1909004) (-1111 "SORTPAK.spad" 1908330 1908343 1908741 1908746) (-1110 "SOLVETRA.spad" 1906087 1906098 1908320 1908325) (-1109 "SOLVESER.spad" 1904607 1904618 1906077 1906082) (-1108 "SOLVERAD.spad" 1900617 1900628 1904597 1904602) (-1107 "SOLVEFOR.spad" 1899037 1899055 1900607 1900612) (-1106 "SNTSCAT.spad" 1898625 1898642 1898993 1899032) (-1105 "SMTS.spad" 1896885 1896911 1898190 1898287) (-1104 "SMP.spad" 1894324 1894344 1894714 1894841) (-1103 "SMITH.spad" 1893167 1893192 1894314 1894319) (-1102 "SMATCAT.spad" 1891265 1891295 1893099 1893162) (-1101 "SMATCAT.spad" 1889307 1889339 1891143 1891148) (-1100 "SKAGG.spad" 1888256 1888267 1889263 1889302) (-1099 "SINT.spad" 1886564 1886573 1888122 1888251) (-1098 "SIMPAN.spad" 1886292 1886301 1886554 1886559) (-1097 "SIG.spad" 1885620 1885629 1886282 1886287) (-1096 "SIGNRF.spad" 1884728 1884739 1885610 1885615) (-1095 "SIGNEF.spad" 1883997 1884014 1884718 1884723) (-1094 "SIGAST.spad" 1883378 1883387 1883987 1883992) (-1093 "SHP.spad" 1881296 1881311 1883334 1883339) (-1092 "SHDP.spad" 1872281 1872308 1872790 1872921) (-1091 "SGROUP.spad" 1871889 1871898 1872271 1872276) (-1090 "SGROUP.spad" 1871495 1871506 1871879 1871884) (-1089 "SGCF.spad" 1864376 1864385 1871485 1871490) (-1088 "SFRTCAT.spad" 1863292 1863309 1864332 1864371) (-1087 "SFRGCD.spad" 1862355 1862375 1863282 1863287) (-1086 "SFQCMPK.spad" 1856992 1857012 1862345 1862350) (-1085 "SFORT.spad" 1856427 1856441 1856982 1856987) (-1084 "SEXOF.spad" 1856270 1856310 1856417 1856422) (-1083 "SEX.spad" 1856162 1856171 1856260 1856265) (-1082 "SEXCAT.spad" 1853266 1853306 1856152 1856157) (-1081 "SET.spad" 1851566 1851577 1852687 1852726) (-1080 "SETMN.spad" 1850000 1850017 1851556 1851561) (-1079 "SETCAT.spad" 1849485 1849494 1849990 1849995) (-1078 "SETCAT.spad" 1848968 1848979 1849475 1849480) (-1077 "SETAGG.spad" 1845477 1845488 1848936 1848963) (-1076 "SETAGG.spad" 1842006 1842019 1845467 1845472) (-1075 "SEQAST.spad" 1841709 1841718 1841996 1842001) (-1074 "SEGXCAT.spad" 1840821 1840834 1841689 1841704) (-1073 "SEG.spad" 1840634 1840645 1840740 1840745) (-1072 "SEGCAT.spad" 1839453 1839464 1840614 1840629) (-1071 "SEGBIND.spad" 1838525 1838536 1839408 1839413) (-1070 "SEGBIND2.spad" 1838221 1838234 1838515 1838520) (-1069 "SEGAST.spad" 1837935 1837944 1838211 1838216) (-1068 "SEG2.spad" 1837360 1837373 1837891 1837896) (-1067 "SDVAR.spad" 1836636 1836647 1837350 1837355) (-1066 "SDPOL.spad" 1834026 1834037 1834317 1834444) (-1065 "SCPKG.spad" 1832105 1832116 1834016 1834021) (-1064 "SCOPE.spad" 1831250 1831259 1832095 1832100) (-1063 "SCACHE.spad" 1829932 1829943 1831240 1831245) (-1062 "SASTCAT.spad" 1829841 1829850 1829922 1829927) (-1061 "SAOS.spad" 1829713 1829722 1829831 1829836) (-1060 "SAERFFC.spad" 1829426 1829446 1829703 1829708) (-1059 "SAE.spad" 1827601 1827617 1828212 1828347) (-1058 "SAEFACT.spad" 1827302 1827322 1827591 1827596) (-1057 "RURPK.spad" 1824943 1824959 1827292 1827297) (-1056 "RULESET.spad" 1824384 1824408 1824933 1824938) (-1055 "RULE.spad" 1822588 1822612 1824374 1824379) (-1054 "RULECOLD.spad" 1822440 1822453 1822578 1822583) (-1053 "RSTRCAST.spad" 1822157 1822166 1822430 1822435) (-1052 "RSETGCD.spad" 1818535 1818555 1822147 1822152) (-1051 "RSETCAT.spad" 1808307 1808324 1818491 1818530) (-1050 "RSETCAT.spad" 1798111 1798130 1808297 1808302) (-1049 "RSDCMPK.spad" 1796563 1796583 1798101 1798106) (-1048 "RRCC.spad" 1794947 1794977 1796553 1796558) (-1047 "RRCC.spad" 1793329 1793361 1794937 1794942) (-1046 "RPTAST.spad" 1793031 1793040 1793319 1793324) (-1045 "RPOLCAT.spad" 1772391 1772406 1792899 1793026) (-1044 "RPOLCAT.spad" 1751465 1751482 1771975 1771980) (-1043 "ROUTINE.spad" 1747328 1747337 1750112 1750139) (-1042 "ROMAN.spad" 1746560 1746569 1747194 1747323) (-1041 "ROIRC.spad" 1745640 1745672 1746550 1746555) (-1040 "RNS.spad" 1744543 1744552 1745542 1745635) (-1039 "RNS.spad" 1743532 1743543 1744533 1744538) (-1038 "RNG.spad" 1743267 1743276 1743522 1743527) (-1037 "RMODULE.spad" 1742905 1742916 1743257 1743262) (-1036 "RMCAT2.spad" 1742313 1742370 1742895 1742900) (-1035 "RMATRIX.spad" 1740992 1741011 1741480 1741519) (-1034 "RMATCAT.spad" 1736513 1736544 1740936 1740987) (-1033 "RMATCAT.spad" 1731936 1731969 1736361 1736366) (-1032 "RINTERP.spad" 1731824 1731844 1731926 1731931) (-1031 "RING.spad" 1731181 1731190 1731804 1731819) (-1030 "RING.spad" 1730546 1730557 1731171 1731176) (-1029 "RIDIST.spad" 1729930 1729939 1730536 1730541) (-1028 "RGCHAIN.spad" 1728509 1728525 1729415 1729442) (-1027 "RGBCSPC.spad" 1728290 1728302 1728499 1728504) (-1026 "RGBCMDL.spad" 1727820 1727832 1728280 1728285) (-1025 "RF.spad" 1725434 1725445 1727810 1727815) (-1024 "RFFACTOR.spad" 1724896 1724907 1725424 1725429) (-1023 "RFFACT.spad" 1724631 1724643 1724886 1724891) (-1022 "RFDIST.spad" 1723619 1723628 1724621 1724626) (-1021 "RETSOL.spad" 1723036 1723049 1723609 1723614) (-1020 "RETRACT.spad" 1722464 1722475 1723026 1723031) (-1019 "RETRACT.spad" 1721890 1721903 1722454 1722459) (-1018 "RETAST.spad" 1721702 1721711 1721880 1721885) (-1017 "RESULT.spad" 1719762 1719771 1720349 1720376) (-1016 "RESRING.spad" 1719109 1719156 1719700 1719757) (-1015 "RESLATC.spad" 1718433 1718444 1719099 1719104) (-1014 "REPSQ.spad" 1718162 1718173 1718423 1718428) (-1013 "REP.spad" 1715714 1715723 1718152 1718157) (-1012 "REPDB.spad" 1715419 1715430 1715704 1715709) (-1011 "REP2.spad" 1704991 1705002 1715261 1715266) (-1010 "REP1.spad" 1698981 1698992 1704941 1704946) (-1009 "REGSET.spad" 1696778 1696795 1698627 1698654) (-1008 "REF.spad" 1696107 1696118 1696733 1696738) (-1007 "REDORDER.spad" 1695283 1695300 1696097 1696102) (-1006 "RECLOS.spad" 1694066 1694086 1694770 1694863) (-1005 "REALSOLV.spad" 1693198 1693207 1694056 1694061) (-1004 "REAL.spad" 1693070 1693079 1693188 1693193) (-1003 "REAL0Q.spad" 1690352 1690367 1693060 1693065) (-1002 "REAL0.spad" 1687180 1687195 1690342 1690347) (-1001 "RDUCEAST.spad" 1686901 1686910 1687170 1687175) (-1000 "RDIV.spad" 1686552 1686577 1686891 1686896) (-999 "RDIST.spad" 1686116 1686126 1686542 1686547) (-998 "RDETRS.spad" 1684913 1684930 1686106 1686111) (-997 "RDETR.spad" 1683021 1683038 1684903 1684908) (-996 "RDEEFS.spad" 1682095 1682111 1683011 1683016) (-995 "RDEEF.spad" 1681092 1681108 1682085 1682090) (-994 "RCFIELD.spad" 1678279 1678287 1680994 1681087) (-993 "RCFIELD.spad" 1675552 1675562 1678269 1678274) (-992 "RCAGG.spad" 1673455 1673465 1675532 1675547) (-991 "RCAGG.spad" 1671295 1671307 1673374 1673379) (-990 "RATRET.spad" 1670656 1670666 1671285 1671290) (-989 "RATFACT.spad" 1670349 1670360 1670646 1670651) (-988 "RANDSRC.spad" 1669669 1669677 1670339 1670344) (-987 "RADUTIL.spad" 1669424 1669432 1669659 1669664) (-986 "RADIX.spad" 1666214 1666227 1667891 1667984) (-985 "RADFF.spad" 1664628 1664664 1664746 1664902) (-984 "RADCAT.spad" 1664222 1664230 1664618 1664623) (-983 "RADCAT.spad" 1663814 1663824 1664212 1664217) (-982 "QUEUE.spad" 1663157 1663167 1663421 1663448) (-981 "QUAT.spad" 1661739 1661749 1662081 1662146) (-980 "QUATCT2.spad" 1661358 1661376 1661729 1661734) (-979 "QUATCAT.spad" 1659523 1659533 1661288 1661353) (-978 "QUATCAT.spad" 1657439 1657451 1659206 1659211) (-977 "QUAGG.spad" 1656253 1656263 1657395 1657434) (-976 "QQUTAST.spad" 1656022 1656030 1656243 1656248) (-975 "QFORM.spad" 1655485 1655499 1656012 1656017) (-974 "QFCAT.spad" 1654176 1654186 1655375 1655480) (-973 "QFCAT.spad" 1652470 1652482 1653671 1653676) (-972 "QFCAT2.spad" 1652161 1652177 1652460 1652465) (-971 "QEQUAT.spad" 1651718 1651726 1652151 1652156) (-970 "QCMPACK.spad" 1646465 1646484 1651708 1651713) (-969 "QALGSET.spad" 1642540 1642572 1646379 1646384) (-968 "QALGSET2.spad" 1640536 1640554 1642530 1642535) (-967 "PWFFINTB.spad" 1637846 1637867 1640526 1640531) (-966 "PUSHVAR.spad" 1637175 1637194 1637836 1637841) (-965 "PTRANFN.spad" 1633301 1633311 1637165 1637170) (-964 "PTPACK.spad" 1630389 1630399 1633291 1633296) (-963 "PTFUNC2.spad" 1630210 1630224 1630379 1630384) (-962 "PTCAT.spad" 1629292 1629302 1630166 1630205) (-961 "PSQFR.spad" 1628599 1628623 1629282 1629287) (-960 "PSEUDLIN.spad" 1627457 1627467 1628589 1628594) (-959 "PSETPK.spad" 1612890 1612906 1627335 1627340) (-958 "PSETCAT.spad" 1606798 1606821 1612858 1612885) (-957 "PSETCAT.spad" 1600692 1600717 1606754 1606759) (-956 "PSCURVE.spad" 1599675 1599683 1600682 1600687) (-955 "PSCAT.spad" 1598442 1598471 1599573 1599670) (-954 "PSCAT.spad" 1597299 1597330 1598432 1598437) (-953 "PRTITION.spad" 1596142 1596150 1597289 1597294) (-952 "PRTDAST.spad" 1595861 1595869 1596132 1596137) (-951 "PRS.spad" 1585423 1585440 1595817 1595822) (-950 "PRQAGG.spad" 1584842 1584852 1585379 1585418) (-949 "PROPLOG.spad" 1584245 1584253 1584832 1584837) (-948 "PROPFRML.spad" 1582163 1582174 1584235 1584240) (-947 "PROPERTY.spad" 1581657 1581665 1582153 1582158) (-946 "PRODUCT.spad" 1579337 1579349 1579623 1579678) (-945 "PR.spad" 1577723 1577735 1578428 1578555) (-944 "PRINT.spad" 1577475 1577483 1577713 1577718) (-943 "PRIMES.spad" 1575726 1575736 1577465 1577470) (-942 "PRIMELT.spad" 1573707 1573721 1575716 1575721) (-941 "PRIMCAT.spad" 1573330 1573338 1573697 1573702) (-940 "PRIMARR.spad" 1572335 1572345 1572513 1572540) (-939 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"LODO1.spad" 1031414 1031424 1031694 1031733) (-637 "LODEEF.spad" 1030186 1030204 1031404 1031409) (-636 "LNAGG.spad" 1025978 1025988 1030166 1030181) (-635 "LNAGG.spad" 1021744 1021756 1025934 1025939) (-634 "LMOPS.spad" 1018480 1018497 1021734 1021739) (-633 "LMODULE.spad" 1018122 1018132 1018470 1018475) (-632 "LMDICT.spad" 1017405 1017415 1017673 1017700) (-631 "LITERAL.spad" 1017311 1017322 1017395 1017400) (-630 "LIST.spad" 1015029 1015039 1016458 1016485) (-629 "LIST3.spad" 1014320 1014334 1015019 1015024) (-628 "LIST2.spad" 1012960 1012972 1014310 1014315) (-627 "LIST2MAP.spad" 1009837 1009849 1012950 1012955) (-626 "LINEXP.spad" 1009269 1009279 1009817 1009832) (-625 "LINDEP.spad" 1008046 1008058 1009181 1009186) (-624 "LIMITRF.spad" 1005960 1005970 1008036 1008041) (-623 "LIMITPS.spad" 1004843 1004856 1005950 1005955) (-622 "LIE.spad" 1002857 1002869 1004133 1004278) (-621 "LIECAT.spad" 1002333 1002343 1002783 1002852) (-620 "LIECAT.spad" 1001837 1001849 1002289 1002294) (-619 "LIB.spad" 999885 999893 1000496 1000511) (-618 "LGROBP.spad" 997238 997257 999875 999880) (-617 "LF.spad" 996157 996173 997228 997233) (-616 "LFCAT.spad" 995176 995184 996147 996152) (-615 "LEXTRIPK.spad" 990679 990694 995166 995171) (-614 "LEXP.spad" 988682 988709 990659 990674) (-613 "LETAST.spad" 988381 988389 988672 988677) (-612 "LEADCDET.spad" 986765 986782 988371 988376) (-611 "LAZM3PK.spad" 985469 985491 986755 986760) (-610 "LAUPOL.spad" 984158 984171 985062 985131) (-609 "LAPLACE.spad" 983731 983747 984148 984153) (-608 "LA.spad" 983171 983185 983653 983692) (-607 "LALG.spad" 982947 982957 983151 983166) (-606 "LALG.spad" 982731 982743 982937 982942) (-605 "KVTFROM.spad" 982340 982350 982721 982726) (-604 "KTVLOGIC.spad" 981763 981771 982330 982335) (-603 "KRCFROM.spad" 981379 981389 981753 981758) (-602 "KOVACIC.spad" 980092 980109 981369 981374) (-601 "KONVERT.spad" 979814 979824 980082 980087) (-600 "KOERCE.spad" 979551 979561 979804 979809) (-599 "KERNEL.spad" 978086 978096 979335 979340) (-598 "KERNEL2.spad" 977789 977801 978076 978081) (-597 "KDAGG.spad" 976880 976902 977757 977784) (-596 "KDAGG.spad" 975991 976015 976870 976875) (-595 "KAFILE.spad" 974954 974970 975189 975216) (-594 "JORDAN.spad" 972781 972793 974244 974389) (-593 "JOINAST.spad" 972475 972483 972771 972776) (-592 "JAVACODE.spad" 972241 972249 972465 972470) (-591 "IXAGG.spad" 970354 970378 972221 972236) (-590 "IXAGG.spad" 968332 968358 970201 970206) (-589 "IVECTOR.spad" 967103 967118 967258 967285) (-588 "ITUPLE.spad" 966248 966258 967093 967098) (-587 "ITRIGMNP.spad" 965059 965078 966238 966243) (-586 "ITFUN3.spad" 964553 964567 965049 965054) (-585 "ITFUN2.spad" 964283 964295 964543 964548) (-584 "ITAYLOR.spad" 962075 962090 964119 964244) (-583 "ISUPS.spad" 954486 954501 961049 961146) (-582 "ISUMP.spad" 953983 953999 954476 954481) (-581 "ISTRING.spad" 952986 952999 953152 953179) (-580 "ISAST.spad" 952705 952713 952976 952981) (-579 "IRURPK.spad" 951418 951437 952695 952700) (-578 "IRSN.spad" 949378 949386 951408 951413) (-577 "IRRF2F.spad" 947853 947863 949334 949339) (-576 "IRREDFFX.spad" 947454 947465 947843 947848) (-575 "IROOT.spad" 945785 945795 947444 947449) (-574 "IR.spad" 943574 943588 945640 945667) (-573 "IR2.spad" 942594 942610 943564 943569) (-572 "IR2F.spad" 941794 941810 942584 942589) (-571 "IPRNTPK.spad" 941554 941562 941784 941789) (-570 "IPF.spad" 941119 941131 941359 941452) (-569 "IPADIC.spad" 940880 940906 941045 941114) (-568 "IP4ADDR.spad" 940428 940436 940870 940875) (-567 "IOMODE.spad" 940049 940057 940418 940423) (-566 "IOBFILE.spad" 939410 939418 940039 940044) (-565 "IOBCON.spad" 939275 939283 939400 939405) (-564 "INVLAPLA.spad" 938920 938936 939265 939270) (-563 "INTTR.spad" 932166 932183 938910 938915) (-562 "INTTOOLS.spad" 929877 929893 931740 931745) (-561 "INTSLPE.spad" 929183 929191 929867 929872) (-560 "INTRVL.spad" 928749 928759 929097 929178) (-559 "INTRF.spad" 927113 927127 928739 928744) (-558 "INTRET.spad" 926545 926555 927103 927108) (-557 "INTRAT.spad" 925220 925237 926535 926540) (-556 "INTPM.spad" 923583 923599 924863 924868) (-555 "INTPAF.spad" 921351 921369 923515 923520) (-554 "INTPACK.spad" 911661 911669 921341 921346) (-553 "INT.spad" 911022 911030 911515 911656) (-552 "INTHERTR.spad" 910288 910305 911012 911017) (-551 "INTHERAL.spad" 909954 909978 910278 910283) (-550 "INTHEORY.spad" 906367 906375 909944 909949) (-549 "INTG0.spad" 899830 899848 906299 906304) (-548 "INTFTBL.spad" 893859 893867 899820 899825) (-547 "INTFACT.spad" 892918 892928 893849 893854) (-546 "INTEF.spad" 891233 891249 892908 892913) (-545 "INTDOM.spad" 889848 889856 891159 891228) (-544 "INTDOM.spad" 888525 888535 889838 889843) (-543 "INTCAT.spad" 886778 886788 888439 888520) (-542 "INTBIT.spad" 886281 886289 886768 886773) (-541 "INTALG.spad" 885463 885490 886271 886276) (-540 "INTAF.spad" 884955 884971 885453 885458) (-539 "INTABL.spad" 883473 883504 883636 883663) (-538 "INS.spad" 880940 880948 883375 883468) (-537 "INS.spad" 878493 878503 880930 880935) (-536 "INPSIGN.spad" 877927 877940 878483 878488) (-535 "INPRODPF.spad" 876993 877012 877917 877922) (-534 "INPRODFF.spad" 876051 876075 876983 876988) (-533 "INNMFACT.spad" 875022 875039 876041 876046) (-532 "INMODGCD.spad" 874506 874536 875012 875017) (-531 "INFSP.spad" 872791 872813 874496 874501) (-530 "INFPROD0.spad" 871841 871860 872781 872786) (-529 "INFORM.spad" 869002 869010 871831 871836) (-528 "INFORM1.spad" 868627 868637 868992 868997) (-527 "INFINITY.spad" 868179 868187 868617 868622) (-526 "INETCLTS.spad" 868156 868164 868169 868174) (-525 "INEP.spad" 866688 866710 868146 868151) (-524 "INDE.spad" 866417 866434 866678 866683) (-523 "INCRMAPS.spad" 865838 865848 866407 866412) (-522 "INBFILE.spad" 864910 864918 865828 865833) (-521 "INBFF.spad" 860680 860691 864900 864905) (-520 "INBCON.spad" 859979 859987 860670 860675) (-519 "INBCON.spad" 859276 859286 859969 859974) (-518 "INAST.spad" 858941 858949 859266 859271) (-517 "IMPTAST.spad" 858649 858657 858931 858936) (-516 "IMATRIX.spad" 857594 857620 858106 858133) (-515 "IMATQF.spad" 856688 856732 857550 857555) (-514 "IMATLIN.spad" 855293 855317 856644 856649) (-513 "ILIST.spad" 853949 853964 854476 854503) (-512 "IIARRAY2.spad" 853337 853375 853556 853583) (-511 "IFF.spad" 852747 852763 853018 853111) (-510 "IFAST.spad" 852361 852369 852737 852742) (-509 "IFARRAY.spad" 849848 849863 851544 851571) (-508 "IFAMON.spad" 849710 849727 849804 849809) (-507 "IEVALAB.spad" 849099 849111 849700 849705) (-506 "IEVALAB.spad" 848486 848500 849089 849094) (-505 "IDPO.spad" 848284 848296 848476 848481) (-504 "IDPOAMS.spad" 848040 848052 848274 848279) (-503 "IDPOAM.spad" 847760 847772 848030 848035) (-502 "IDPC.spad" 846694 846706 847750 847755) (-501 "IDPAM.spad" 846439 846451 846684 846689) (-500 "IDPAG.spad" 846186 846198 846429 846434) (-499 "IDENT.spad" 846103 846111 846176 846181) (-498 "IDECOMP.spad" 843340 843358 846093 846098) (-497 "IDEAL.spad" 838263 838302 843275 843280) (-496 "ICDEN.spad" 837414 837430 838253 838258) (-495 "ICARD.spad" 836603 836611 837404 837409) (-494 "IBPTOOLS.spad" 835196 835213 836593 836598) (-493 "IBITS.spad" 834395 834408 834832 834859) (-492 "IBATOOL.spad" 831270 831289 834385 834390) (-491 "IBACHIN.spad" 829757 829772 831260 831265) (-490 "IARRAY2.spad" 828745 828771 829364 829391) (-489 "IARRAY1.spad" 827790 827805 827928 827955) (-488 "IAN.spad" 826003 826011 827606 827699) (-487 "IALGFACT.spad" 825604 825637 825993 825998) (-486 "HYPCAT.spad" 825028 825036 825594 825599) (-485 "HYPCAT.spad" 824450 824460 825018 825023) (-484 "HOSTNAME.spad" 824258 824266 824440 824445) (-483 "HOMOTOP.spad" 824001 824011 824248 824253) (-482 "HOAGG.spad" 821259 821269 823981 823996) (-481 "HOAGG.spad" 818302 818314 821026 821031) (-480 "HEXADEC.spad" 816171 816179 816769 816862) (-479 "HEUGCD.spad" 815186 815197 816161 816166) (-478 "HELLFDIV.spad" 814776 814800 815176 815181) (-477 "HEAP.spad" 814168 814178 814383 814410) (-476 "HEADAST.spad" 813699 813707 814158 814163) (-475 "HDP.spad" 804816 804832 805193 805324) (-474 "HDMP.spad" 801992 802007 802610 802737) (-473 "HB.spad" 800229 800237 801982 801987) (-472 "HASHTBL.spad" 798699 798730 798910 798937) (-471 "HASAST.spad" 798415 798423 798689 798694) (-470 "HACKPI.spad" 797898 797906 798317 798410) (-469 "GTSET.spad" 796837 796853 797544 797571) (-468 "GSTBL.spad" 795356 795391 795530 795545) (-467 "GSERIES.spad" 792523 792550 793488 793637) (-466 "GROUP.spad" 791792 791800 792503 792518) (-465 "GROUP.spad" 791069 791079 791782 791787) (-464 "GROEBSOL.spad" 789557 789578 791059 791064) (-463 "GRMOD.spad" 788128 788140 789547 789552) (-462 "GRMOD.spad" 786697 786711 788118 788123) (-461 "GRIMAGE.spad" 779302 779310 786687 786692) (-460 "GRDEF.spad" 777681 777689 779292 779297) (-459 "GRAY.spad" 776140 776148 777671 777676) (-458 "GRALG.spad" 775187 775199 776130 776135) (-457 "GRALG.spad" 774232 774246 775177 775182) (-456 "GPOLSET.spad" 773686 773709 773914 773941) (-455 "GOSPER.spad" 772951 772969 773676 773681) (-454 "GMODPOL.spad" 772089 772116 772919 772946) (-453 "GHENSEL.spad" 771158 771172 772079 772084) (-452 "GENUPS.spad" 767259 767272 771148 771153) (-451 "GENUFACT.spad" 766836 766846 767249 767254) (-450 "GENPGCD.spad" 766420 766437 766826 766831) (-449 "GENMFACT.spad" 765872 765891 766410 766415) (-448 "GENEEZ.spad" 763811 763824 765862 765867) (-447 "GDMP.spad" 760829 760846 761605 761732) (-446 "GCNAALG.spad" 754724 754751 760623 760690) (-445 "GCDDOM.spad" 753896 753904 754650 754719) (-444 "GCDDOM.spad" 753130 753140 753886 753891) (-443 "GB.spad" 750648 750686 753086 753091) (-442 "GBINTERN.spad" 746668 746706 750638 750643) (-441 "GBF.spad" 742425 742463 746658 746663) (-440 "GBEUCLID.spad" 740299 740337 742415 742420) (-439 "GAUSSFAC.spad" 739596 739604 740289 740294) (-438 "GALUTIL.spad" 737918 737928 739552 739557) (-437 "GALPOLYU.spad" 736364 736377 737908 737913) (-436 "GALFACTU.spad" 734529 734548 736354 736359) (-435 "GALFACT.spad" 724662 724673 734519 734524) (-434 "FVFUN.spad" 721675 721683 724642 724657) (-433 "FVC.spad" 720717 720725 721655 721670) (-432 "FUNCTION.spad" 720566 720578 720707 720712) (-431 "FT.spad" 718778 718786 720556 720561) (-430 "FTEM.spad" 717941 717949 718768 718773) (-429 "FSUPFACT.spad" 716841 716860 717877 717882) (-428 "FST.spad" 714927 714935 716831 716836) (-427 "FSRED.spad" 714405 714421 714917 714922) (-426 "FSPRMELT.spad" 713229 713245 714362 714367) (-425 "FSPECF.spad" 711306 711322 713219 713224) (-424 "FS.spad" 705356 705366 711069 711301) (-423 "FS.spad" 699196 699208 704911 704916) (-422 "FSINT.spad" 698854 698870 699186 699191) (-421 "FSERIES.spad" 698041 698053 698674 698773) (-420 "FSCINT.spad" 697354 697370 698031 698036) (-419 "FSAGG.spad" 696459 696469 697298 697349) (-418 "FSAGG.spad" 695538 695550 696379 696384) (-417 "FSAGG2.spad" 694237 694253 695528 695533) (-416 "FS2UPS.spad" 688626 688660 694227 694232) (-415 "FS2.spad" 688271 688287 688616 688621) (-414 "FS2EXPXP.spad" 687394 687417 688261 688266) (-413 "FRUTIL.spad" 686336 686346 687384 687389) (-412 "FR.spad" 680030 680040 685360 685429) (-411 "FRNAALG.spad" 675117 675127 679972 680025) (-410 "FRNAALG.spad" 670216 670228 675073 675078) (-409 "FRNAAF2.spad" 669670 669688 670206 670211) (-408 "FRMOD.spad" 669064 669094 669601 669606) (-407 "FRIDEAL.spad" 668259 668280 669044 669059) (-406 "FRIDEAL2.spad" 667861 667893 668249 668254) (-405 "FRETRCT.spad" 667372 667382 667851 667856) (-404 "FRETRCT.spad" 666749 666761 667230 667235) (-403 "FRAMALG.spad" 665077 665090 666705 666744) (-402 "FRAMALG.spad" 663437 663452 665067 665072) (-401 "FRAC.spad" 660536 660546 660939 661112) (-400 "FRAC2.spad" 660139 660151 660526 660531) (-399 "FR2.spad" 659473 659485 660129 660134) (-398 "FPS.spad" 656282 656290 659363 659468) (-397 "FPS.spad" 653119 653129 656202 656207) (-396 "FPC.spad" 652161 652169 653021 653114) (-395 "FPC.spad" 651289 651299 652151 652156) (-394 "FPATMAB.spad" 651041 651051 651269 651284) (-393 "FPARFRAC.spad" 649514 649531 651031 651036) (-392 "FORTRAN.spad" 648020 648063 649504 649509) (-391 "FORT.spad" 646949 646957 648010 648015) (-390 "FORTFN.spad" 644109 644117 646929 646944) (-389 "FORTCAT.spad" 643783 643791 644089 644104) (-388 "FORMULA.spad" 641121 641129 643773 643778) (-387 "FORMULA1.spad" 640600 640610 641111 641116) (-386 "FORDER.spad" 640291 640315 640590 640595) (-385 "FOP.spad" 639492 639500 640281 640286) (-384 "FNLA.spad" 638916 638938 639460 639487) (-383 "FNCAT.spad" 637244 637252 638906 638911) (-382 "FNAME.spad" 637136 637144 637234 637239) (-381 "FMTC.spad" 636934 636942 637062 637131) (-380 "FMONOID.spad" 633989 633999 636890 636895) (-379 "FM.spad" 633684 633696 633923 633950) (-378 "FMFUN.spad" 630704 630712 633664 633679) (-377 "FMC.spad" 629746 629754 630684 630699) (-376 "FMCAT.spad" 627400 627418 629714 629741) (-375 "FM1.spad" 626757 626769 627334 627361) (-374 "FLOATRP.spad" 624478 624492 626747 626752) (-373 "FLOAT.spad" 617642 617650 624344 624473) (-372 "FLOATCP.spad" 615059 615073 617632 617637) (-371 "FLINEXP.spad" 614771 614781 615039 615054) (-370 "FLINEXP.spad" 614437 614449 614707 614712) (-369 "FLASORT.spad" 613757 613769 614427 614432) (-368 "FLALG.spad" 611403 611422 613683 613752) (-367 "FLAGG.spad" 608409 608419 611371 611398) (-366 "FLAGG.spad" 605328 605340 608292 608297) (-365 "FLAGG2.spad" 604009 604025 605318 605323) (-364 "FINRALG.spad" 602038 602051 603965 604004) (-363 "FINRALG.spad" 599993 600008 601922 601927) (-362 "FINITE.spad" 599145 599153 599983 599988) (-361 "FINAALG.spad" 588126 588136 599087 599140) (-360 "FINAALG.spad" 577119 577131 588082 588087) (-359 "FILE.spad" 576702 576712 577109 577114) (-358 "FILECAT.spad" 575220 575237 576692 576697) (-357 "FIELD.spad" 574626 574634 575122 575215) (-356 "FIELD.spad" 574118 574128 574616 574621) (-355 "FGROUP.spad" 572727 572737 574098 574113) (-354 "FGLMICPK.spad" 571514 571529 572717 572722) (-353 "FFX.spad" 570889 570904 571230 571323) (-352 "FFSLPE.spad" 570378 570399 570879 570884) (-351 "FFPOLY.spad" 561630 561641 570368 570373) (-350 "FFPOLY2.spad" 560690 560707 561620 561625) (-349 "FFP.spad" 560087 560107 560406 560499) (-348 "FF.spad" 559535 559551 559768 559861) (-347 "FFNBX.spad" 558047 558067 559251 559344) (-346 "FFNBP.spad" 556560 556577 557763 557856) (-345 "FFNB.spad" 555025 555046 556241 556334) (-344 "FFINTBAS.spad" 552439 552458 555015 555020) (-343 "FFIELDC.spad" 550014 550022 552341 552434) (-342 "FFIELDC.spad" 547675 547685 550004 550009) (-341 "FFHOM.spad" 546423 546440 547665 547670) (-340 "FFF.spad" 543858 543869 546413 546418) (-339 "FFCGX.spad" 542705 542725 543574 543667) (-338 "FFCGP.spad" 541594 541614 542421 542514) (-337 "FFCG.spad" 540386 540407 541275 541368) (-336 "FFCAT.spad" 533413 533435 540225 540381) (-335 "FFCAT.spad" 526519 526543 533333 533338) (-334 "FFCAT2.spad" 526264 526304 526509 526514) (-333 "FEXPR.spad" 517973 518019 526020 526059) (-332 "FEVALAB.spad" 517679 517689 517963 517968) (-331 "FEVALAB.spad" 517170 517182 517456 517461) (-330 "FDIV.spad" 516612 516636 517160 517165) (-329 "FDIVCAT.spad" 514654 514678 516602 516607) (-328 "FDIVCAT.spad" 512694 512720 514644 514649) (-327 "FDIV2.spad" 512348 512388 512684 512689) (-326 "FCPAK1.spad" 510901 510909 512338 512343) (-325 "FCOMP.spad" 510280 510290 510891 510896) (-324 "FC.spad" 500105 500113 510270 510275) (-323 "FAXF.spad" 493040 493054 500007 500100) (-322 "FAXF.spad" 486027 486043 492996 493001) (-321 "FARRAY.spad" 484173 484183 485210 485237) (-320 "FAMR.spad" 482293 482305 484071 484168) (-319 "FAMR.spad" 480397 480411 482177 482182) (-318 "FAMONOID.spad" 480047 480057 480351 480356) (-317 "FAMONC.spad" 478269 478281 480037 480042) (-316 "FAGROUP.spad" 477875 477885 478165 478192) (-315 "FACUTIL.spad" 476071 476088 477865 477870) (-314 "FACTFUNC.spad" 475247 475257 476061 476066) (-313 "EXPUPXS.spad" 472080 472103 473379 473528) (-312 "EXPRTUBE.spad" 469308 469316 472070 472075) (-311 "EXPRODE.spad" 466180 466196 469298 469303) (-310 "EXPR.spad" 461455 461465 462169 462576) (-309 "EXPR2UPS.spad" 457547 457560 461445 461450) (-308 "EXPR2.spad" 457250 457262 457537 457542) (-307 "EXPEXPAN.spad" 454188 454213 454822 454915) (-306 "EXIT.spad" 453859 453867 454178 454183) (-305 "EXITAST.spad" 453595 453603 453849 453854) (-304 "EVALCYC.spad" 453053 453067 453585 453590) (-303 "EVALAB.spad" 452617 452627 453043 453048) (-302 "EVALAB.spad" 452179 452191 452607 452612) (-301 "EUCDOM.spad" 449721 449729 452105 452174) (-300 "EUCDOM.spad" 447325 447335 449711 449716) (-299 "ESTOOLS.spad" 439165 439173 447315 447320) (-298 "ESTOOLS2.spad" 438766 438780 439155 439160) (-297 "ESTOOLS1.spad" 438451 438462 438756 438761) (-296 "ES.spad" 430998 431006 438441 438446) (-295 "ES.spad" 423451 423461 430896 430901) (-294 "ESCONT.spad" 420224 420232 423441 423446) (-293 "ESCONT1.spad" 419973 419985 420214 420219) (-292 "ES2.spad" 419468 419484 419963 419968) (-291 "ES1.spad" 419034 419050 419458 419463) (-290 "ERROR.spad" 416355 416363 419024 419029) (-289 "EQTBL.spad" 414827 414849 415036 415063) (-288 "EQ.spad" 409701 409711 412500 412612) (-287 "EQ2.spad" 409417 409429 409691 409696) (-286 "EP.spad" 405731 405741 409407 409412) (-285 "ENV.spad" 404433 404441 405721 405726) (-284 "ENTIRER.spad" 404101 404109 404377 404428) (-283 "EMR.spad" 403302 403343 404027 404096) (-282 "ELTAGG.spad" 401542 401561 403292 403297) (-281 "ELTAGG.spad" 399746 399767 401498 401503) (-280 "ELTAB.spad" 399193 399211 399736 399741) (-279 "ELFUTS.spad" 398572 398591 399183 399188) (-278 "ELEMFUN.spad" 398261 398269 398562 398567) (-277 "ELEMFUN.spad" 397948 397958 398251 398256) (-276 "ELAGG.spad" 395879 395889 397916 397943) (-275 "ELAGG.spad" 393759 393771 395798 395803) (-274 "ELABEXPR.spad" 392690 392698 393749 393754) (-273 "EFUPXS.spad" 389466 389496 392646 392651) (-272 "EFULS.spad" 386302 386325 389422 389427) (-271 "EFSTRUC.spad" 384257 384273 386292 386297) (-270 "EF.spad" 379023 379039 384247 384252) (-269 "EAB.spad" 377299 377307 379013 379018) (-268 "E04UCFA.spad" 376835 376843 377289 377294) (-267 "E04NAFA.spad" 376412 376420 376825 376830) (-266 "E04MBFA.spad" 375992 376000 376402 376407) (-265 "E04JAFA.spad" 375528 375536 375982 375987) (-264 "E04GCFA.spad" 375064 375072 375518 375523) (-263 "E04FDFA.spad" 374600 374608 375054 375059) (-262 "E04DGFA.spad" 374136 374144 374590 374595) (-261 "E04AGNT.spad" 369978 369986 374126 374131) (-260 "DVARCAT.spad" 366663 366673 369968 369973) (-259 "DVARCAT.spad" 363346 363358 366653 366658) (-258 "DSMP.spad" 360777 360791 361082 361209) (-257 "DROPT.spad" 354722 354730 360767 360772) (-256 "DROPT1.spad" 354385 354395 354712 354717) (-255 "DROPT0.spad" 349212 349220 354375 354380) (-254 "DRAWPT.spad" 347367 347375 349202 349207) (-253 "DRAW.spad" 339967 339980 347357 347362) (-252 "DRAWHACK.spad" 339275 339285 339957 339962) (-251 "DRAWCX.spad" 336717 336725 339265 339270) (-250 "DRAWCURV.spad" 336254 336269 336707 336712) (-249 "DRAWCFUN.spad" 325426 325434 336244 336249) (-248 "DQAGG.spad" 323582 323592 325382 325421) (-247 "DPOLCAT.spad" 318923 318939 323450 323577) (-246 "DPOLCAT.spad" 314350 314368 318879 318884) (-245 "DPMO.spad" 307653 307669 307791 308092) (-244 "DPMM.spad" 300969 300987 301094 301395) (-243 "DOMAIN.spad" 300240 300248 300959 300964) (-242 "DMP.spad" 297462 297477 298034 298161) (-241 "DLP.spad" 296810 296820 297452 297457) (-240 "DLIST.spad" 295222 295232 295993 296020) (-239 "DLAGG.spad" 293623 293633 295202 295217) (-238 "DIVRING.spad" 293165 293173 293567 293618) (-237 "DIVRING.spad" 292751 292761 293155 293160) (-236 "DISPLAY.spad" 290931 290939 292741 292746) (-235 "DIRPROD.spad" 281785 281801 282425 282556) (-234 "DIRPROD2.spad" 280593 280611 281775 281780) (-233 "DIRPCAT.spad" 279523 279539 280445 280588) (-232 "DIRPCAT.spad" 278194 278212 279118 279123) (-231 "DIOSP.spad" 277019 277027 278184 278189) (-230 "DIOPS.spad" 275991 276001 276987 277014) (-229 "DIOPS.spad" 274949 274961 275947 275952) (-228 "DIFRING.spad" 274241 274249 274929 274944) (-227 "DIFRING.spad" 273541 273551 274231 274236) (-226 "DIFEXT.spad" 272700 272710 273521 273536) (-225 "DIFEXT.spad" 271776 271788 272599 272604) (-224 "DIAGG.spad" 271394 271404 271744 271771) (-223 "DIAGG.spad" 271032 271044 271384 271389) (-222 "DHMATRIX.spad" 269336 269346 270489 270516) (-221 "DFSFUN.spad" 262744 262752 269326 269331) (-220 "DFLOAT.spad" 259465 259473 262634 262739) (-219 "DFINTTLS.spad" 257674 257690 259455 259460) (-218 "DERHAM.spad" 255584 255616 257654 257669) (-217 "DEQUEUE.spad" 254902 254912 255191 255218) (-216 "DEGRED.spad" 254517 254531 254892 254897) (-215 "DEFINTRF.spad" 252042 252052 254507 254512) (-214 "DEFINTEF.spad" 250538 250554 252032 252037) (-213 "DEFAST.spad" 249906 249914 250528 250533) (-212 "DECIMAL.spad" 247787 247795 248373 248466) (-211 "DDFACT.spad" 245586 245603 247777 247782) (-210 "DBLRESP.spad" 245184 245208 245576 245581) (-209 "DBASE.spad" 243756 243766 245174 245179) (-208 "DATAARY.spad" 243218 243231 243746 243751) (-207 "D03FAFA.spad" 243046 243054 243208 243213) (-206 "D03EEFA.spad" 242866 242874 243036 243041) (-205 "D03AGNT.spad" 241946 241954 242856 242861) (-204 "D02EJFA.spad" 241408 241416 241936 241941) (-203 "D02CJFA.spad" 240886 240894 241398 241403) (-202 "D02BHFA.spad" 240376 240384 240876 240881) (-201 "D02BBFA.spad" 239866 239874 240366 240371) (-200 "D02AGNT.spad" 234670 234678 239856 239861) (-199 "D01WGTS.spad" 232989 232997 234660 234665) (-198 "D01TRNS.spad" 232966 232974 232979 232984) (-197 "D01GBFA.spad" 232488 232496 232956 232961) (-196 "D01FCFA.spad" 232010 232018 232478 232483) (-195 "D01ASFA.spad" 231478 231486 232000 232005) (-194 "D01AQFA.spad" 230924 230932 231468 231473) (-193 "D01APFA.spad" 230348 230356 230914 230919) (-192 "D01ANFA.spad" 229842 229850 230338 230343) (-191 "D01AMFA.spad" 229352 229360 229832 229837) (-190 "D01ALFA.spad" 228892 228900 229342 229347) (-189 "D01AKFA.spad" 228418 228426 228882 228887) (-188 "D01AJFA.spad" 227941 227949 228408 228413) (-187 "D01AGNT.spad" 224000 224008 227931 227936) (-186 "CYCLOTOM.spad" 223506 223514 223990 223995) (-185 "CYCLES.spad" 220338 220346 223496 223501) (-184 "CVMP.spad" 219755 219765 220328 220333) (-183 "CTRIGMNP.spad" 218245 218261 219745 219750) (-182 "CTOR.spad" 217688 217696 218235 218240) (-181 "CTORKIND.spad" 217303 217311 217678 217683) (-180 "CTORCALL.spad" 216891 216899 217293 217298) (-179 "CSTTOOLS.spad" 216134 216147 216881 216886) (-178 "CRFP.spad" 209838 209851 216124 216129) (-177 "CRCEAST.spad" 209558 209566 209828 209833) (-176 "CRAPACK.spad" 208601 208611 209548 209553) (-175 "CPMATCH.spad" 208101 208116 208526 208531) (-174 "CPIMA.spad" 207806 207825 208091 208096) (-173 "COORDSYS.spad" 202699 202709 207796 207801) (-172 "CONTOUR.spad" 202101 202109 202689 202694) (-171 "CONTFRAC.spad" 197713 197723 202003 202096) (-170 "CONDUIT.spad" 197471 197479 197703 197708) (-169 "COMRING.spad" 197145 197153 197409 197466) (-168 "COMPPROP.spad" 196659 196667 197135 197140) (-167 "COMPLPAT.spad" 196426 196441 196649 196654) (-166 "COMPLEX.spad" 190462 190472 190706 190955) (-165 "COMPLEX2.spad" 190175 190187 190452 190457) (-164 "COMPFACT.spad" 189777 189791 190165 190170) (-163 "COMPCAT.spad" 187903 187913 189511 189772) (-162 "COMPCAT.spad" 185722 185734 187332 187337) (-161 "COMMUPC.spad" 185468 185486 185712 185717) (-160 "COMMONOP.spad" 185001 185009 185458 185463) (-159 "COMM.spad" 184810 184818 184991 184996) (-158 "COMMAAST.spad" 184573 184581 184800 184805) (-157 "COMBOPC.spad" 183478 183486 184563 184568) (-156 "COMBINAT.spad" 182223 182233 183468 183473) (-155 "COMBF.spad" 179591 179607 182213 182218) (-154 "COLOR.spad" 178428 178436 179581 179586) (-153 "COLONAST.spad" 178094 178102 178418 178423) (-152 "CMPLXRT.spad" 177803 177820 178084 178089) (-151 "CLLCTAST.spad" 177465 177473 177793 177798) (-150 "CLIP.spad" 173557 173565 177455 177460) (-149 "CLIF.spad" 172196 172212 173513 173552) (-148 "CLAGG.spad" 168671 168681 172176 172191) (-147 "CLAGG.spad" 165027 165039 168534 168539) (-146 "CINTSLPE.spad" 164352 164365 165017 165022) (-145 "CHVAR.spad" 162430 162452 164342 164347) (-144 "CHARZ.spad" 162345 162353 162410 162425) (-143 "CHARPOL.spad" 161853 161863 162335 162340) (-142 "CHARNZ.spad" 161606 161614 161833 161848) (-141 "CHAR.spad" 159474 159482 161596 161601) (-140 "CFCAT.spad" 158790 158798 159464 159469) (-139 "CDEN.spad" 157948 157962 158780 158785) (-138 "CCLASS.spad" 156097 156105 157359 157398) (-137 "CATEGORY.spad" 155876 155884 156087 156092) (-136 "CATAST.spad" 155503 155511 155866 155871) (-135 "CASEAST.spad" 155217 155225 155493 155498) (-134 "CARTEN.spad" 150320 150344 155207 155212) (-133 "CARTEN2.spad" 149706 149733 150310 150315) (-132 "CARD.spad" 146995 147003 149680 149701) (-131 "CAPSLAST.spad" 146769 146777 146985 146990) (-130 "CACHSET.spad" 146391 146399 146759 146764) (-129 "CABMON.spad" 145944 145952 146381 146386) (-128 "BYTE.spad" 145118 145126 145934 145939) (-127 "BYTEBUF.spad" 142940 142948 144287 144314) (-126 "BTREE.spad" 142009 142019 142547 142574) (-125 "BTOURN.spad" 141012 141022 141616 141643) (-124 "BTCAT.spad" 140388 140398 140968 141007) (-123 "BTCAT.spad" 139796 139808 140378 140383) (-122 "BTAGG.spad" 138906 138914 139752 139791) (-121 "BTAGG.spad" 138048 138058 138896 138901) (-120 "BSTREE.spad" 136783 136793 137655 137682) (-119 "BRILL.spad" 134978 134989 136773 136778) (-118 "BRAGG.spad" 133892 133902 134958 134973) (-117 "BRAGG.spad" 132780 132792 133848 133853) (-116 "BPADICRT.spad" 130761 130773 131016 131109) (-115 "BPADIC.spad" 130425 130437 130687 130756) (-114 "BOUNDZRO.spad" 130081 130098 130415 130420) (-113 "BOP.spad" 125545 125553 130071 130076) (-112 "BOP1.spad" 122931 122941 125501 125506) (-111 "BOOLEAN.spad" 122255 122263 122921 122926) (-110 "BMODULE.spad" 121967 121979 122223 122250) (-109 "BITS.spad" 121386 121394 121603 121630) (-108 "BINDING.spad" 120805 120813 121376 121381) (-107 "BINARY.spad" 118695 118703 119272 119365) (-106 "BGAGG.spad" 117880 117890 118663 118690) (-105 "BGAGG.spad" 117085 117097 117870 117875) (-104 "BFUNCT.spad" 116649 116657 117065 117080) (-103 "BEZOUT.spad" 115783 115810 116599 116604) (-102 "BBTREE.spad" 112602 112612 115390 115417) (-101 "BASTYPE.spad" 112274 112282 112592 112597) (-100 "BASTYPE.spad" 111944 111954 112264 112269) (-99 "BALFACT.spad" 111384 111396 111934 111939) (-98 "AUTOMOR.spad" 110831 110840 111364 111379) (-97 "ATTREG.spad" 107550 107557 110583 110826) (-96 "ATTRBUT.spad" 103573 103580 107530 107545) (-95 "ATTRAST.spad" 103290 103297 103563 103568) (-94 "ATRIG.spad" 102760 102767 103280 103285) (-93 "ATRIG.spad" 102228 102237 102750 102755) (-92 "ASTCAT.spad" 102030 102037 102218 102223) (-91 "ASTCAT.spad" 101830 101839 102020 102025) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2273376 2273381 2273386 2273391) (-2 NIL 2273356 2273361 2273366 2273371) (-1 NIL 2273336 2273341 2273346 2273351) (0 NIL 2273316 2273321 2273326 2273331) (-1266 "ZMOD.spad" 2273125 2273138 2273254 2273311) (-1265 "ZLINDEP.spad" 2272169 2272180 2273115 2273120) (-1264 "ZDSOLVE.spad" 2262018 2262040 2272159 2272164) (-1263 "YSTREAM.spad" 2261511 2261522 2262008 2262013) (-1262 "XRPOLY.spad" 2260731 2260751 2261367 2261436) (-1261 "XPR.spad" 2258522 2258535 2260449 2260548) (-1260 "XPOLY.spad" 2258077 2258088 2258378 2258447) (-1259 "XPOLYC.spad" 2257394 2257410 2258003 2258072) (-1258 "XPBWPOLY.spad" 2255831 2255851 2257174 2257243) (-1257 "XF.spad" 2254292 2254307 2255733 2255826) (-1256 "XF.spad" 2252733 2252750 2254176 2254181) (-1255 "XFALG.spad" 2249757 2249773 2252659 2252728) (-1254 "XEXPPKG.spad" 2249008 2249034 2249747 2249752) (-1253 "XDPOLY.spad" 2248622 2248638 2248864 2248933) (-1252 "XALG.spad" 2248282 2248293 2248578 2248617) (-1251 "WUTSET.spad" 2244121 2244138 2247928 2247955) (-1250 "WP.spad" 2243320 2243364 2243979 2244046) (-1249 "WHILEAST.spad" 2243118 2243127 2243310 2243315) (-1248 "WHEREAST.spad" 2242789 2242798 2243108 2243113) (-1247 "WFFINTBS.spad" 2240352 2240374 2242779 2242784) (-1246 "WEIER.spad" 2238566 2238577 2240342 2240347) (-1245 "VSPACE.spad" 2238239 2238250 2238534 2238561) (-1244 "VSPACE.spad" 2237932 2237945 2238229 2238234) (-1243 "VOID.spad" 2237609 2237618 2237922 2237927) (-1242 "VIEW.spad" 2235231 2235240 2237599 2237604) (-1241 "VIEWDEF.spad" 2230428 2230437 2235221 2235226) (-1240 "VIEW3D.spad" 2214263 2214272 2230418 2230423) (-1239 "VIEW2D.spad" 2202000 2202009 2214253 2214258) (-1238 "VECTOR.spad" 2200675 2200686 2200926 2200953) (-1237 "VECTOR2.spad" 2199302 2199315 2200665 2200670) (-1236 "VECTCAT.spad" 2197202 2197213 2199270 2199297) (-1235 "VECTCAT.spad" 2194910 2194923 2196980 2196985) (-1234 "VARIABLE.spad" 2194690 2194705 2194900 2194905) (-1233 "UTYPE.spad" 2194334 2194343 2194680 2194685) (-1232 "UTSODETL.spad" 2193627 2193651 2194290 2194295) (-1231 "UTSODE.spad" 2191815 2191835 2193617 2193622) (-1230 "UTS.spad" 2186604 2186632 2190282 2190379) (-1229 "UTSCAT.spad" 2184055 2184071 2186502 2186599) (-1228 "UTSCAT.spad" 2181150 2181168 2183599 2183604) (-1227 "UTS2.spad" 2180743 2180778 2181140 2181145) (-1226 "URAGG.spad" 2175375 2175386 2180733 2180738) (-1225 "URAGG.spad" 2169971 2169984 2175331 2175336) (-1224 "UPXSSING.spad" 2167614 2167640 2169052 2169185) (-1223 "UPXS.spad" 2164762 2164790 2165746 2165895) (-1222 "UPXSCONS.spad" 2162519 2162539 2162894 2163043) (-1221 "UPXSCCA.spad" 2161084 2161104 2162365 2162514) (-1220 "UPXSCCA.spad" 2159791 2159813 2161074 2161079) (-1219 "UPXSCAT.spad" 2158372 2158388 2159637 2159786) (-1218 "UPXS2.spad" 2157913 2157966 2158362 2158367) (-1217 "UPSQFREE.spad" 2156325 2156339 2157903 2157908) (-1216 "UPSCAT.spad" 2153918 2153942 2156223 2156320) (-1215 "UPSCAT.spad" 2151217 2151243 2153524 2153529) (-1214 "UPOLYC.spad" 2146195 2146206 2151059 2151212) (-1213 "UPOLYC.spad" 2141065 2141078 2145931 2145936) (-1212 "UPOLYC2.spad" 2140534 2140553 2141055 2141060) (-1211 "UP.spad" 2137691 2137706 2138084 2138237) (-1210 "UPMP.spad" 2136581 2136594 2137681 2137686) (-1209 "UPDIVP.spad" 2136144 2136158 2136571 2136576) (-1208 "UPDECOMP.spad" 2134381 2134395 2136134 2136139) (-1207 "UPCDEN.spad" 2133588 2133604 2134371 2134376) (-1206 "UP2.spad" 2132950 2132971 2133578 2133583) (-1205 "UNISEG.spad" 2132303 2132314 2132869 2132874) (-1204 "UNISEG2.spad" 2131796 2131809 2132259 2132264) (-1203 "UNIFACT.spad" 2130897 2130909 2131786 2131791) (-1202 "ULS.spad" 2121449 2121477 2122542 2122971) (-1201 "ULSCONS.spad" 2113843 2113863 2114215 2114364) (-1200 "ULSCCAT.spad" 2111572 2111592 2113689 2113838) (-1199 "ULSCCAT.spad" 2109409 2109431 2111528 2111533) (-1198 "ULSCAT.spad" 2107625 2107641 2109255 2109404) (-1197 "ULS2.spad" 2107137 2107190 2107615 2107620) (-1196 "UFD.spad" 2106202 2106211 2107063 2107132) (-1195 "UFD.spad" 2105329 2105340 2106192 2106197) (-1194 "UDVO.spad" 2104176 2104185 2105319 2105324) (-1193 "UDPO.spad" 2101603 2101614 2104132 2104137) (-1192 "TYPE.spad" 2101535 2101544 2101593 2101598) (-1191 "TYPEAST.spad" 2101454 2101463 2101525 2101530) (-1190 "TWOFACT.spad" 2100104 2100119 2101444 2101449) (-1189 "TUPLE.spad" 2099588 2099599 2100003 2100008) (-1188 "TUBETOOL.spad" 2096425 2096434 2099578 2099583) (-1187 "TUBE.spad" 2095066 2095083 2096415 2096420) (-1186 "TS.spad" 2093655 2093671 2094631 2094728) (-1185 "TSETCAT.spad" 2080782 2080799 2093623 2093650) (-1184 "TSETCAT.spad" 2067895 2067914 2080738 2080743) (-1183 "TRMANIP.spad" 2062261 2062278 2067601 2067606) (-1182 "TRIMAT.spad" 2061220 2061245 2062251 2062256) (-1181 "TRIGMNIP.spad" 2059737 2059754 2061210 2061215) (-1180 "TRIGCAT.spad" 2059249 2059258 2059727 2059732) (-1179 "TRIGCAT.spad" 2058759 2058770 2059239 2059244) (-1178 "TREE.spad" 2057330 2057341 2058366 2058393) (-1177 "TRANFUN.spad" 2057161 2057170 2057320 2057325) (-1176 "TRANFUN.spad" 2056990 2057001 2057151 2057156) (-1175 "TOPSP.spad" 2056664 2056673 2056980 2056985) (-1174 "TOOLSIGN.spad" 2056327 2056338 2056654 2056659) (-1173 "TEXTFILE.spad" 2054884 2054893 2056317 2056322) (-1172 "TEX.spad" 2052016 2052025 2054874 2054879) (-1171 "TEX1.spad" 2051572 2051583 2052006 2052011) (-1170 "TEMUTL.spad" 2051127 2051136 2051562 2051567) (-1169 "TBCMPPK.spad" 2049220 2049243 2051117 2051122) (-1168 "TBAGG.spad" 2048256 2048279 2049200 2049215) (-1167 "TBAGG.spad" 2047300 2047325 2048246 2048251) (-1166 "TANEXP.spad" 2046676 2046687 2047290 2047295) (-1165 "TABLE.spad" 2045087 2045110 2045357 2045384) (-1164 "TABLEAU.spad" 2044568 2044579 2045077 2045082) (-1163 "TABLBUMP.spad" 2041351 2041362 2044558 2044563) (-1162 "SYSTEM.spad" 2040625 2040634 2041341 2041346) (-1161 "SYSSOLP.spad" 2038098 2038109 2040615 2040620) (-1160 "SYNTAX.spad" 2034368 2034377 2038088 2038093) (-1159 "SYMTAB.spad" 2032424 2032433 2034358 2034363) (-1158 "SYMS.spad" 2028409 2028418 2032414 2032419) (-1157 "SYMPOLY.spad" 2027416 2027427 2027498 2027625) (-1156 "SYMFUNC.spad" 2026891 2026902 2027406 2027411) (-1155 "SYMBOL.spad" 2024318 2024327 2026881 2026886) (-1154 "SWITCH.spad" 2021075 2021084 2024308 2024313) (-1153 "SUTS.spad" 2017974 2018002 2019542 2019639) (-1152 "SUPXS.spad" 2015109 2015137 2016106 2016255) (-1151 "SUP.spad" 2011878 2011889 2012659 2012812) (-1150 "SUPFRACF.spad" 2010983 2011001 2011868 2011873) (-1149 "SUP2.spad" 2010373 2010386 2010973 2010978) (-1148 "SUMRF.spad" 2009339 2009350 2010363 2010368) (-1147 "SUMFS.spad" 2008972 2008989 2009329 2009334) (-1146 "SULS.spad" 1999511 1999539 2000617 2001046) (-1145 "SUCHTAST.spad" 1999280 1999289 1999501 1999506) (-1144 "SUCH.spad" 1998960 1998975 1999270 1999275) (-1143 "SUBSPACE.spad" 1990967 1990982 1998950 1998955) (-1142 "SUBRESP.spad" 1990127 1990141 1990923 1990928) (-1141 "STTF.spad" 1986226 1986242 1990117 1990122) (-1140 "STTFNC.spad" 1982694 1982710 1986216 1986221) (-1139 "STTAYLOR.spad" 1975092 1975103 1982575 1982580) (-1138 "STRTBL.spad" 1973597 1973614 1973746 1973773) (-1137 "STRING.spad" 1973006 1973015 1973020 1973047) (-1136 "STRICAT.spad" 1972794 1972803 1972974 1973001) (-1135 "STREAM.spad" 1969652 1969663 1972319 1972334) (-1134 "STREAM3.spad" 1969197 1969212 1969642 1969647) (-1133 "STREAM2.spad" 1968265 1968278 1969187 1969192) (-1132 "STREAM1.spad" 1967969 1967980 1968255 1968260) (-1131 "STINPROD.spad" 1966875 1966891 1967959 1967964) (-1130 "STEP.spad" 1966076 1966085 1966865 1966870) (-1129 "STBL.spad" 1964602 1964630 1964769 1964784) (-1128 "STAGG.spad" 1963677 1963688 1964592 1964597) (-1127 "STAGG.spad" 1962750 1962763 1963667 1963672) (-1126 "STACK.spad" 1962101 1962112 1962357 1962384) (-1125 "SREGSET.spad" 1959805 1959822 1961747 1961774) (-1124 "SRDCMPK.spad" 1958350 1958370 1959795 1959800) (-1123 "SRAGG.spad" 1953447 1953456 1958318 1958345) (-1122 "SRAGG.spad" 1948564 1948575 1953437 1953442) (-1121 "SQMATRIX.spad" 1946180 1946198 1947096 1947183) (-1120 "SPLTREE.spad" 1940732 1940745 1945616 1945643) (-1119 "SPLNODE.spad" 1937320 1937333 1940722 1940727) (-1118 "SPFCAT.spad" 1936097 1936106 1937310 1937315) (-1117 "SPECOUT.spad" 1934647 1934656 1936087 1936092) (-1116 "SPADXPT.spad" 1926786 1926795 1934637 1934642) (-1115 "spad-parser.spad" 1926251 1926260 1926776 1926781) (-1114 "SPADAST.spad" 1925952 1925961 1926241 1926246) (-1113 "SPACEC.spad" 1909965 1909976 1925942 1925947) (-1112 "SPACE3.spad" 1909741 1909752 1909955 1909960) (-1111 "SORTPAK.spad" 1909286 1909299 1909697 1909702) (-1110 "SOLVETRA.spad" 1907043 1907054 1909276 1909281) (-1109 "SOLVESER.spad" 1905563 1905574 1907033 1907038) (-1108 "SOLVERAD.spad" 1901573 1901584 1905553 1905558) (-1107 "SOLVEFOR.spad" 1899993 1900011 1901563 1901568) (-1106 "SNTSCAT.spad" 1899593 1899610 1899961 1899988) (-1105 "SMTS.spad" 1897853 1897879 1899158 1899255) (-1104 "SMP.spad" 1895292 1895312 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(-1066 "SDPOL.spad" 1834313 1834324 1834604 1834731) (-1065 "SCPKG.spad" 1832392 1832403 1834303 1834308) (-1064 "SCOPE.spad" 1831537 1831546 1832382 1832387) (-1063 "SCACHE.spad" 1830219 1830230 1831527 1831532) (-1062 "SASTCAT.spad" 1830128 1830137 1830209 1830214) (-1061 "SAOS.spad" 1830000 1830009 1830118 1830123) (-1060 "SAERFFC.spad" 1829713 1829733 1829990 1829995) (-1059 "SAE.spad" 1827888 1827904 1828499 1828634) (-1058 "SAEFACT.spad" 1827589 1827609 1827878 1827883) (-1057 "RURPK.spad" 1825230 1825246 1827579 1827584) (-1056 "RULESET.spad" 1824671 1824695 1825220 1825225) (-1055 "RULE.spad" 1822875 1822899 1824661 1824666) (-1054 "RULECOLD.spad" 1822727 1822740 1822865 1822870) (-1053 "RSTRCAST.spad" 1822444 1822453 1822717 1822722) (-1052 "RSETGCD.spad" 1818822 1818842 1822434 1822439) (-1051 "RSETCAT.spad" 1808606 1808623 1818790 1818817) (-1050 "RSETCAT.spad" 1798410 1798429 1808596 1808601) (-1049 "RSDCMPK.spad" 1796862 1796882 1798400 1798405) (-1048 "RRCC.spad" 1795246 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"RIDIST.spad" 1730708 1730717 1731314 1731319) (-1028 "RGCHAIN.spad" 1729287 1729303 1730193 1730220) (-1027 "RGBCSPC.spad" 1729068 1729080 1729277 1729282) (-1026 "RGBCMDL.spad" 1728598 1728610 1729058 1729063) (-1025 "RF.spad" 1726212 1726223 1728588 1728593) (-1024 "RFFACTOR.spad" 1725674 1725685 1726202 1726207) (-1023 "RFFACT.spad" 1725409 1725421 1725664 1725669) (-1022 "RFDIST.spad" 1724397 1724406 1725399 1725404) (-1021 "RETSOL.spad" 1723814 1723827 1724387 1724392) (-1020 "RETRACT.spad" 1723242 1723253 1723804 1723809) (-1019 "RETRACT.spad" 1722668 1722681 1723232 1723237) (-1018 "RETAST.spad" 1722480 1722489 1722658 1722663) (-1017 "RESULT.spad" 1720540 1720549 1721127 1721154) (-1016 "RESRING.spad" 1719887 1719934 1720478 1720535) (-1015 "RESLATC.spad" 1719211 1719222 1719877 1719882) (-1014 "REPSQ.spad" 1718940 1718951 1719201 1719206) (-1013 "REP.spad" 1716492 1716501 1718930 1718935) (-1012 "REPDB.spad" 1716197 1716208 1716482 1716487) (-1011 "REP2.spad" 1705769 1705780 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518569 518574) (-329 "FDIVCAT.spad" 516063 516087 518011 518016) (-328 "FDIVCAT.spad" 514103 514129 516053 516058) (-327 "FDIV2.spad" 513757 513797 514093 514098) (-326 "FCPAK1.spad" 512310 512318 513747 513752) (-325 "FCOMP.spad" 511689 511699 512300 512305) (-324 "FC.spad" 501604 501612 511679 511684) (-323 "FAXF.spad" 494539 494553 501506 501599) (-322 "FAXF.spad" 487526 487542 494495 494500) (-321 "FARRAY.spad" 485672 485682 486709 486736) (-320 "FAMR.spad" 483792 483804 485570 485667) (-319 "FAMR.spad" 481896 481910 483676 483681) (-318 "FAMONOID.spad" 481546 481556 481850 481855) (-317 "FAMONC.spad" 479768 479780 481536 481541) (-316 "FAGROUP.spad" 479374 479384 479664 479691) (-315 "FACUTIL.spad" 477570 477587 479364 479369) (-314 "FACTFUNC.spad" 476746 476756 477560 477565) (-313 "EXPUPXS.spad" 473579 473602 474878 475027) (-312 "EXPRTUBE.spad" 470807 470815 473569 473574) (-311 "EXPRODE.spad" 467679 467695 470797 470802) (-310 "EXPR.spad" 462954 462964 463668 464075) (-309 "EXPR2UPS.spad" 459046 459059 462944 462949) (-308 "EXPR2.spad" 458749 458761 459036 459041) (-307 "EXPEXPAN.spad" 455687 455712 456321 456414) (-306 "EXIT.spad" 455358 455366 455677 455682) (-305 "EXITAST.spad" 455094 455102 455348 455353) (-304 "EVALCYC.spad" 454552 454566 455084 455089) (-303 "EVALAB.spad" 454116 454126 454542 454547) (-302 "EVALAB.spad" 453678 453690 454106 454111) (-301 "EUCDOM.spad" 451220 451228 453604 453673) (-300 "EUCDOM.spad" 448824 448834 451210 451215) (-299 "ESTOOLS.spad" 440664 440672 448814 448819) (-298 "ESTOOLS2.spad" 440265 440279 440654 440659) (-297 "ESTOOLS1.spad" 439950 439961 440255 440260) (-296 "ES.spad" 432497 432505 439940 439945) (-295 "ES.spad" 424950 424960 432395 432400) (-294 "ESCONT.spad" 421723 421731 424940 424945) (-293 "ESCONT1.spad" 421472 421484 421713 421718) (-292 "ES2.spad" 420967 420983 421462 421467) (-291 "ES1.spad" 420533 420549 420957 420962) (-290 "ERROR.spad" 417854 417862 420523 420528) (-289 "EQTBL.spad" 416326 416348 416535 416562) (-288 "EQ.spad" 411200 411210 413999 414111) (-287 "EQ2.spad" 410916 410928 411190 411195) (-286 "EP.spad" 407230 407240 410906 410911) (-285 "ENV.spad" 405932 405940 407220 407225) (-284 "ENTIRER.spad" 405600 405608 405876 405927) (-283 "EMR.spad" 404801 404842 405526 405595) (-282 "ELTAGG.spad" 403041 403060 404791 404796) (-281 "ELTAGG.spad" 401245 401266 402997 403002) (-280 "ELTAB.spad" 400692 400710 401235 401240) (-279 "ELFUTS.spad" 400071 400090 400682 400687) (-278 "ELEMFUN.spad" 399760 399768 400061 400066) (-277 "ELEMFUN.spad" 399447 399457 399750 399755) (-276 "ELAGG.spad" 397390 397400 399427 399442) (-275 "ELAGG.spad" 395270 395282 397309 397314) (-274 "ELABEXPR.spad" 394201 394209 395260 395265) (-273 "EFUPXS.spad" 390977 391007 394157 394162) (-272 "EFULS.spad" 387813 387836 390933 390938) (-271 "EFSTRUC.spad" 385768 385784 387803 387808) (-270 "EF.spad" 380534 380550 385758 385763) (-269 "EAB.spad" 378810 378818 380524 380529) (-268 "E04UCFA.spad" 378346 378354 378800 378805) (-267 "E04NAFA.spad" 377923 377931 378336 378341) (-266 "E04MBFA.spad" 377503 377511 377913 377918) (-265 "E04JAFA.spad" 377039 377047 377493 377498) (-264 "E04GCFA.spad" 376575 376583 377029 377034) (-263 "E04FDFA.spad" 376111 376119 376565 376570) (-262 "E04DGFA.spad" 375647 375655 376101 376106) (-261 "E04AGNT.spad" 371489 371497 375637 375642) (-260 "DVARCAT.spad" 368174 368184 371479 371484) (-259 "DVARCAT.spad" 364857 364869 368164 368169) (-258 "DSMP.spad" 362288 362302 362593 362720) (-257 "DROPT.spad" 356233 356241 362278 362283) (-256 "DROPT1.spad" 355896 355906 356223 356228) (-255 "DROPT0.spad" 350723 350731 355886 355891) (-254 "DRAWPT.spad" 348878 348886 350713 350718) (-253 "DRAW.spad" 341478 341491 348868 348873) (-252 "DRAWHACK.spad" 340786 340796 341468 341473) (-251 "DRAWCX.spad" 338228 338236 340776 340781) (-250 "DRAWCURV.spad" 337765 337780 338218 338223) (-249 "DRAWCFUN.spad" 326937 326945 337755 337760) (-248 "DQAGG.spad" 325105 325115 326905 326932) (-247 "DPOLCAT.spad" 320446 320462 324973 325100) (-246 "DPOLCAT.spad" 315873 315891 320402 320407) (-245 "DPMO.spad" 308099 308115 308237 308538) (-244 "DPMM.spad" 300338 300356 300463 300764) (-243 "DOMAIN.spad" 299609 299617 300328 300333) (-242 "DMP.spad" 296831 296846 297403 297530) (-241 "DLP.spad" 296179 296189 296821 296826) (-240 "DLIST.spad" 294758 294768 295362 295389) (-239 "DLAGG.spad" 293169 293179 294748 294753) (-238 "DIVRING.spad" 292711 292719 293113 293164) (-237 "DIVRING.spad" 292297 292307 292701 292706) (-236 "DISPLAY.spad" 290477 290485 292287 292292) (-235 "DIRPROD.spad" 280057 280073 280697 280828) (-234 "DIRPROD2.spad" 278865 278883 280047 280052) (-233 "DIRPCAT.spad" 277807 277823 278729 278860) (-232 "DIRPCAT.spad" 276478 276496 277402 277407) (-231 "DIOSP.spad" 275303 275311 276468 276473) (-230 "DIOPS.spad" 274287 274297 275283 275298) (-229 "DIOPS.spad" 273245 273257 274243 274248) (-228 "DIFRING.spad" 272537 272545 273225 273240) (-227 "DIFRING.spad" 271837 271847 272527 272532) (-226 "DIFEXT.spad" 270996 271006 271817 271832) (-225 "DIFEXT.spad" 270072 270084 270895 270900) (-224 "DIAGG.spad" 269702 269712 270052 270067) (-223 "DIAGG.spad" 269340 269352 269692 269697) (-222 "DHMATRIX.spad" 267644 267654 268797 268824) (-221 "DFSFUN.spad" 261052 261060 267634 267639) (-220 "DFLOAT.spad" 257773 257781 260942 261047) (-219 "DFINTTLS.spad" 255982 255998 257763 257768) (-218 "DERHAM.spad" 253892 253924 255962 255977) (-217 "DEQUEUE.spad" 253210 253220 253499 253526) (-216 "DEGRED.spad" 252825 252839 253200 253205) (-215 "DEFINTRF.spad" 250350 250360 252815 252820) (-214 "DEFINTEF.spad" 248846 248862 250340 250345) (-213 "DEFAST.spad" 248214 248222 248836 248841) (-212 "DECIMAL.spad" 246320 246328 246681 246774) (-211 "DDFACT.spad" 244119 244136 246310 246315) (-210 "DBLRESP.spad" 243717 243741 244109 244114) (-209 "DBASE.spad" 242371 242381 243707 243712) (-208 "DATAARY.spad" 241833 241846 242361 242366) (-207 "D03FAFA.spad" 241661 241669 241823 241828) (-206 "D03EEFA.spad" 241481 241489 241651 241656) (-205 "D03AGNT.spad" 240561 240569 241471 241476) (-204 "D02EJFA.spad" 240023 240031 240551 240556) (-203 "D02CJFA.spad" 239501 239509 240013 240018) (-202 "D02BHFA.spad" 238991 238999 239491 239496) (-201 "D02BBFA.spad" 238481 238489 238981 238986) (-200 "D02AGNT.spad" 233285 233293 238471 238476) (-199 "D01WGTS.spad" 231604 231612 233275 233280) (-198 "D01TRNS.spad" 231581 231589 231594 231599) (-197 "D01GBFA.spad" 231103 231111 231571 231576) (-196 "D01FCFA.spad" 230625 230633 231093 231098) (-195 "D01ASFA.spad" 230093 230101 230615 230620) (-194 "D01AQFA.spad" 229539 229547 230083 230088) (-193 "D01APFA.spad" 228963 228971 229529 229534) (-192 "D01ANFA.spad" 228457 228465 228953 228958) (-191 "D01AMFA.spad" 227967 227975 228447 228452) (-190 "D01ALFA.spad" 227507 227515 227957 227962) (-189 "D01AKFA.spad" 227033 227041 227497 227502) (-188 "D01AJFA.spad" 226556 226564 227023 227028) (-187 "D01AGNT.spad" 222615 222623 226546 226551) (-186 "CYCLOTOM.spad" 222121 222129 222605 222610) (-185 "CYCLES.spad" 218953 218961 222111 222116) (-184 "CVMP.spad" 218370 218380 218943 218948) (-183 "CTRIGMNP.spad" 216860 216876 218360 218365) (-182 "CTOR.spad" 216303 216311 216850 216855) (-181 "CTORKIND.spad" 215918 215926 216293 216298) (-180 "CTORCALL.spad" 215506 215514 215908 215913) (-179 "CSTTOOLS.spad" 214749 214762 215496 215501) (-178 "CRFP.spad" 208453 208466 214739 214744) (-177 "CRCEAST.spad" 208173 208181 208443 208448) (-176 "CRAPACK.spad" 207216 207226 208163 208168) (-175 "CPMATCH.spad" 206716 206731 207141 207146) (-174 "CPIMA.spad" 206421 206440 206706 206711) (-173 "COORDSYS.spad" 201314 201324 206411 206416) (-172 "CONTOUR.spad" 200716 200724 201304 201309) (-171 "CONTFRAC.spad" 196328 196338 200618 200711) (-170 "CONDUIT.spad" 196086 196094 196318 196323) (-169 "COMRING.spad" 195760 195768 196024 196081) (-168 "COMPPROP.spad" 195274 195282 195750 195755) (-167 "COMPLPAT.spad" 195041 195056 195264 195269) (-166 "COMPLEX.spad" 189077 189087 189321 189570) (-165 "COMPLEX2.spad" 188790 188802 189067 189072) (-164 "COMPFACT.spad" 188392 188406 188780 188785) (-163 "COMPCAT.spad" 186530 186540 188138 188387) (-162 "COMPCAT.spad" 184349 184361 185959 185964) (-161 "COMMUPC.spad" 184095 184113 184339 184344) (-160 "COMMONOP.spad" 183628 183636 184085 184090) (-159 "COMM.spad" 183437 183445 183618 183623) (-158 "COMMAAST.spad" 183200 183208 183427 183432) (-157 "COMBOPC.spad" 182105 182113 183190 183195) (-156 "COMBINAT.spad" 180850 180860 182095 182100) (-155 "COMBF.spad" 178218 178234 180840 180845) (-154 "COLOR.spad" 177055 177063 178208 178213) (-153 "COLONAST.spad" 176721 176729 177045 177050) (-152 "CMPLXRT.spad" 176430 176447 176711 176716) (-151 "CLLCTAST.spad" 176092 176100 176420 176425) (-150 "CLIP.spad" 172184 172192 176082 176087) (-149 "CLIF.spad" 170823 170839 172140 172179) (-148 "CLAGG.spad" 167308 167318 170813 170818) (-147 "CLAGG.spad" 163664 163676 167171 167176) (-146 "CINTSLPE.spad" 162989 163002 163654 163659) (-145 "CHVAR.spad" 161067 161089 162979 162984) (-144 "CHARZ.spad" 160982 160990 161047 161062) (-143 "CHARPOL.spad" 160490 160500 160972 160977) (-142 "CHARNZ.spad" 160243 160251 160470 160485) (-141 "CHAR.spad" 158111 158119 160233 160238) (-140 "CFCAT.spad" 157427 157435 158101 158106) (-139 "CDEN.spad" 156585 156599 157417 157422) (-138 "CCLASS.spad" 154734 154742 155996 156035) (-137 "CATEGORY.spad" 154513 154521 154724 154729) (-136 "CATAST.spad" 154140 154148 154503 154508) (-135 "CASEAST.spad" 153854 153862 154130 154135) (-134 "CARTEN.spad" 148957 148981 153844 153849) (-133 "CARTEN2.spad" 148343 148370 148947 148952) (-132 "CARD.spad" 145632 145640 148317 148338) (-131 "CAPSLAST.spad" 145406 145414 145622 145627) (-130 "CACHSET.spad" 145028 145036 145396 145401) (-129 "CABMON.spad" 144581 144589 145018 145023) (-128 "BYTE.spad" 143902 143910 144571 144576) (-127 "BYTEBUF.spad" 141724 141732 143071 143098) (-126 "BTREE.spad" 140793 140803 141331 141358) (-125 "BTOURN.spad" 139796 139806 140400 140427) (-124 "BTCAT.spad" 139184 139194 139764 139791) (-123 "BTCAT.spad" 138592 138604 139174 139179) (-122 "BTAGG.spad" 137714 137722 138560 138587) (-121 "BTAGG.spad" 136856 136866 137704 137709) (-120 "BSTREE.spad" 135591 135601 136463 136490) (-119 "BRILL.spad" 133786 133797 135581 135586) (-118 "BRAGG.spad" 132710 132720 133776 133781) (-117 "BRAGG.spad" 131598 131610 132666 132671) (-116 "BPADICRT.spad" 129579 129591 129834 129927) (-115 "BPADIC.spad" 129243 129255 129505 129574) (-114 "BOUNDZRO.spad" 128899 128916 129233 129238) (-113 "BOP.spad" 124363 124371 128889 128894) (-112 "BOP1.spad" 121749 121759 124319 124324) (-111 "BOOLEAN.spad" 121073 121081 121739 121744) (-110 "BMODULE.spad" 120785 120797 121041 121068) (-109 "BITS.spad" 120204 120212 120421 120448) (-108 "BINDING.spad" 119623 119631 120194 120199) (-107 "BINARY.spad" 117734 117742 118090 118183) (-106 "BGAGG.spad" 116931 116941 117714 117729) (-105 "BGAGG.spad" 116136 116148 116921 116926) (-104 "BFUNCT.spad" 115700 115708 116116 116131) (-103 "BEZOUT.spad" 114834 114861 115650 115655) (-102 "BBTREE.spad" 111653 111663 114441 114468) (-101 "BASTYPE.spad" 111325 111333 111643 111648) (-100 "BASTYPE.spad" 110995 111005 111315 111320) (-99 "BALFACT.spad" 110435 110447 110985 110990) (-98 "AUTOMOR.spad" 109882 109891 110415 110430) (-97 "ATTREG.spad" 106601 106608 109634 109877) (-96 "ATTRBUT.spad" 102624 102631 106581 106596) (-95 "ATTRAST.spad" 102341 102348 102614 102619) (-94 "ATRIG.spad" 101811 101818 102331 102336) (-93 "ATRIG.spad" 101279 101288 101801 101806) (-92 "ASTCAT.spad" 101183 101190 101269 101274) (-91 "ASTCAT.spad" 101085 101094 101173 101178) (-90 "ASTACK.spad" 100418 100427 100692 100719) (-89 "ASSOCEQ.spad" 99218 99229 100374 100379) (-88 "ASP9.spad" 98299 98312 99208 99213) (-87 "ASP8.spad" 97342 97355 98289 98294) (-86 "ASP80.spad" 96664 96677 97332 97337) (-85 "ASP7.spad" 95824 95837 96654 96659) (-84 "ASP78.spad" 95275 95288 95814 95819) (-83 "ASP77.spad" 94644 94657 95265 95270) (-82 "ASP74.spad" 93736 93749 94634 94639) (-81 "ASP73.spad" 93007 93020 93726 93731) (-80 "ASP6.spad" 91874 91887 92997 93002) (-79 "ASP55.spad" 90383 90396 91864 91869) (-78 "ASP50.spad" 88200 88213 90373 90378) (-77 "ASP4.spad" 87495 87508 88190 88195) (-76 "ASP49.spad" 86494 86507 87485 87490) (-75 "ASP42.spad" 84901 84940 86484 86489) (-74 "ASP41.spad" 83480 83519 84891 84896) (-73 "ASP35.spad" 82468 82481 83470 83475) (-72 "ASP34.spad" 81769 81782 82458 82463) (-71 "ASP33.spad" 81329 81342 81759 81764) (-70 "ASP31.spad" 80469 80482 81319 81324) (-69 "ASP30.spad" 79361 79374 80459 80464) (-68 "ASP29.spad" 78827 78840 79351 79356) (-67 "ASP28.spad" 70100 70113 78817 78822) (-66 "ASP27.spad" 68997 69010 70090 70095) (-65 "ASP24.spad" 68084 68097 68987 68992) (-64 "ASP20.spad" 67548 67561 68074 68079) (-63 "ASP1.spad" 66929 66942 67538 67543) (-62 "ASP19.spad" 61615 61628 66919 66924) (-61 "ASP12.spad" 61029 61042 61605 61610) (-60 "ASP10.spad" 60300 60313 61019 61024) (-59 "ARRAY2.spad" 59660 59669 59907 59934) (-58 "ARRAY1.spad" 58495 58504 58843 58870) (-57 "ARRAY12.spad" 57164 57175 58485 58490) (-56 "ARR2CAT.spad" 52826 52847 57132 57159) (-55 "ARR2CAT.spad" 48508 48531 52816 52821) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 98ad5051..e007c40e 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(153062 . 3436193633) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((#0=(-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) #0#) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|))))) -(((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) +(161702 . 3437447587) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((#0=(-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) #0#) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|))))) +((((-553)) . 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T)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) (((|#2|) . T)) ((((-553) |#3|) . T)) (((|#2|) . T)) @@ -1329,7 +1390,7 @@ (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((#0=(-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) #0#) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((#0=(-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) #0#) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|))))) (((|#2| |#2|) . T)) (((|#1|) . T)) (|has| |#2| (-357)) @@ -1341,6 +1402,7 @@ ((((-553) (-141)) . T)) ((((-141)) . T)) ((((-845)) . T)) +((((-1160)) . T)) ((((-111)) . T)) (|has| |#1| (-144)) (((|#1|) . T)) @@ -1351,6 +1413,7 @@ ((($) . T)) (((|#1|) . T)) (((|#2|) . T) (((-553)) |has| |#2| (-626 (-553)))) +((((-141)) . T)) ((((-845)) . T)) ((((-553)) |has| |#1| (-626 (-553))) ((|#1|) . T)) ((((-553)) |has| |#1| (-626 (-553))) ((|#1|) . T)) @@ -1360,19 +1423,19 @@ (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) (((|#1| |#2|) . T)) ((((-553) (-141)) . T)) -(((#0=(-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) #0#) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) -((($) -4028 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) +(((#0=(-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) #0#) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) +((($) -3988 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) (|has| |#1| (-833)) (((|#2| (-757) (-1061)) . T)) (((|#1| |#2|) . T)) -(-4028 (|has| |#1| (-169)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-169)) (|has| |#1| (-545))) (|has| |#1| (-777)) (((|#1|) |has| |#1| (-169))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4028 (|has| |#1| (-144)) (-12 (|has| |#1| (-357)) (|has| |#2| (-144)))) -(-4028 (|has| |#1| (-142)) (-12 (|has| |#1| (-357)) (|has| |#2| (-142)))) +(-3988 (|has| |#1| (-144)) (-12 (|has| |#1| (-357)) (|has| |#2| (-144)))) +(-3988 (|has| |#1| (-142)) (-12 (|has| |#1| (-357)) (|has| |#2| (-142)))) (((|#4|) . T)) (|has| |#1| (-142)) ((((-1137) |#1|) . T)) @@ -1386,13 +1449,14 @@ (((|#3|) . T)) ((((-1230 |#1| |#2| |#3|)) |has| |#1| (-357))) ((((-845)) . T)) -(-4028 (|has| |#1| (-833)) (|has| |#1| (-1079))) +(-3988 (|has| |#1| (-833)) (|has| |#1| (-1079))) (((|#1|) . T)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079))) (((-940 |#1|)) . T)) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079))) (((-940 |#1|)) . T)) (|has| |#1| (-831)) (|has| |#1| (-831)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) +((((-940 |#1|)) . T)) (|has| |#2| (-357)) (((|#1|) |has| |#1| (-169))) (((|#2|) |has| |#2| (-1031))) @@ -1402,8 +1466,8 @@ ((($) . T)) ((((-382) (-1137)) . T)) ((($) |has| |#1| (-545)) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) -((((-845)) -4028 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-600 (-845))) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) (((-1238 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2669 (-1137)) (|:| -3359 #0#))) . T)) +((((-845)) -3988 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-600 (-845))) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) (((-1238 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2578 (-1137)) (|:| -3256 #0#))) . T)) (((|#1|) . T)) ((((-845)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) @@ -1411,27 +1475,28 @@ (|has| |#2| (-142)) (|has| |#2| (-144)) (|has| |#1| (-466)) -(-4028 (|has| |#1| (-466)) (|has| |#1| (-712)) (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) +(-3988 (|has| |#1| (-466)) (|has| |#1| (-712)) (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) (|has| |#1| (-357)) ((((-845)) . T)) (|has| |#1| (-38 (-401 (-553)))) ((((-401 (-553))) |has| |#1| (-38 (-401 (-553)))) ((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-545))) ((($) |has| |#1| (-545))) +((((-1160)) . T)) (|has| |#1| (-831)) (|has| |#1| (-831)) ((((-845)) . T)) (((|#2|) . T)) -((((-401 (-553))) -4028 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) (($) -4028 (|has| |#1| (-357)) (|has| |#1| (-545))) (((-1230 |#1| |#2| |#3|)) |has| |#1| (-357)) ((|#1|) |has| |#1| (-169))) -(((|#1|) |has| |#1| (-169)) (((-401 (-553))) -4028 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) (($) -4028 (|has| |#1| (-357)) (|has| |#1| (-545)))) +((((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) (($) -3988 (|has| |#1| (-357)) (|has| |#1| (-545))) (((-1230 |#1| |#2| |#3|)) |has| |#1| (-357)) ((|#1|) |has| |#1| (-169))) +(((|#1|) |has| |#1| (-169)) (((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) (($) -3988 (|has| |#1| (-357)) (|has| |#1| (-545)))) ((($) |has| |#1| (-545)) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) -((((-805 |#1|)) . T)) +(((|#2|) . T) (((-553)) . T) (((-805 |#1|)) . T)) (((|#1| |#2|) . T)) ((((-1155)) |has| |#1| (-882 (-1155)))) ((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T)) ((((-845)) . T)) ((((-845)) . T)) (|has| |#1| (-1079)) -(((|#2| (-475 (-2656 |#1|) (-757)) (-847 |#1|)) . T)) +(((|#2| (-475 (-2563 |#1|) (-757)) (-847 |#1|)) . T)) ((((-401 (-553))) . #0=(|has| |#2| (-357))) (($) . #0#)) (((|#1| (-524 (-1155)) (-1155)) . T)) (((|#1|) . T)) @@ -1451,16 +1516,16 @@ (|has| |#1| (-144)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) -((((-2 (|:| -2669 (-1155)) (|:| -3359 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) +((((-2 (|:| -2578 (-1155)) (|:| -3256 (-52)))) . T)) ((((-1153 |#1| |#2| |#3|)) |has| |#1| (-357))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((((-1155) (-52)) . T)) ((($ $) . T)) (((|#1| (-553)) . T)) ((((-892 |#1|)) . T)) -(((|#1|) -4028 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-1031))) (($) -4028 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031)))) +(((|#1|) -3988 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-1031))) (($) -3988 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031)))) (((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) (|has| |#1| (-833)) (|has| |#1| (-833)) @@ -1469,7 +1534,7 @@ ((((-1230 |#1| |#2| |#3|)) -12 (|has| (-1230 |#1| |#2| |#3|) (-303 (-1230 |#1| |#2| |#3|))) (|has| |#1| (-357)))) (|has| |#1| (-833)) ((((-674 |#2|)) . T) (((-845)) . T)) -((((-401 (-553))) . T) (((-553)) . T)) +((((-401 (-553))) . T) (((-553)) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-401 (-934 |#1|))) . T)) (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1079)))) @@ -1478,19 +1543,20 @@ (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1079)))) (|has| |#2| (-833)) (|has| |#1| (-833)) -(((|#3|) -4028 (|has| |#3| (-169)) (|has| |#3| (-357)))) -(-4028 (|has| |#2| (-357)) (|has| |#2| (-445)) (|has| |#2| (-891))) +(((|#3|) -3988 (|has| |#3| (-169)) (|has| |#3| (-357)))) +(-3988 (|has| |#2| (-357)) (|has| |#2| (-445)) (|has| |#2| (-891))) ((($ $) . T) ((#0=(-401 (-553)) #0#) . T)) ((((-553) |#2|) . T)) -(((|#2|) -4028 (|has| |#2| (-169)) (|has| |#2| (-357)))) +(((|#2|) -3988 (|has| |#2| (-169)) (|has| |#2| (-357)))) (|has| |#1| (-343)) (((|#3| |#3|) -12 (|has| |#3| (-303 |#3|)) (|has| |#3| (-1079)))) +(((|#2|) . T) (((-553)) . T)) ((($) . T) (((-401 (-553))) . T)) ((((-553) (-111)) . T)) (|has| |#1| (-806)) (|has| |#1| (-806)) (((|#1|) . T)) -(-4028 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343))) (|has| |#1| (-831)) (|has| |#1| (-831)) (|has| |#1| (-831)) @@ -1499,16 +1565,17 @@ ((((-553)) . T) (($) . T) (((-401 (-553))) . T)) (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-343))) (|has| |#1| (-38 (-401 (-553)))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((((-1155)) |has| |#1| (-882 (-1155))) (((-1061)) . T)) (((|#1|) . T)) (|has| |#1| (-831)) -(((#0=(-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) #0#) |has| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (-303 (-2 (|:| -2669 (-1137)) (|:| -3359 (-52)))))) +(((#0=(-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) #0#) |has| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (-303 (-2 (|:| -2578 (-1137)) (|:| -3256 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) (|has| |#1| (-1079)) ((((-845)) . T) (((-1160)) . T)) +((((-1160)) . T)) (((|#1|) . T)) (((|#2| |#2|) . T)) (((|#1|) . T)) @@ -1522,11 +1589,12 @@ ((((-141)) . T) (((-757)) . T) (((-845)) . T)) (((|#1| (-757) (-1061)) . T)) (((|#3|) . T)) -((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) |has| |#1| (-1020 (-553))) ((|#1|) . T)) +((((-141)) . T)) +((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) -3988 (|has| |#1| (-831)) (|has| |#1| (-1020 (-553)))) ((|#1|) . T)) (((|#1|) . T)) ((((-141)) . T)) (((|#2|) |has| |#2| (-169))) -(-4028 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) +(-3988 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) (((|#1|) . T)) (|has| |#1| (-142)) (|has| |#1| (-144)) @@ -1544,36 +1612,37 @@ ((((-1153 |#1| |#2| |#3|)) |has| |#1| (-357))) ((($) |has| |#1| (-831))) (|has| |#1| (-891)) +((((-1155)) . T)) ((((-845)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) (|has| |#1| (-806)) @@ -1723,8 +1795,8 @@ (|has| |#1| (-831)) (|has| |#1| (-831)) (((|#1| (-553) (-1061)) . T)) -(-4028 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +(-3988 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (((|#1| (-401 (-553)) (-1061)) . T)) (((|#1| (-757) (-1061)) . T)) (|has| |#1| (-833)) @@ -1737,31 +1809,33 @@ (|has| |#1| (-1079)) ((((-892 |#1|)) . T) (($) . T) (((-401 (-553))) . T)) (|has| |#1| (-1079)) +((((-553)) -3988 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031)))) (((|#1|) . 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T)) (|has| |#1| (-891)) (((|#2|) |has| |#2| (-1031))) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) (((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|))))) +((((-1160)) . T)) (|has| |#1| (-357)) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) (((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|))))) (((|#1|) |has| |#1| (-169))) (((|#1| |#1|) . T)) ((((-852 |#1|)) . T)) @@ -1819,7 +1895,8 @@ (((|#2|) |has| |#2| (-1079))) (|has| |#2| (-833)) (((|#1|) . T)) -((((-401 (-553))) |has| #0=(-401 |#2|) (-1020 (-401 (-553)))) (((-553)) |has| #0# (-1020 (-553))) ((#0#) . T)) +((((-401 |#2|)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) +((((-630 $)) . T) (((-1137)) . T) (((-1155)) . T) (((-553)) . T) (((-220)) . T) (((-845)) . T)) ((((-401 (-553))) . T) (((-553)) . T) (((-599 $)) . T)) (((|#1|) . T)) ((((-845)) . T)) @@ -1835,7 +1912,7 @@ (((|#1| (-401 (-553)) (-1061)) . T)) (((|#1| (-757) (-1061)) . T)) (((#0=(-401 |#2|) #0#) . T) ((#1=(-401 (-553)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-553)) -4028 (|has| (-401 (-553)) (-1020 (-553))) (|has| |#1| (-1020 (-553)))) (((-401 (-553))) . T)) +(((|#1|) . T) (((-553)) -3988 (|has| (-401 (-553)) (-1020 (-553))) (|has| |#1| (-1020 (-553)))) (((-401 (-553))) . T)) (((|#1| (-589 |#1| |#3|) (-589 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) @@ -1849,31 +1926,32 @@ ((((-845)) . T)) (((|#1| |#3|) . T)) ((((-845)) . T)) +(((|#1|) |has| |#1| (-169)) (((-934 |#1|)) . T) (((-553)) . T)) (((|#1|) |has| |#1| (-169))) ((((-684)) . T)) ((((-684)) . T)) (((|#2|) |has| |#2| (-169))) (|has| |#2| (-831)) -(((|#2|) . 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T)) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) (((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|))))) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) (((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|))))) ((((-373)) . T)) ((((-684)) . T)) ((((-401 (-553))) . #0=(|has| |#2| (-357))) (($) . #0#)) (((|#1|) |has| |#1| (-169))) ((((-401 (-934 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4028 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) -(-4028 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(-3988 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) +(-3988 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (((|#2|) . T)) (|has| |#2| (-833)) (|has| |#2| (-891)) @@ -1883,14 +1961,14 @@ (((|#3|) |has| |#3| (-1031))) ((((-1155)) |has| |#2| (-882 (-1155)))) ((((-845)) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((((-401 (-553))) . T) (($) . T)) (|has| |#1| (-466)) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-357)) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-466)) (|has| |#1| (-545)) (|has| |#1| (-1031)) (|has| |#1| (-1091))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-466)) (|has| |#1| (-545)) (|has| |#1| (-1031)) (|has| |#1| (-1091))) (|has| |#1| (-38 (-401 (-553)))) ((((-115 |#1|)) . T)) ((((-115 |#1|)) . T)) @@ -1911,11 +1989,11 @@ (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-833)) -((((-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))) . T)) +((((-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-144)) (|has| |#1| (-142)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) |has| (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)) (-303 (-2 (|:| -2669 |#1|) (|:| -3359 |#2|)))) ((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) |has| (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)) (-303 (-2 (|:| -2578 |#1|) (|:| -3256 |#2|)))) ((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) (((|#2|) . T)) (((|#3|) . T)) ((((-115 |#1|)) . T)) @@ -1933,11 +2011,11 @@ ((((-529)) |has| |#1| (-601 (-529))) (((-874 (-553))) |has| |#1| (-601 (-874 (-553)))) (((-874 (-373))) |has| |#1| (-601 (-874 (-373)))) (((-373)) . #0=(|has| |#1| (-1004))) (((-220)) . #0#)) (((|#1|) |has| |#1| (-357))) ((((-845)) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((($ $) . T) (((-599 $) $) . T)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) ((($) . T) (((-1224 |#1| |#2| |#3| |#4|)) . T) (((-401 (-553))) . T)) -((($) -4028 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1031))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-545))) +((($) -3988 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1031))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-545))) (|has| |#1| (-357)) (|has| |#1| (-357)) (|has| |#1| (-357)) @@ -1948,27 +2026,28 @@ ((((-373)) . T)) (((|#3|) -12 (|has| |#3| (-303 |#3|)) (|has| |#3| (-1079)))) ((((-845)) . T)) -(-4028 (|has| |#2| (-445)) (|has| |#2| (-891))) +(-3988 (|has| |#2| (-445)) (|has| |#2| (-891))) (((|#1|) . T)) (|has| |#1| (-833)) (|has| |#1| (-833)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) ((((-529)) |has| |#1| (-601 (-529)))) (((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) (|has| |#1| (-1079)) ((((-845)) . T)) ((((-1155)) . T) (((-845)) . T) (((-1160)) . T)) +((((-1160)) . T)) ((((-401 (-553))) . T) (((-553)) . T) (((-599 $)) . T)) (|has| |#1| (-142)) (|has| |#1| (-144)) ((((-553)) . T)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) (((#0=(-1223 |#2| |#3| |#4|)) . T) (((-401 (-553))) |has| #0# (-38 (-401 (-553)))) (($) . T)) ((((-553)) . T)) (|has| |#1| (-357)) -(-4028 (-12 (|has| (-1230 |#1| |#2| |#3|) (-144)) (|has| |#1| (-357))) (|has| |#1| (-144))) -(-4028 (-12 (|has| (-1230 |#1| |#2| |#3|) (-142)) (|has| |#1| (-357))) (|has| |#1| (-142))) +(-3988 (-12 (|has| (-1230 |#1| |#2| |#3|) (-144)) (|has| |#1| (-357))) (|has| |#1| (-144))) +(-3988 (-12 (|has| (-1230 |#1| |#2| |#3|) (-142)) (|has| |#1| (-357))) (|has| |#1| (-142))) (|has| |#1| (-357)) (|has| |#1| (-142)) (|has| |#1| (-144)) @@ -1983,22 +2062,23 @@ (((|#2|) . T)) (|has| |#1| (-1079)) (((|#1| |#2|) . T)) -(((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) +((((-553)) . T) ((|#1|) . T) (((-401 (-553))) -3988 (|has| |#1| (-357)) (|has| |#1| (-1020 (-401 (-553)))))) (((|#1|) . T) (((-553)) |has| |#1| (-626 (-553)))) (((|#3|) |has| |#3| (-169))) -(-4028 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) +(-3988 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) ((((-845)) . T)) ((((-553)) . T)) (((|#1| $) |has| |#1| (-280 |#1| |#1|))) ((((-401 (-553))) . T) (($) . T) (((-401 |#1|)) . T) ((|#1|) . T)) -((((-845)) . T)) +((((-934 |#1|)) . T) (((-845)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4028 (|has| |#1| (-284)) (|has| |#1| (-357))) ((#0=(-401 (-553)) #0#) |has| |#1| (-357))) -((((-2 (|:| -2669 (-1155)) (|:| -3359 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -3988 (|has| |#1| (-284)) (|has| |#1| (-357))) ((#0=(-401 (-553)) #0#) |has| |#1| (-357))) +((((-2 (|:| -2578 (-1155)) (|:| -3256 (-52)))) . T)) +((((-934 |#1|)) . T)) ((($) . T)) ((((-553) |#1|) . T)) ((((-1155)) |has| (-401 |#2|) (-882 (-1155)))) -(((|#1|) . T) (($) -4028 (|has| |#1| (-284)) (|has| |#1| (-357))) (((-401 (-553))) |has| |#1| (-357))) +(((|#1|) . T) (($) -3988 (|has| |#1| (-284)) (|has| |#1| (-357))) (((-401 (-553))) |has| |#1| (-357))) ((((-529)) |has| |#2| (-601 (-529)))) ((((-674 |#2|)) . T) (((-845)) . T)) (((|#1|) . T)) @@ -2006,8 +2086,8 @@ (((|#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1079)))) ((((-852 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) -(-4028 (|has| |#4| (-779)) (|has| |#4| (-831))) -(-4028 (|has| |#3| (-779)) (|has| |#3| (-831))) +(-3988 (|has| |#4| (-779)) (|has| |#4| (-831))) +(-3988 (|has| |#3| (-779)) (|has| |#3| (-831))) ((((-845)) . T)) ((((-845)) . T)) (((|#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1079)))) @@ -2023,17 +2103,17 @@ ((((-401 (-553))) . T) (($) . T)) ((((-401 (-553))) . T) (($) . T)) ((((-401 (-553))) . T) (($) . T)) -(-4028 (|has| |#1| (-445)) (|has| |#1| (-1196))) +(-3988 (|has| |#1| (-445)) (|has| |#1| (-1196))) ((($) . T)) ((((-401 (-553))) |has| #0=(-401 |#2|) (-1020 (-401 (-553)))) (((-553)) |has| #0# (-1020 (-553))) ((#0#) . T)) (((|#2|) . T) (((-553)) |has| |#2| (-626 (-553)))) (((|#1| (-757)) . T)) (|has| |#1| (-833)) (((|#1|) . T) (((-553)) |has| |#1| (-626 (-553)))) -((($) -4028 (|has| |#1| (-357)) (|has| |#1| (-343))) (((-401 (-553))) -4028 (|has| |#1| (-357)) (|has| |#1| (-343))) ((|#1|) . T)) +((($) -3988 (|has| |#1| (-357)) (|has| |#1| (-343))) (((-401 (-553))) -3988 (|has| |#1| (-357)) (|has| |#1| (-343))) ((|#1|) . T)) ((((-553)) . T)) (|has| |#1| (-38 (-401 (-553)))) -((((-2 (|:| -2669 (-1137)) (|:| -3359 (-52)))) |has| (-2 (|:| -2669 (-1137)) (|:| -3359 (-52))) (-303 (-2 (|:| -2669 (-1137)) (|:| -3359 (-52)))))) +((((-2 (|:| -2578 (-1137)) (|:| -3256 (-52)))) |has| (-2 (|:| -2578 (-1137)) (|:| -3256 (-52))) (-303 (-2 (|:| -2578 (-1137)) (|:| -3256 (-52)))))) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) (|has| |#1| (-831)) (|has| |#1| (-38 (-401 (-553)))) @@ -2056,29 +2136,29 @@ (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) ((((-1137)) . T) (((-1155)) . T) (((-220)) . T) (((-553)) . T)) -((((-1061)) . T) ((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) +(((|#2|) . T) (((-553)) . T) (($) -3988 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (((-1061)) . T) ((|#1|) . T) (((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-1020 (-401 (-553)))))) (((|#1| |#2|) . T)) ((((-141)) . T)) ((((-766 |#1| (-847 |#2|))) . T)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) (|has| |#1| (-1177)) ((((-845)) . T)) (((|#1|) . T)) -(-4028 (|has| |#3| (-25)) (|has| |#3| (-129)) (|has| |#3| (-169)) (|has| |#3| (-357)) (|has| |#3| (-362)) (|has| |#3| (-712)) (|has| |#3| (-779)) (|has| |#3| (-831)) (|has| |#3| (-1031)) (|has| |#3| (-1079))) +(-3988 (|has| |#3| (-25)) (|has| |#3| (-129)) (|has| |#3| (-169)) (|has| |#3| (-357)) (|has| |#3| (-362)) (|has| |#3| (-712)) (|has| |#3| (-779)) (|has| |#3| (-831)) (|has| |#3| (-1031)) (|has| |#3| (-1079))) ((((-1155) |#1|) |has| |#1| (-507 (-1155) |#1|))) (((|#2|) . T)) -((($ $) -4028 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1| |#1|) . T) ((#0=(-401 (-553)) #0#) |has| |#1| (-38 (-401 (-553))))) +((($ $) -3988 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1| |#1|) . T) ((#0=(-401 (-553)) #0#) |has| |#1| (-38 (-401 (-553))))) ((((-892 |#1|)) . T)) ((($) . T)) ((((-401 (-934 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) -((($) -4028 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) . T) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) +((($) -3988 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) . T) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) ((((-529)) |has| |#4| (-601 (-529)))) ((((-845)) . T) (((-630 |#4|)) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-831)) -(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079))) (((-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))) |has| (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|)) (-303 (-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))))) +(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079))) (((-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))) |has| (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|)) (-303 (-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))))) (|has| |#1| (-1079)) (|has| |#1| (-357)) (|has| |#1| (-833)) @@ -2087,16 +2167,16 @@ (((|#1|) . T)) ((((-657 |#1|)) . T)) ((($) . T) (((-401 (-553))) . T)) -((($) -4028 (|has| |#1| (-357)) (|has| |#1| (-545))) (((-401 (-553))) -4028 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) ((|#1|) |has| |#1| (-169))) +((($) -3988 (|has| |#1| (-357)) (|has| |#1| (-545))) (((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-357))) ((|#1|) |has| |#1| (-169))) (|has| |#1| (-142)) (|has| |#1| (-144)) -(-4028 (-12 (|has| (-1153 |#1| |#2| |#3|) (-144)) (|has| |#1| (-357))) (|has| |#1| (-144))) -(-4028 (-12 (|has| (-1153 |#1| |#2| |#3|) (-142)) (|has| |#1| (-357))) (|has| |#1| (-142))) +(-3988 (-12 (|has| (-1153 |#1| |#2| |#3|) (-144)) (|has| |#1| (-357))) (|has| |#1| (-144))) +(-3988 (-12 (|has| (-1153 |#1| |#2| |#3|) (-142)) (|has| |#1| (-357))) (|has| |#1| (-142))) (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-144)) (|has| |#1| (-142)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) ((((-1230 |#1| |#2| |#3|)) |has| |#1| (-357))) (|has| |#1| (-831)) (((|#1| |#2|) . T)) @@ -2105,7 +2185,7 @@ ((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T)) (|has| |#1| (-1079)) (((|#1|) . T) (($) . T) (((-401 (-553))) . T) (((-553)) . T)) -((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) |has| |#1| (-1020 (-553))) ((|#1|) . T)) +((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) ((|#1|) . T) (((-553)) . T)) (|has| |#2| (-142)) (|has| |#2| (-144)) ((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T)) @@ -2120,16 +2200,16 @@ ((((-845)) . T)) ((((-845)) . T)) ((((-529)) |has| |#1| (-601 (-529)))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((((-1155) |#1|) |has| |#1| (-507 (-1155) |#1|)) ((|#1| |#1|) |has| |#1| (-303 |#1|))) -(((|#1|) -4028 (|has| |#1| (-169)) (|has| |#1| (-357)))) +(((|#1|) -3988 (|has| |#1| (-169)) (|has| |#1| (-357)))) ((((-310 |#1|)) . T)) (((|#2|) |has| |#2| (-357))) (((|#2|) . T)) ((((-401 (-553))) . T) (((-684)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) (((#0=(-766 |#1| (-847 |#2|)) #0#) |has| (-766 |#1| (-847 |#2|)) (-303 (-766 |#1| (-847 |#2|))))) -((((-553)) . T)) +((((-553)) . T) (($) . T)) ((((-847 |#1|)) . T)) (((|#2|) |has| |#2| (-169))) (((|#1|) |has| |#1| (-169))) @@ -2144,13 +2224,13 @@ (|has| |#1| (-142)) (|has| |#1| (-144)) ((($ $) . T)) -(-4028 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-466)) (|has| |#1| (-712)) (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031)) (|has| |#1| (-1091)) (|has| |#1| (-1079))) +(-3988 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-466)) (|has| |#1| (-712)) (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031)) (|has| |#1| (-1091)) (|has| |#1| (-1079))) (|has| |#1| (-545)) (((|#2|) . T)) ((((-553)) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (((|#1|) . T)) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1031))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1031))) ((((-570 |#1|)) . T)) ((($) . T)) (((|#1| (-58 |#1|) (-58 |#1|)) . T)) @@ -2165,8 +2245,8 @@ (((|#3|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-1223 |#2| |#3| |#4|)) . T) (((-1224 |#1| |#2| |#3| |#4|)) . T)) -((((-48)) -12 (|has| |#1| (-545)) (|has| |#1| (-1020 (-553)))) (((-599 $)) . T) ((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) -4028 (-12 (|has| |#1| (-545)) (|has| |#1| (-1020 (-553)))) (|has| |#1| (-1020 (-401 (-553))))) (((-401 (-934 |#1|))) |has| |#1| (-545)) (((-934 |#1|)) |has| |#1| (-1031)) (((-1155)) . T)) +((((-1223 |#2| |#3| |#4|)) . T) (((-553)) . T) (((-1224 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-401 (-553))) . T)) +((((-48)) -12 (|has| |#1| (-545)) (|has| |#1| (-1020 (-553)))) (((-553)) -3988 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1020 (-553))) (|has| |#1| (-1031))) ((|#1|) . T) (((-599 $)) . T) (($) |has| |#1| (-545)) (((-401 (-553))) -3988 (|has| |#1| (-545)) (|has| |#1| (-1020 (-401 (-553))))) (((-401 (-934 |#1|))) |has| |#1| (-545)) (((-934 |#1|)) |has| |#1| (-1031)) (((-1155)) . T)) ((((-401 (-553))) |has| |#2| (-1020 (-401 (-553)))) (((-553)) |has| |#2| (-1020 (-553))) ((|#2|) . T) (((-847 |#1|)) . T)) ((($) . T) (((-115 |#1|)) . T) (((-401 (-553))) . T)) ((((-1104 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) @@ -2179,12 +2259,12 @@ (((|#1| |#2|) . T)) ((((-1155) |#1|) . T)) (((|#4|) . T)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-343))) ((((-1155) (-52)) . T)) ((((-1223 |#2| |#3| |#4|) (-313 |#2| |#3| |#4|)) . T)) ((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) |has| |#1| (-1020 (-553))) ((|#1|) . T)) ((((-845)) . T)) -(-4028 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) +(-3988 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-362)) (|has| |#2| (-712)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031)) (|has| |#2| (-1079))) (((#0=(-1224 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-401 (-553)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-169)) ((#0=(-401 (-553)) #0#) |has| |#1| (-545)) (($ $) |has| |#1| (-545))) (((|#1|) . T) (($) . T) (((-401 (-553))) . T)) @@ -2200,18 +2280,18 @@ (((|#3|) |has| |#3| (-357))) (((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) ((((-1155)) . T)) -((((-1223 |#2| |#3| |#4|)) . T)) +((($) . T) (((-1223 |#2| |#3| |#4|)) . T) (((-401 (-553))) |has| (-1223 |#2| |#3| |#4|) (-38 (-401 (-553)))) (((-553)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079)))) (((|#2| |#3|) . T)) -(-4028 (|has| |#2| (-357)) (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) +(-3988 (|has| |#2| (-357)) (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) (((|#1| (-524 |#2|)) . T)) (((|#1| (-757)) . T)) (((|#1| (-524 (-1067 (-1155)))) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (|has| |#2| (-891)) -(-4028 (|has| |#2| (-779)) (|has| |#2| (-831))) +(-3988 (|has| |#2| (-779)) (|has| |#2| (-831))) ((((-845)) . T)) ((($ $) . T) ((#0=(-1223 |#2| |#3| |#4|) #0#) . T) ((#1=(-401 (-553)) #1#) |has| #0# (-38 (-401 (-553))))) ((((-892 |#1|)) . T)) @@ -2220,14 +2300,14 @@ ((((-845)) . T)) ((($) . T)) ((($) . T)) -(-4028 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343)) (|has| |#1| (-545))) (|has| |#1| (-357)) (|has| |#1| (-357)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1223 |#2| |#3| |#4|)) . T) (((-401 (-553))) |has| #0# (-38 (-401 (-553))))) ((((-1153 |#1| |#2| |#3|)) |has| |#1| (-357))) -(-4028 (-12 (|has| |#1| (-301)) (|has| |#1| (-891))) (|has| |#1| (-357)) (|has| |#1| (-343))) -(-4028 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) +(-3988 (-12 (|has| |#1| (-301)) (|has| |#1| (-891))) (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-882 (-1155))) (|has| |#1| (-1031))) ((((-553)) |has| |#1| (-626 (-553))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-845)) . T)) @@ -2243,6 +2323,7 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) +((((-553)) . T)) ((((-845)) . T)) (|has| |#1| (-1079)) (((|#4|) . T)) @@ -2259,27 +2340,27 @@ (((|#1|) |has| |#1| (-169))) ((((-845)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1079)))) -(((|#2|) -4028 (|has| |#2| (-6 (-4371 "*"))) (|has| |#2| (-169)))) -(-4028 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) -(-4028 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(((|#2|) -3988 (|has| |#2| (-6 (-4371 "*"))) (|has| |#2| (-169)))) +(-3988 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) +(-3988 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (|has| |#2| (-833)) (|has| |#2| (-891)) (|has| |#1| (-891)) (((|#2|) |has| |#2| (-169))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((((-1230 |#1| |#2| |#3|)) |has| |#1| (-357))) ((((-845)) . T)) ((((-845)) . T)) ((((-529)) . T) (((-553)) . T) (((-874 (-553))) . T) (((-373)) . T) (((-220)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) -((((-2 (|:| -2669 (-1137)) (|:| -3359 (-52)))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) +((((-2 (|:| -2578 (-1137)) (|:| -3256 (-52)))) . T)) (((|#1|) . T)) ((((-845)) . T)) (((|#1| |#2|) . T)) (((|#1| (-401 (-553))) . T)) (((|#1|) . T)) -(-4028 (|has| |#1| (-284)) (|has| |#1| (-357))) +(-3988 (|has| |#1| (-284)) (|has| |#1| (-357))) ((((-141)) . T)) ((((-401 |#2|)) . T) (((-401 (-553))) . T) (($) . T)) (|has| |#1| (-831)) @@ -2294,7 +2375,7 @@ ((((-401 (-553))) . T) (($) . T)) ((((-845)) . T)) ((((-845)) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-845)) . T)) ((((-845)) . T)) @@ -2305,8 +2386,9 @@ (((|#1|) . T)) ((((-630 (-141))) . T) (((-1137)) . T)) ((((-845)) . T)) -((((-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))) . T)) +((((-1137)) . T)) ((((-1155) |#1|) |has| |#1| (-507 (-1155) |#1|)) ((|#1| |#1|) |has| |#1| (-303 |#1|))) +((((-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))) . T)) (|has| |#1| (-833)) ((((-845)) . T)) ((((-529)) |has| |#1| (-601 (-529)))) @@ -2317,21 +2399,21 @@ ((((-845)) . T) (((-630 |#4|)) . T)) (((|#2|) . T)) ((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T)) -((((-401 (-553))) . T) (((-553)) . T) (((-599 $)) . T)) -(-4028 (|has| |#4| (-169)) (|has| |#4| (-712)) (|has| |#4| (-831)) (|has| |#4| (-1031))) -(-4028 (|has| |#3| (-169)) (|has| |#3| (-712)) (|has| |#3| (-831)) (|has| |#3| (-1031))) +((($) . T) (((-553)) . T) (((-401 (-553))) . T) (((-599 $)) . T)) +(-3988 (|has| |#4| (-169)) (|has| |#4| (-712)) (|has| |#4| (-831)) (|has| |#4| (-1031))) +(-3988 (|has| |#3| (-169)) (|has| |#3| (-712)) (|has| |#3| (-831)) (|has| |#3| (-1031))) ((((-1155) (-52)) . T)) -(-4028 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(-3988 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4028 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) -(-4028 (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +(-3988 (|has| |#2| (-25)) (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +(-3988 (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-831)) (|has| |#2| (-1031))) (|has| |#1| (-891)) -((((-892 |#1|)) . T)) +((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) (|has| |#1| (-891)) -(((|#1|) . T) (((-553)) -4028 (|has| (-401 (-553)) (-1020 (-553))) (|has| |#1| (-1020 (-553)))) (((-401 (-553))) . T)) +(((|#1|) . T) (((-553)) . T) (((-401 (-553))) . T) (($) . T)) (((|#2|) . T)) (((|#1|) . T)) ((((-845)) . T)) @@ -2344,12 +2426,12 @@ (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (|has| |#1| (-806)) (((#0=(-892 |#1|) #0#) . T) (($ $) . T) ((#1=(-401 (-553)) #1#) . T)) ((((-401 |#2|)) . T)) (|has| |#1| (-831)) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) +((((-1178 |#1|)) . T) (((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-1079)))) (((|#1| |#1|) . T) ((#0=(-401 (-553)) #0#) . T) ((#1=(-553) #1#) . T) (($ $) . T)) ((((-892 |#1|)) . T) (($) . T) (((-401 (-553))) . T)) (((|#2|) |has| |#2| (-1031)) (((-553)) -12 (|has| |#2| (-626 (-553))) (|has| |#2| (-1031)))) @@ -2359,26 +2441,26 @@ (|has| |#1| (-142)) (((|#2|) . T)) ((((-845)) . T)) -((((-684)) . T) (((-401 (-553))) . T) (((-553)) . T)) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) -((((-2 (|:| -2669 (-1155)) (|:| -3359 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2669 (-1155)) (|:| -3359 #0#))) . T)) +((((-401 (-553))) . T) (((-684)) . T) (($) . T) (((-553)) . T)) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) +((((-2 (|:| -2578 (-1155)) (|:| -3256 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2578 (-1155)) (|:| -3256 #0#))) . T)) (|has| |#1| (-343)) ((((-553)) . T)) ((((-845)) . T)) (((#0=(-1224 |#1| |#2| |#3| |#4|) $) |has| #0# (-280 #0# #0#))) (|has| |#1| (-357)) (((#0=(-1061) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-343))) (((#0=(-401 (-553)) #0#) . T) ((#1=(-684) #1#) . T) (($ $) . T)) ((((-310 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-401 (-553))) |has| |#1| (-357))) (|has| |#1| (-1079)) (((|#1|) . T)) -(((|#1|) -4028 (|has| |#2| (-361 |#1|)) (|has| |#2| (-411 |#1|)))) -(((|#1|) -4028 (|has| |#2| (-361 |#1|)) (|has| |#2| (-411 |#1|)))) +(((|#1|) -3988 (|has| |#2| (-361 |#1|)) (|has| |#2| (-411 |#1|)))) +(((|#1|) -3988 (|has| |#2| (-361 |#1|)) (|has| |#2| (-411 |#1|)))) (((|#2|) . T)) ((((-401 (-553))) . T) (((-684)) . T) (($) . T)) ((((-568)) . T)) @@ -2386,21 +2468,22 @@ (|has| |#2| (-228)) ((((-847 |#1|)) . T)) ((((-1155)) |has| |#1| (-882 (-1155))) ((|#3|) . T)) +((((-630 $)) . T) ((|#1|) . T) ((|#2|) . T) ((|#3|) . T) ((|#4|) . T) ((|#5|) . T)) (-12 (|has| |#1| (-357)) (|has| |#2| (-1004))) ((((-1153 |#1| |#2| |#3|)) |has| |#1| (-357))) ((((-845)) . T)) (|has| |#1| (-357)) (|has| |#1| (-357)) ((((-401 (-553))) . T) (($) . T) (((-401 |#1|)) . T) ((|#1|) . T)) -((((-115 |#1|)) . T)) +((((-553)) . T) (((-115 |#1|)) . T) (($) . T) (((-401 (-553))) . T)) ((((-553)) . T)) (((|#3|) . T)) (|has| |#1| (-1079)) (((|#2|) . T)) (((|#1|) . T)) ((((-553)) . T)) -(((|#2|) . T) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) |has| |#1| (-1020 (-553))) ((|#1|) . T)) -(-4028 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) +(((|#2|) . T) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) ((|#1|) . T) (($) . T) (((-553)) . T)) +(-3988 (|has| |#1| (-169)) (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (((|#2|) . T) (((-553)) |has| |#2| (-626 (-553)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2428,7 +2511,7 @@ ((((-141)) . T)) ((($) . T)) ((($) . T) ((|#1|) . T) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) -((((-373)) . T) (((-553)) . T) (((-401 (-553))) . T)) +((((-373)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) ((($) . T) ((|#1|) . T) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) (((|#1|) . T)) (|has| |#2| (-891)) @@ -2438,7 +2521,7 @@ (|has| |#2| (-1004)) ((($) . T)) (|has| |#1| (-891)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2446,26 +2529,28 @@ ((($) . T)) (|has| |#1| (-357)) ((((-892 |#1|)) . T)) -((($) -4028 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) +((($) -3988 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) |has| |#1| (-169)) (((-401 (-553))) |has| |#1| (-38 (-401 (-553))))) ((($ $) . T) ((#0=(-401 (-553)) #0#) . T)) -(-4028 (|has| |#1| (-362)) (|has| |#1| (-833))) +(-3988 (|has| |#1| (-362)) (|has| |#1| (-833))) (((|#1|) . 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T)) +(((#0=(-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) #0#) |has| (-2 (|:| -2578 (-1155)) (|:| -3256 (-52))) (-303 (-2 (|:| -2578 (-1155)) (|:| -3256 (-52)))))) +((((-1137)) . T)) (|has| |#1| (-891)) (|has| |#2| (-357)) -(-4028 (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +(-3988 (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) ((((-166 (-373))) . T) (((-220)) . T) (((-373)) . T)) ((((-845)) . T)) (((|#1|) . T)) @@ -2482,11 +2567,11 @@ (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) -(-4028 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343))) (|has| |#1| (-38 (-401 (-553)))) (-12 (|has| |#1| (-538)) (|has| |#1| (-814))) ((((-845)) . T)) -((((-1155)) -4028 (-12 (|has| |#1| (-15 * (|#1| (-553) |#1|))) (|has| |#1| (-882 (-1155)))) (-12 (|has| |#1| (-357)) (|has| |#2| (-882 (-1155)))))) +((((-1155)) -3988 (-12 (|has| |#1| (-15 * (|#1| (-553) |#1|))) (|has| |#1| (-882 (-1155)))) (-12 (|has| |#1| (-357)) (|has| |#2| (-882 (-1155)))))) (|has| |#1| (-357)) ((((-1155)) -12 (|has| |#1| (-15 * (|#1| (-401 (-553)) |#1|))) (|has| |#1| (-882 (-1155))))) (|has| |#1| (-357)) @@ -2496,7 +2581,8 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-357))) (((|#2|) |has| |#1| (-357))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +((((-553)) . T) (($) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) @@ -2521,9 +2607,9 @@ ((((-373)) -12 (|has| |#1| (-357)) (|has| |#2| (-868 (-373)))) (((-553)) -12 (|has| |#1| (-357)) (|has| |#2| (-868 (-553))))) (|has| |#1| (-357)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) (|has| |#1| (-357)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) (|has| |#1| (-357)) (|has| |#1| (-545)) (((|#1|) . T)) @@ -2531,23 +2617,23 @@ (((|#3|) . T)) ((((-1137)) . T) (((-1155)) . T) (((-220)) . T) (((-553)) . T)) (((|#1|) . T)) -((((-401 (-553))) |has| #0=(-401 |#2|) (-1020 (-401 (-553)))) (((-553)) |has| #0# (-1020 (-553))) ((#0#) . T)) -(-4028 (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +((((-401 |#2|)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) +(-3988 (|has| |#2| (-129)) (|has| |#2| (-169)) (|has| |#2| (-357)) (|has| |#2| (-779)) (|has| |#2| (-831)) (|has| |#2| (-1031))) (((|#2|) . T)) (((|#2|) . T)) -(-4028 (|has| |#2| (-169)) (|has| |#2| (-712)) (|has| |#2| (-831)) (|has| |#2| (-1031))) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) -((((-2 (|:| -2669 (-1137)) (|:| -3359 |#1|))) . T)) -((((-2 (|:| -2669 |#1|) (|:| -3359 |#2|))) . T)) +(-3988 (|has| |#2| (-169)) (|has| |#2| (-712)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) +((((-2 (|:| -2578 (-1137)) (|:| -3256 |#1|))) . T)) +((((-2 (|:| -2578 |#1|) (|:| -3256 |#2|))) . T)) (|has| |#1| (-38 (-401 (-553)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-401 (-553)))) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) (|has| |#1| (-144)) ((((-1137) |#1|) . T)) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) (|has| |#1| (-144)) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-362))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-362))) (|has| |#1| (-144)) ((((-570 |#1|)) . T)) ((($) . T)) @@ -2555,7 +2641,7 @@ (|has| |#1| (-545)) (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553)))) -(-4028 (|has| |#1| (-142)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-343))) (|has| |#1| (-144)) ((((-845)) . T)) ((($) . T)) @@ -2579,9 +2665,10 @@ (|has| |#1| (-1079)) (|has| |#1| (-777)) (|has| |#1| (-777)) -((((-892 |#1|)) . T)) +((((-845)) . T)) +((((-892 |#1|)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) ((((-529)) |has| |#1| (-601 (-529)))) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-833)) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-833)) (|has| |#1| (-1079)))) ((((-113)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2602,7 +2689,7 @@ ((((-553)) . T)) ((((-845)) . T)) ((((-553)) . T)) -(-4028 (|has| |#2| (-779)) (|has| |#2| (-831))) +(-3988 (|has| |#2| (-779)) (|has| |#2| (-831))) ((((-166 (-373))) . T) (((-220)) . T) (((-373)) . T)) ((((-845)) . T)) ((((-845)) . T)) @@ -2614,15 +2701,15 @@ (((|#1|) . T) (($) . T) (((-401 (-553))) . 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T)) ((((-845)) . T)) @@ -2635,8 +2722,8 @@ (((|#1|) . T)) (|has| |#1| (-545)) ((((-401 |#2|)) . T) (((-401 (-553))) . T) (($) . T)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) ((((-373)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2645,7 +2732,7 @@ (|has| |#1| (-545)) (|has| |#1| (-1079)) ((((-766 |#1| (-847 |#2|))) |has| (-766 |#1| (-847 |#2|)) (-303 (-766 |#1| (-847 |#2|))))) -(-4028 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) +(-3988 (|has| |#2| (-445)) (|has| |#2| (-545)) (|has| |#2| (-891))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2655,15 +2742,15 @@ (|has| |#1| (-228)) (((|#1| (-524 (-1067 (-1155)))) . T)) (|has| |#2| (-357)) -((((-570 |#1|)) . T)) -((($) . T)) -((((-2 (|:| -2669 (-1137)) (|:| -3359 (-52)))) . T)) -(((|#1|) . T)) +((((-570 |#1|)) . T) (((-401 (-553))) . T) (($) . T) (((-553)) . T)) +((((-553)) . T) (((-401 (-553))) . T) (($) . T)) +((((-2 (|:| -2578 (-1137)) (|:| -3256 (-52)))) . T)) (((|#1|) . T)) +(((|#1|) . T) (((-553)) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079)))) ((((-845)) . T)) ((((-845)) . T)) -(-4028 (|has| |#3| (-779)) (|has| |#3| (-831))) +(-3988 (|has| |#3| (-779)) (|has| |#3| (-831))) ((((-845)) . T)) ((((-1099)) . T) (((-845)) . T)) ((((-845)) . T)) @@ -2674,12 +2761,12 @@ ((((-553)) . T)) (((|#3|) . T)) ((((-845)) . T)) -(-4028 (|has| |#1| (-301)) (|has| |#1| (-357)) (|has| |#1| (-343))) -((((-401 (-553))) |has| |#2| (-1020 (-401 (-553)))) (((-553)) |has| |#2| (-1020 (-553))) ((|#2|) . T) (((-847 |#1|)) . T)) -((((-1104 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-553)) |has| |#1| (-1020 (-553))) (((-401 (-553))) |has| |#1| (-1020 (-401 (-553))))) -((((-1151 |#1|)) . T) (((-1061)) . T) ((|#1|) . 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T) (($) -3988 (|has| |#1| (-357)) (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) (((-1061)) . T) ((|#1|) . T) (((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-1020 (-401 (-553)))))) +(-3988 (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-169)) (|has| |#1| (-545)) (|has| |#1| (-1031))) +((((-1104 |#1| (-1155))) . T) (((-553)) . T) (((-1067 (-1155))) . T) (($) -3988 (|has| |#1| (-445)) (|has| |#1| (-545)) (|has| |#1| (-891))) ((|#1|) . T) (((-401 (-553))) -3988 (|has| |#1| (-38 (-401 (-553)))) (|has| |#1| (-1020 (-401 (-553))))) (((-1155)) . T)) (((#0=(-570 |#1|) #0#) . T) (($ $) . T) ((#1=(-401 (-553)) #1#) . T)) ((($ $) . T) ((#0=(-401 (-553)) #0#) . T)) (((|#1|) |has| |#1| (-169))) @@ -2689,11 +2776,11 @@ ((($) . T) (((-401 (-553))) . T)) (((|#2|) |has| |#2| (-6 (-4371 "*")))) (((|#1|) . T)) -((((-401 (-553))) |has| |#1| (-1020 (-401 (-553)))) (((-553)) |has| |#1| (-1020 (-553))) ((|#1|) . 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T)) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-343))) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-343))) +((((-1160)) . T)) +((((-1160)) . T)) (|has| |#1| (-357)) (|has| |#1| (-357)) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-343))) -(-4028 (|has| |#1| (-169)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-169)) (|has| |#1| (-545))) (((|#1| (-553)) . T)) (((|#1| (-401 (-553))) . T)) (((|#1| (-757)) . T)) @@ -3169,16 +3290,16 @@ ((((-874 (-373))) . T) (((-874 (-553))) . T) (((-1155)) . T) (((-529)) . T)) (((|#1|) . T)) ((((-845)) . 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T)) -(-4028 (|has| |#2| (-169)) (|has| |#2| (-712)) (|has| |#2| (-831)) (|has| |#2| (-1031))) +(-3988 (|has| |#2| (-169)) (|has| |#2| (-712)) (|has| |#2| (-831)) (|has| |#2| (-1031))) ((((-1155)) -12 (|has| |#2| (-882 (-1155))) (|has| |#2| (-1031)))) -(-4028 (-12 (|has| |#1| (-466)) (|has| |#2| (-466))) (-12 (|has| |#1| (-712)) (|has| |#2| (-712)))) +(-3988 (-12 (|has| |#1| (-466)) (|has| |#2| (-466))) (-12 (|has| |#1| (-712)) (|has| |#2| (-712)))) (|has| |#1| (-142)) (|has| |#1| (-144)) (|has| |#1| (-357)) @@ -3202,10 +3323,12 @@ ((((-1137) (-1155) (-553) (-220) (-845)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -((((-113)) . T) ((|#1|) . T)) -(-4028 (|has| |#1| (-343)) (|has| |#1| (-362))) +((((-553)) . T) ((|#2|) |has| |#2| (-169))) +((((-113)) . T) ((|#1|) . T) (((-553)) . T)) +(-3988 (|has| |#1| (-343)) (|has| |#1| (-362))) (((|#1| |#2|) . T)) -((((-553)) . T) (((-401 (-553))) . T)) +((((-220)) . T)) +((((-401 (-553))) . T) (($) . T) (((-553)) . T)) ((($) . T) ((|#1|) . T)) ((((-845)) . T)) ((($) . T) (((-401 (-553))) |has| |#1| (-38 (-401 (-553)))) ((|#1|) . T)) @@ -3214,7 +3337,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-529)) |has| |#1| (-601 (-529)))) -((((-845)) -4028 (|has| |#1| (-600 (-845))) (|has| |#1| (-833)) (|has| |#1| (-1079)))) +((((-845)) -3988 (|has| |#1| (-600 (-845))) (|has| |#1| (-833)) (|has| |#1| (-1079)))) ((($) . T) (((-401 (-553))) . T)) (|has| |#1| (-891)) (|has| |#1| (-891)) @@ -3223,14 +3346,16 @@ ((((-845)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-169))) -(-4028 (|has| |#1| (-357)) (|has| |#1| (-545))) -(-4028 (|has| |#1| (-21)) (|has| |#1| (-831))) +(((|#1|) . T) (((-553)) . T)) +((((-1160)) . T)) +(-3988 (|has| |#1| (-357)) (|has| |#1| (-545))) +(-3988 (|has| |#1| (-21)) (|has| |#1| (-831))) (((|#2|) . T)) -(-4028 (|has| |#1| (-21)) (|has| |#1| (-831))) +(-3988 (|has| |#1| (-21)) (|has| |#1| (-831))) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (((|#1|) . T)) -((((-845)) -4028 (-12 (|has| |#1| (-600 (-845))) (|has| |#2| (-600 (-845)))) (-12 (|has| |#1| (-1079)) (|has| |#2| (-1079))))) +((((-845)) -3988 (-12 (|has| |#1| (-600 (-845))) (|has| |#2| (-600 (-845)))) (-12 (|has| |#1| (-1079)) (|has| |#2| (-1079))))) ((((-401 |#2|) |#3|) . T)) ((((-401 (-553))) . T) (($) . T)) (|has| |#1| (-38 (-401 (-553)))) @@ -3242,18 +3367,19 @@ (((|#1|) . T) (((-401 (-553))) . T) (((-553)) . T) (($) . T)) (((#0=(-553) #0#) . T)) ((($) . T) (((-401 (-553))) . T)) -(-4028 (|has| |#4| (-169)) (|has| |#4| (-712)) (|has| |#4| (-831)) (|has| |#4| (-1031))) -(-4028 (|has| |#3| (-169)) (|has| |#3| (-712)) (|has| |#3| (-831)) (|has| |#3| (-1031))) +(-3988 (|has| |#4| (-169)) (|has| |#4| (-712)) (|has| |#4| (-831)) (|has| |#4| (-1031))) +(-3988 (|has| |#3| (-169)) (|has| |#3| (-712)) (|has| |#3| (-831)) (|has| |#3| (-1031))) ((((-845)) . T) (((-1160)) . 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130803) ((-569 . -284) T) ((-553 . -284) T) ((-662 . -1020) 130787) ((-488 . -284) T) ((-134 . -463) 130742) ((-48 . -1079) T) ((-698 . -226) 130726) ((-853 . -882) NIL) ((-1211 . -868) NIL) ((-871 . -101) T) ((-867 . -101) T) ((-382 . -1079) T) ((-166 . -371) 130710) ((-166 . -332) 130694) ((-1211 . -1020) 130574) ((-838 . -1020) 130470) ((-1121 . -101) T) ((-638 . -129) T) ((-116 . -507) 130378) ((-647 . -778) 130357) ((-647 . -781) 130336) ((-560 . -1020) 130318) ((-288 . -1245) 130288) ((-848 . -101) T) ((-945 . -545) 130267) ((-1186 . -1037) 130150) ((-475 . -626) 130056) ((-886 . -1079) T) ((-1006 . -703) 129993) ((-697 . -1037) 129958) ((-604 . -101) T) ((-589 . -34) T) ((-1126 . -1192) T) ((-1186 . -110) 129827) ((-467 . -633) 129724) ((-348 . -703) 129669) ((-166 . -882) 129628) ((-684 . -284) T) ((-679 . -169) T) ((-697 . -110) 129584) ((-1266 . -1038) T) ((-1211 . -371) 129568) ((-412 . -1196) 129546) ((-1097 . -600) 129528) ((-307 . -831) NIL) ((-412 . -545) T) ((-220 . -301) T) ((-1201 . -777) 129481) ((-1201 . -780) 129434) ((-1222 . -712) T) ((-1201 . -712) T) ((-48 . -703) 129399) ((-220 . -1004) T) ((-345 . -1245) 129376) ((-1224 . -405) 129342) ((-704 . -712) T) ((-1211 . -882) 129285) ((-1186 . -603) 129167) ((-111 . -600) 129149) ((-111 . -601) 129131) ((-704 . -466) T) ((-697 . -603) 129081) ((-475 . -21) 128991) ((-126 . -482) 128975) ((-120 . -482) 128959) ((-475 . -25) 128810) ((-610 . -284) T) ((-574 . -1037) 128785) ((-431 . -1079) T) ((-1042 . -301) T) ((-116 . -284) T) ((-1083 . -101) T) ((-985 . -101) T) ((-574 . -110) 128753) ((-1121 . -303) 128691) ((-1186 . -1031) T) ((-1042 . -1004) T) ((-65 . -1192) T) ((-1035 . -25) T) ((-1035 . -21) T) ((-697 . -1031) T) ((-379 . -21) T) ((-379 . -25) T) ((-679 . -507) NIL) ((-1006 . -169) T) ((-697 . -238) T) ((-1042 . -538) T) ((-499 . -101) T) ((-495 . -101) T) ((-348 . -169) T) ((-337 . -600) 128673) ((-388 . -600) 128655) ((-467 . -712) T) ((-1099 . -831) T) ((-874 . -1020) 128623) ((-107 . -833) T) ((-643 . -1037) 128607) ((-480 . -129) T) ((-1224 . -1038) T) ((-212 . -129) T) ((-1135 . -101) 128585) ((-98 . -1079) T) ((-240 . -651) 128569) ((-240 . -636) 128553) ((-643 . -110) 128532) ((-574 . -603) 128516) ((-310 . -405) 128500) ((-240 . -367) 128484) ((-1138 . -230) 128431) ((-981 . -226) 128415) ((-73 . -1192) T) ((-48 . -169) T) ((-686 . -381) T) ((-686 . -140) T) ((-1261 . -101) T) ((-1172 . -603) 128397) ((-1066 . -1037) 128240) ((-258 . -891) 128219) ((-242 . -891) 128198) ((-768 . -1037) 128021) ((-766 . -1037) 127864) ((-595 . -1192) T) ((-1143 . -600) 127846) ((-1066 . -110) 127675) ((-1028 . -101) T) ((-468 . -1192) T) ((-454 . -1037) 127646) ((-447 . -1037) 127489) ((-649 . -633) 127473) ((-853 . -301) T) ((-768 . -110) 127282) ((-766 . -110) 127111) ((-349 . -633) 127063) ((-346 . -633) 127015) ((-338 . -633) 126967) ((-258 . -633) 126892) ((-242 . -633) 126817) ((-1137 . -833) T) ((-1067 . -1020) 126801) ((-454 . -110) 126762) ((-447 . -110) 126591) 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. -703) 108422) ((-1186 . -47) 108391) ((-244 . -129) T) ((-245 . -129) T) ((-1083 . -1079) T) ((-985 . -1079) T) ((-61 . -600) 108373) ((-1146 . -833) NIL) ((-1006 . -778) T) ((-1006 . -781) T) ((-1266 . -1037) 108360) ((-1266 . -110) 108345) ((-852 . -633) 108332) ((-1230 . -25) T) ((-1230 . -21) T) ((-1223 . -21) T) ((-1223 . -25) T) ((-1202 . -21) T) ((-1202 . -25) T) ((-1009 . -148) 108316) ((-854 . -806) 108295) ((-854 . -902) T) ((-698 . -280) 108222) ((-584 . -21) T) ((-584 . -25) T) ((-583 . -21) T) ((-40 . -712) T) ((-217 . -507) 108155) ((-583 . -25) T) ((-469 . -148) 108139) ((-456 . -148) 108123) ((-903 . -780) T) ((-903 . -712) T) ((-757 . -779) T) ((-757 . -780) T) ((-499 . -1079) T) ((-495 . -1079) T) ((-757 . -712) T) ((-220 . -357) T) ((-1135 . -1079) 108101) ((-853 . -1196) T) ((-639 . -600) 108083) ((-853 . -545) T) ((-679 . -362) NIL) ((-1266 . -603) 108065) ((-353 . -1245) 108049) ((-655 . -101) T) ((-347 . -1245) 108033) ((-339 . -1245) 108017) ((-1261 . -1079) 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-390) T) ((-76 . -389) T) ((-638 . -641) 84737) ((-138 . -1192) T) ((-853 . -144) T) ((-853 . -142) NIL) ((-1191 . -92) T) ((-345 . -1031) T) ((-69 . -377) T) ((-69 . -389) T) ((-1144 . -101) T) ((-655 . -507) 84670) ((-674 . -303) 84608) ((-945 . -38) 84505) ((-721 . -38) 84475) ((-539 . -303) 84279) ((-310 . -1192) T) ((-345 . -228) T) ((-345 . -238) T) ((-307 . -1192) T) ((-283 . -1079) T) ((-1159 . -600) 84261) ((-697 . -1196) T) ((-1135 . -636) 84245) ((-1186 . -545) 84224) ((-697 . -545) T) ((-310 . -866) 84208) ((-310 . -868) 84133) ((-307 . -866) 84094) ((-307 . -868) NIL) ((-785 . -303) 84059) ((-313 . -703) 83900) ((-318 . -317) 83877) ((-478 . -101) T) ((-467 . -25) T) ((-467 . -21) T) ((-412 . -38) 83851) ((-310 . -1020) 83514) ((-220 . -1177) T) ((-220 . -1180) T) ((-3 . -600) 83496) ((-307 . -1020) 83426) ((-2 . -1079) T) ((-2 . |RecordCategory|) T) ((-819 . -600) 83408) ((-1092 . -1038) 83338) ((-569 . -902) T) ((-553 . -806) T) ((-553 . -902) T) ((-488 . -902) T) ((-134 . -1020) 83322) ((-220 . -94) T) ((-74 . -434) T) ((-74 . -389) T) ((0 . -600) 83304) ((-166 . -144) 83283) ((-166 . -142) 83234) ((-220 . -35) T) ((-49 . -600) 83216) ((-470 . -1038) T) ((-480 . -226) 83198) ((-477 . -950) 83182) ((-475 . -831) 83161) ((-212 . -226) 83143) ((-80 . -434) T) ((-80 . -389) T) ((-1125 . -34) T) ((-801 . -169) 83122) ((-717 . -101) T) ((-1008 . -600) 83089) ((-493 . -280) 83064) ((-310 . -371) 83033) ((-307 . -371) 82994) ((-307 . -332) 82955) ((-1064 . -600) 82937) ((-802 . -931) 82884) ((-647 . -129) T) ((-1211 . -142) 82863) ((-1211 . -144) 82842) ((-1153 . -101) T) ((-1152 . -101) T) ((-1146 . -101) T) ((-1138 . -1079) T) ((-1105 . -101) T) ((-217 . -34) T) ((-283 . -703) 82829) ((-1138 . -597) 82805) ((-581 . -303) NIL) ((-477 . -1079) 82783) ((-384 . -600) 82765) ((-503 . -833) T) ((-1129 . -224) 82715) ((-1230 . -1229) 82699) ((-1230 . -1216) 82676) ((-1223 . -1221) 82637) ((-1223 . -1216) 82607) ((-1223 . -1219) 82591) ((-1202 . -1200) 82552) 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. -601) 34073) ((-220 . -1079) T) ((-986 . -600) 34033) ((-953 . -600) 33993) ((-953 . -601) 33968) ((-896 . -600) 33950) ((-684 . -144) T) ((-686 . -902) T) ((-686 . -806) T) ((-421 . -600) 33932) ((-1099 . -21) T) ((-1099 . -25) T) ((-655 . -371) 33916) ((-115 . -902) T) ((-854 . -226) 33900) ((-77 . -1192) T) ((-125 . -124) 33884) ((-1035 . -34) T) ((-1260 . -1020) 33858) ((-1258 . -1020) 33815) ((-1211 . -1038) T) ((-838 . -1038) T) ((-475 . -777) 33794) ((-349 . -1130) 33773) ((-346 . -1130) 33752) ((-338 . -1130) 33731) ((-475 . -780) 33682) ((-475 . -779) 33661) ((-222 . -34) T) ((-475 . -712) 33571) ((-785 . -603) 33419) ((-59 . -482) 33403) ((-560 . -1038) T) ((-1151 . -169) 33294) ((-1104 . -169) 33205) ((-1042 . -1079) T) ((-1066 . -931) 33150) ((-934 . -1079) T) ((-803 . -633) 33101) ((-768 . -931) 33070) ((-699 . -1079) T) ((-766 . -931) 33037) ((-509 . -276) 33021) ((-655 . -882) 32980) ((-474 . -1079) T) ((-447 . -931) 32947) ((-78 . -1192) T) ((-349 . -38) 32912) ((-346 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index bb79d261..625ea913 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3436193626) +(30 . 3437447578) (4372 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -471,659 +471,658 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |suffix?| |rightUnit| |finiteBound| |e04ucf| - |expandLog| |rightMinimalPolynomial| |saturate| |floor| |callForm?| - |expressIdealMember| |minPol| |result| |expenseOfEvaluation| - |coerceImages| |deepExpand| |cTan| |quatern| |lhs| |roughBasicSet| - |divisors| |hasSolution?| |prefix?| |properties| |factorial| - 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|addBadValue| |autoCoerce| |pseudoQuotient| |rightScalarTimes!| - |composites| |d02bhf| |laguerre| |physicalLength| |seriesSolve| |move| - |d01fcf| |convert| |rectangularMatrix| |viewDeltaYDefault| |monomials| - |isPlus| |shade| |createLowComplexityTable| |hMonic| |cSinh| |show| - |sizeMultiplication| |dominantTerm| |rootBound| |evenInfiniteProduct| - |newSubProgram| |solve1| |rotate!| |subscript| |color| |shallowCopy| - |aromberg| |rename!| |primitivePart!| |f01rcf| - |removeIrreducibleRedundantFactors| |isTimes| |vspace| |trace| - |curveColorPalette| |zeroDim?| |rightOne| |scale| |createThreeSpace| - |entries| |closedCurve?| |putColorInfo| |coord| |logpart| |monomial?| - |setnext!| |every?| |radicalEigenvector| |doubleRank| |df2fi| - |torsion?| |elliptic?| |denominators| |removeDuplicates!| - |expextendedint| |newTypeLists| |monicDivide| |tablePow| |octon| - |node?| |curve?| |OMlistCDs| |roughUnitIdeal?| |divisorCascade| - |seriesToOutputForm| |nor| |rk4| |numFunEvals3D| |epilogue| - |completeHermite| |realRoots| |contours| |ref| |UpTriBddDenomInv| - |kovacic| |constantKernel| |viewZoomDefault| - |ScanFloatIgnoreSpacesIfCan| |csc2sin| |makeSketch| |tanIfCan| - LODO2FUN |drawStyle| |extractIfCan| |OMputEndAtp| |dot| - |indicialEquations| |shift| |indiceSubResultant| |d01aqf| - |moreAlgebraic?| |midpoint| |stoseInvertible?reg| |compBound| - |freeOf?| |setTex!| |complexEigenvalues| = |scopes| |setProperty!| - |constantToUnaryFunction| |modTree| |integrate| |innerEigenvectors| - |countable?| |lighting| |addPoint| |LagrangeInterpolation| |rombergo| - |expt| |rightAlternative?| |product| |s18adf| |sumSquares| - |OMgetVariable| |and?| < |integralBasisAtInfinity| |leftDivide| - |leftCharacteristicPolynomial| |stronglyReduce| |genericLeftNorm| - |plusInfinity| |generalSqFr| |df2mf| |conditionsForIdempotents| - |representationType| |functionIsContinuousAtEndPoints| > - |clearTheFTable| |ScanFloatIgnoreSpaces| |systemCommand| - |nextsousResultant2| |minusInfinity| |addPoint2| |hexDigit| - |numberOfFractionalTerms| |deriv| |listexp| <= |fi2df| |stack| - |conjugates| |algebraicVariables| |insertBottom!| |groebnerIdeal| - |solveid| |tubeRadius| |seed| |LyndonCoordinates| >= - |subResultantGcdEuclidean| |jordanAlgebra?| |s21baf| |s13adf| - |oddintegers| |rangeIsFinite| |pointLists| |totalGroebner| - |represents| |chvar| |normalizeIfCan| |fortranTypeOf| |gcdPrimitive| - |normal| |primPartElseUnitCanonical!| |times| |c02agf| - |constantOperator| |iisqrt3| |minus!| |semicolonSeparate| - |rightDiscriminant| |unitNormal| |clipParametric| |karatsubaOnce| - |clearCache| |point| |clearFortranOutputStack| |doubleComplex?| - |expintegrate| |ipow| + |leftScalarTimes!| |taylorQuoByVar| |e02ahf| - |showFortranOutputStack| |inR?| |s17agf| |outputGeneral| |sqfrFactor| - |createPrimitiveNormalPoly| |type| - |symbolTable| |zag| |romberg| - |oddInfiniteProduct| |matrixConcat3D| |enumerate| |makeprod| - |rubiksGroup| |zero?| |att2Result| / |quadratic| |bitCoef| - |totalfract| |paren| |tab| |series| |monom| |pdf2ef| - 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|computePowers| |possiblyInfinite?| |sin2csc| |showSummary| - |useEisensteinCriterion| |inRadical?| |setValue!| |loopPoints| - |checkPrecision| |viewWriteAvailable| |binomThmExpt| |extractBottom!| - |linGenPos| |OMgetEndBind| |sn| |probablyZeroDim?| |nlde| |cfirst| - |arrayStack| |numberOfNormalPoly| |hcrf| |commutative?| |predicate| - |errorKind| |setlast!| |showAttributes| |d02bbf| |mapGen| |logIfCan| - |iiexp| |separateFactors| |iicot| |init| |twoFactor| |operation| - |scalarTypeOf| |uniform| |testModulus| |s17dgf| - |firstUncouplingMatrix| |factorByRecursion| |cyclotomicDecomposition| - |permutationRepresentation| |OMclose| |quoByVar| |exponents| |iilog| - |s17dhf| |ode2| |bezoutResultant| - |solveLinearPolynomialEquationByFractions| |position!| - |leadingCoefficientRicDE| |tanhIfCan| |fill!| |nthExponent| |s18aef| - |byteBuffer| |fortranDouble| |pile| |lazy?| |eyeDistance| |rootRadius| - |c05adf| |coerceP| |max| |delete| |splitSquarefree| |parametric?| - |unrankImproperPartitions1| |mpsode| |list?| |safeFloor| |eof?| - 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|f2st| |index?| |collectUnder| |mapExpon| |s14baf| - |univariatePolynomials| |extractClosed| |oneDimensionalArray| |subst| - |asinhIfCan| |Ei| |outputAsFortran| |ellipticCylindrical| |maxdeg| - |precision| |PDESolve| |padicallyExpand| |orbit| |linear| |positive?| - GE |removeCosSq| |leftFactorIfCan| |semiResultantEuclidean2| - |rightUnits| |mathieu11| |critMTonD1| |lazyEvaluate| |constantOpIfCan| - |critB| |ptree| |basicSet| |second| |imagJ| |eigenMatrix| |singRicDE| - GT |option| |scaleRoots| |startStats!| |factorSFBRlcUnit| |lists| - |f04mbf| |subresultantVector| |setleft!| |perfectSquare?| |third| - |polynomial| |setFormula!| |acscIfCan| |inverseColeman| LE - |inconsistent?| |f02aaf| |nthr| |eulerPhi| |superscript| |directory| - |elRow2!| |rightTrim| |graphCurves| |restorePrecision| |startTable!| - LT |generalTwoFactor| |heapSort| |exteriorDifferential| |atanIfCan| - |An| |charthRoot| |beauzamyBound| |leftTrim| |denominator| - |halfExtendedSubResultantGcd1| |mathieu23| |redmat| |approxNthRoot| - |polarCoordinates| |henselFact| |omError| |listYoungTableaus| |exQuo| - |Aleph| |stFuncN| |optpair| |removeZero| |groebner| |mix| - |monicDecomposeIfCan| |contract| |checkRur| |lepol| |number?| - |currentCategoryFrame| |generalizedInverse| |negative?| |erf| - |OMgetEndError| |reify| |nthFactor| |nextSublist| - |removeRoughlyRedundantFactorsInContents| |c06fqf| |push!| |tanNa| - |iiacsc| |divideExponents| |f01bsf| |ListOfTerms| - |removeRoughlyRedundantFactorsInPol| |primintegrate| |repeating?| - |removeSinhSq| |f07adf| |initiallyReduce| |numFunEvals| |power| - |wrregime| |space| |pointColor| |rk4a| |adaptive?| |lp| - |getProperties| |iflist2Result| |OMgetObject| |univariatePolynomial| - |eulerE| |recoverAfterFail| |dilog| |coth2tanh| |setleaves!| - |lazyGintegrate| |term?| |sign| |derivative| |flexible?| |intChoose| - |traverse| |lprop| |modifyPoint| |sin| |zero| |leftExactQuotient| - |minimalPolynomial| |cAsech| |radPoly| |initials| |recur| - |discriminantEuclidean| |currentScope| |powers| |interpretString| - |mkAnswer| |cos| |stop| |stoseInvertible?sqfreg| |symmetricProduct| - |head| |listLoops| |setrest!| |cardinality| |oddlambert| |critpOrder| - |symmetricTensors| |genericRightTraceForm| |nonQsign| |And| |tan| - |vconcat| |systemSizeIF| |rightFactorIfCan| |iisec| |getOperands| - |formula| |any| |dark| |doubleFloatFormat| |preprocess| - |companionBlocks| |unmakeSUP| |Or| |cot| |cyclicGroup| - |leftRankPolynomial| |writeBytes!| |listBranches| |selectPDERoutines| - |expint| |OMencodingXML| |partitions| |pattern| |orOperands| |lllip| - |Not| |sec| |removeSquaresIfCan| |quadratic?| |sturmVariationsOf| - |mapExponents| |typeList| |simpleBounds?| |pmComplexintegrate| - |dequeue!| |distdfact| |extend| |csc| |stopTableGcd!| |qinterval| - |times!| |bipolarCylindrical| |physicalLength!| |fullPartialFraction| - |palglimint0| |primlimitedint| |spherical| |makeResult| |getlo| |asin| - |bat1| |height| |commutativeEquality| |e02bdf| |linearAssociatedExp| - |loadNativeModule| |nrows| |hasTopPredicate?| |regularRepresentation| - 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|rightTraceMatrix| |f2df| |enqueue!| |getButtonValue| |rationalPoints| - |linearAssociatedOrder| |flagFactor| |f02bbf| |rationalApproximation| - |innerSolve1| |tanh| |makeUnit| |f01mcf| |returnType!| - |antiCommutator| |trivialIdeal?| |binaryFunction| |doubleDisc| |pole?| - |quasiRegular| |rename| |pushNewContour| |level| |coth| |OMreadFile| - |implies| |newReduc| |OMputEndApp| |iicsch| |linearDependence| |quote| - |outputSpacing| |e02bbf| |bivariate?| |cyclic| |LyndonBasis| |sech| - |leader| |getMatch| |indices| |rarrow| |ramified?| |connectTo| - |mainForm| |iiacosh| |returnTypeOf| |range| |createNormalElement| - |csch| |triangular?| |xor| |hex| |normDeriv2| |factorsOfDegree| - |e04mbf| |stoseLastSubResultant| |constantIfCan| |partition| |nodes| - |headReduced?| |asinh| |anticoord| |cylindrical| |frst| |lowerCase!| - |viewPosDefault| |source| |virtualDegree| |monicModulo| |li| - |setCondition!| |firstNumer| |Frobenius| |acosh| |binaryTournament| - |changeWeightLevel| |genericRightNorm| |initiallyReduced?| - |splitLinear| |torsionIfCan| |size?| |processTemplate| |equiv| |lcm| - |quasiRegular?| |tanSum| |length| |ramifiedAtInfinity?| |s15adf| - |e04dgf| |removeSuperfluousQuasiComponents| |isExpt| - |purelyTranscendental?| |list| |reduceBasisAtInfinity| - |noncommutativeJordanAlgebra?| |bumptab1| |distance| - |lazyPseudoDivide| |scripts| |buildSyntax| |close| |e02daf| - |getPickedPoints| |strongGenerators| |sinh2csch| |car| |reducedForm| - |cosIfCan| |prinshINFO| |monomialIntPoly| |append| |nextsubResultant2| - |f01qef| |stoseInternalLastSubResultant| |Gamma| |outputBinaryFile| - |rischDEsys| |cdr| |complementaryBasis| |wholePart| |children| |gcd| - |order| |univariateSolve| |totalLex| |display| |startPolynomial| - |exptMod| |baseRDE| |bat| |rightRank| |ravel| |setDifference| |leaves| - |elementary| |invertible?| |false| |BumInSepFFE| |fortran| - |unitsColorDefault| |weierstrass| |modularGcd| |findBinding| - |numberOfMonomials| |fixedPointExquo| |setIntersection| |reshape| - |setPrologue!| |iicsc| |genericRightDiscriminant| |edf2df| |simpson| - |innerint| |rroot| |exponential1| |goodPoint| |OMcloseConn| |setUnion| - |stoseSquareFreePart| |algSplitSimple| |Lazard| |OMbindTCP| |besselI| - |lazyPremWithDefault| |SturmHabichtSequence| |mesh?| - |complexIntegrate| |OMUnknownSymbol?| |apply| |integerBound| |dfRange| - |leftTraceMatrix| |palgLODE0| |paraboloidal| |commaSeparate| - |nullary?| |reorder| |pdf2df| |satisfy?| |infinityNorm| |HenselLift| - |cRationalPower| |red| |remove| |psolve| |sylvesterSequence| |#| - |qualifier| |asechIfCan| |hostPlatform| |printCode| |deepestTail| - |size| |genericRightMinimalPolynomial| |binary| |infieldint| - |numberOfDivisors| |imagI| |nonLinearPart| |key| |test| - |numberOfIrreduciblePoly| |degree| |iidsum| |musserTrials| - |reducedQPowers| |f02aef| |update| |screenResolution3D| |last| - |maxColIndex| |showTheSymbolTable| |fortranLinkerArgs| - |removeRedundantFactorsInPols| |llprop| |scalarMatrix| |showRegion| - |assoc| |rootSimp| |readBytes!| |hitherPlane| |rootNormalize| - |getSyntaxFormsFromFile| |filename| |halfExtendedResultant1| |delta| - 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|simplify| |rightCharacteristicPolynomial| |ran| |sechIfCan| |check| - |cyclicCopy| |getExplanations| |exp| |delete!| |eigenvalues| - |integralRepresents| |closedCurve| |c05nbf| |optimize| - |firstSubsetGray| |factorList| |cCsc| |htrigs| |primeFrobenius| - |redpps| |numberOfComponents| |inHallBasis?| - |solveLinearPolynomialEquationByRecursion| |cycleElt| |complex?| - |pair| |squareFreePolynomial| |zeroDimPrime?| |hash| |compile| - |f02awf| |HermiteIntegrate| |primitive?| |relationsIdeal| |create| - |argumentListOf| |neglist| |univariatePolynomialsGcds| |count| |sub| - |e02adf| |orthonormalBasis| |cPower| |copy!| |qelt| - |degreeSubResultant| |errorInfo| |minrank| |rur| |iicoth| |mathieu24| - |matrixDimensions| |f02fjf| |droot| |super| |qsetelt| |mainVariable| - |tValues| |extractSplittingLeaf| |numberOfFactors| |f02aff| |po| - |gcdcofactprim| |expandTrigProducts| |realElementary| |nthFlag| - |xRange| |lowerCase| |getZechTable| |discreteLog| |decomposeFunc| - |sequences| |showAll?| |quasiComponent| |cycleTail| |f02axf| - 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|leftPower| + |bezoutMatrix| |KrullNumber| |sortConstraints| |reduceByQuasiMonic| + |edf2df| |rewriteSetByReducingWithParticularGenerators| |s17akf| + |double| |e01baf| |laguerreL| |asimpson| |monomialIntPoly| + |lfextendedint| |column| |signature| |romberg| |messagePrint| + |semiResultantReduitEuclidean| |nthExpon| |whitePoint| + |halfExtendedResultant2| |totolex| |zeroMatrix| |preprocess| |edf2ef| + |addBadValue| |uncouplingMatrices| |ref| |constantToUnaryFunction| + |exprHasLogarithmicWeights| |OMreadFile| |cAcosh| |hexDigit| + |firstDenom| |inspect| |evenlambert| |target| |mix| |isList| + |returnTypeOf| |lifting1| |separateDegrees| |quasiMonic?| + |fillPascalTriangle| |elRow2!| |operation| |taylorIfCan| + |irreducible?| |polCase| |space| |acotIfCan| |squareFreePolynomial| + |definingPolynomial| |binding| |selectfirst| |algebraicCoefficients?| + |semiSubResultantGcdEuclidean1| |retractIfCan| |byte| |quadraticForm| + |polyred| |minPoints3D| |tValues| |setnext!| |stopTable!| |coerceP| + |parts| |idealiserMatrix| |declare!| |explicitlyFinite?| |B1solve| + |userOrdered?| |sayLength| |extendedResultant| |iFTable| + |associatorDependence| |subMatrix| |errorKind| |leftMult| + |torsionIfCan| |expandPower| |leftFactorIfCan| |binary| |input| + |simpson| |setScreenResolution| |aQuadratic| |rquo| |OMgetAttr| + |update| |iiacsch| |moebius| |library| |getGraph| BY + |supDimElseRittWu?| |mapmult| |appendPoint| |qPot| |root?| |ldf2vmf| + |parent| |ipow| |cAtan| |transcendent?| |checkForZero| |leastMonomial| + |dot| |euclideanNormalForm| |implies| |critpOrder| |kind| + |tryFunctionalDecomposition| |UpTriBddDenomInv| |dequeue!| |range| + |getDatabase| |f07fdf| |distribute| |invertible?| |cond| |op| + |resultantEuclidean| |mesh| |integralLastSubResultant| |reverse!| + |quotedOperators| |createPrimitiveElement| |mvar| |set| |constantLeft| + |expr| |segment| |intersect| |graphCurves| |leftZero| |position| + |cSec| |over| |connect| |map| |unparse| |stronglyReduce| |call| + |updatF| |selectFiniteRoutines| |leadingIdeal| |splitSquarefree| + |setelt| |f01bsf| |hermite| |zeroDimPrime?| |e01daf| |radix| + |complexEigenvectors| |purelyAlgebraic?| |infieldint| + |numericalOptimization| |isPower| |nextNormalPrimitivePoly| + |blankSeparate| |iiperm| |makeSUP| |viewDefaults| |dioSolve| + |getGoodPrime| |copy| |variable| |cyclic?| |size?| |topPredicate| + |outputAsTex| |retractable?| |quasiAlgebraicSet| |leftAlternative?| + |iterators| |closed?| |triangSolve| |indicialEquations| |iifact| + |cotIfCan| |leftScalarTimes!| |convert| |extractBottom!| |distFact| + |log2| |selectsecond| |match?| |distdfact| |ratDenom| |wreath| + |multiple?| |autoCoerce| |noKaratsuba| |squareFreePart| + |virtualDegree| |removeSinSq| |fortranInteger| |zeroDim?| + |normFactors| |symmetricTensors| |curve| |BumInSepFFE| |realZeros| + |putGraph| |randnum| |oneDimensionalArray| |returnType!| + |squareFreeFactors| |rotatex| |tubePoints| |divisorCascade| + |varselect| |cyclotomic| |pushucoef| |presuper| |components| |show| + |genericLeftNorm| |unitVector| |setright!| |perfectSquare?| + |diagonal?| |fortranReal| |cycleSplit!| |parametric?| + |partialDenominators| |ListOfTerms| |key?| |remainder| + |expressIdealMember| |sizeMultiplication| |realEigenvectors| + |flexibleArray| |trace| |OMgetFloat| |minPoints| |lowerPolynomial| + |OMputEndBVar| |iiasech| |basisOfNucleus| |createZechTable| + |numberOfDivisors| |identity| |changeNameToObjf| |sort!| |cCsc| + |areEquivalent?| |getMultiplicationMatrix| |leftNorm| + |stronglyReduced?| |stopMusserTrials| |mathieu12| |hexDigit?| + |unitNormalize| |indiceSubResultant| |cyclic| |digamma| + |taylorQuoByVar| |linGenPos| |argumentList!| |makeResult| |compose| + |transpose| |yCoord| |positiveSolve| |shift| |bombieriNorm| + |defineProperty| |rationalPower| |ODESolve| |partialFraction| + |inverse| |setProperties| |reciprocalPolynomial| = |weighted| + |genericRightTraceForm| |LowTriBddDenomInv| |unitsColorDefault| + |monicModulo| |clearDenominator| |coefficient| |rightOne| |credPol| + |cAtanh| |postfix| |minPoly| |jacobi| |genericLeftTraceForm| + |hasPredicate?| |minPol| |antiCommutator| |bernoulli| < + |possiblyNewVariety?| |solve| |associates?| |generalSqFr| |bothWays| + |maxPoints3D| |airyAi| |linearPolynomials| |asinhIfCan| + |shanksDiscLogAlgorithm| |sizePascalTriangle| > + |unrankImproperPartitions1| |stack| |seriesToOutputForm| |e04gcf| + |linSolve| |systemCommand| |primitivePart| |laurentRep| + |inGroundField?| |rightPower| <= |setFormula!| |imagI| + |normInvertible?| |removeRoughlyRedundantFactorsInPol| |plusInfinity| + |collect| |d01aqf| |dominantTerm| |viewPhiDefault| >= |permutations| + |OMencodingBinary| |rational| |queue| |minusInfinity| |RittWuCompare| + |complexNormalize| |times| |polarCoordinates| |useSingleFactorBound?| + |badValues| |removeRedundantFactorsInContents| |iicos| |swap!| |getlo| + |normalized?| |normal| |infiniteProduct| |patternMatchTimes| + |lazyIrreducibleFactors| |subResultantGcd| |skewSFunction| |e02ahf| + |functionIsFracPolynomial?| |OMgetEndBind| |bsolve| |htrigs| + |resetAttributeButtons| |mkcomm| |charpol| + + |selectSumOfSquaresRoutines| |numberOfComposites| |nextPrimitivePoly| + |inputOutputBinaryFile| |exprHasAlgebraicWeight| |acosIfCan| + |clearCache| |lyndonIfCan| |LyndonBasis| |insertMatch| - |chebyshevU| + |nonQsign| |stosePrepareSubResAlgo| |weierstrass| |exponentialOrder| + |leftRemainder| |monom| |iisin| |setMinPoints3D| |chebyshevT| + |leadingBasisTerm| / |factorset| |diff| |OMencodingSGML| |changeBase| + |truncate| |expenseOfEvaluation| |singleFactorBound| |scale| + |listOfMonoms| |laurentIfCan| |type| |latex| |df2mf| |binomial| + |rangePascalTriangle| |setCondition!| |linearlyDependent?| |Ei| + |trivialIdeal?| |point| |atrapezoidal| |primintegrate| |mpsode| |arg1| + |d01amf| |s17def| |merge!| |common| |sts2stst| |singularAtInfinity?| + |lquo| |block| |squareTop| |nonLinearPart| |arg2| |e01sef| + |continuedFraction| |clearTable!| |multisect| |moreAlgebraic?| |cTanh| + |meshPar2Var| |rightRecip| |expIfCan| |debug| |fTable| |c06gbf| + |viewDeltaXDefault| |nor| |ideal| |insert| |cSin| |rootBound| + |mightHaveRoots| |d01gaf| |series| D |e02aef| |compactFraction| + |screenResolution| |conditions| |brillhartTrials| |compdegd| |tail| + |henselFact| |morphism| |startTableInvSet!| + |rightRegularRepresentation| |sn| |showFortranOutputStack| |match| + |symFunc| |basisOfCentroid| |acscIfCan| |horizConcat| |rule| + |outputList| |reducedDiscriminant| |rotate| |flatten| |divergence| + |vconcat| |integral?| |critMonD1| |primeFrobenius| |nextColeman| + |OMconnOutDevice| |parabolicCylindrical| |getMatch| |superHeight| + |aQuartic| |modularGcd| |rightRemainder| |addMatch| |bat1| |float?| + |componentUpperBound| |qqq| |mr| |singularitiesOf| |min| |OMserve| + |leftOne| |intPatternMatch| |dimensionOfIrreducibleRepresentation| + |OMputEndObject| |coerceImages| |basisOfRightNucleus| |member?| + |error| |factorPolynomial| |monomRDEsys| |conditionsForIdempotents| + |transform| |OMsupportsSymbol?| |untab| |ddFact| |binaryFunction| + |createThreeSpace| |assert| |divisors| |list?| |exprToGenUPS| + |outputAsScript| |one?| |firstNumer| |odd?| |ellipticCylindrical| + |prologue| |nil?| |numberOfIrreduciblePoly| |chiSquare1| |repeating?| + |socf2socdf| |OMopenFile| |midpoint| |e01sbf| |setPredicates| + |OMgetEndBVar| |euclideanGroebner| |toroidal| |writeByteIfCan!| + |OMlistSymbols| |coleman| |f01qcf| |f04maf| |algebraicDecompose| + |previous| |invertIfCan| |print| |f02ajf| |void| |primlimintfrac| + |tensorProduct| |rk4| |contractSolve| |omError| |jacobiIdentity?| + |tRange| |mantissa| |resolve| |f04axf| |inR?| |iiatanh| |nullSpace| + |capacity| |leadingTerm| |semiResultantEuclidean1| |integerIfCan| + |bounds| |systemSizeIF| |probablyZeroDim?| |ridHack1| + |fortranLiteralLine| |inverseColeman| |length| |typeLists| |indices| + |evenInfiniteProduct| |outerProduct| |makeTerm| |findBinding| + |integers| |commutativeEquality| |redpps| |palgLODE| |scripts| |tanQ| + |entries| |zeroSquareMatrix| |usingTable?| |evaluateInverse| |failed?| + |printHeader| |tanh2coth| |stoseInvertible?reg| |s17aff| |roughBase?| + |representationType| |bitTruth| |getCurve| |myDegree| + |numberOfImproperPartitions| |tanAn| |OMgetInteger| |randomLC| + |OMputSymbol| |checkPrecision| |maxdeg| |iidprod| |showSummary| + |safeFloor| |rightExactQuotient| |notOperand| |determinant| + |subHeight| |bright| |Hausdorff| |listYoungTableaus| |d02kef| + |asinIfCan| |init| |leftGcd| |definingEquations| |removeSinhSq| + |padicFraction| |Frobenius| |wordInGenerators| |ffactor| |slex| + |vertConcat| |printInfo| |showAttributes| |commutator| + |particularSolution| |ksec| |rightLcm| |var2StepsDefault| + |unprotectedRemoveRedundantFactors| |open?| |increment| + |stoseInvertible?sqfreg| |besselK| |currentSubProgram| |unitCanonical| + |sec2cos| |e02gaf| |backOldPos| |identityMatrix| |parseString| |fmecg| + |max| |nlde| |bumptab| |numFunEvals3D| |ode1| |rarrow| |doubleDisc| + |xCoord| |stiffnessAndStabilityOfODEIF| |numberOfMonomials| + |generalizedEigenvectors| |figureUnits| |removeConstantTerm| |Zero| + |nextLatticePermutation| |infRittWu?| |fortranDouble| |bracket| + |taylorRep| |e02bdf| |inconsistent?| |/\\| |One| |removeSquaresIfCan| + |characteristic| |closedCurve?| |cyclicEntries| |basisOfCenter| + |raisePolynomial| |whileLoop| |delete| |OMReadError?| |\\/| + |coercePreimagesImages| |trim| |lowerCase?| |setProperties!| + |constructorName| |qualifier| |blue| |numberOfComponents| |nullity| + |setsubMatrix!| |PDESolve| |newSubProgram| |unitNormal| |sin?| + |sin2csc| |janko2| |part?| |lastSubResultantElseSplit| |dim| |f02akf| + |unit?| |Ci| |symmetricProduct| |startPolynomial| |roughSubIdeal?| + |binaryTournament| |tanintegrate| |insertionSort!| |btwFact| |s15aef| + |direction| |property| |unexpand| |critM| |s01eaf| |equivOperands| + |deepCopy| |transcendentalDecompose| |elt| |cCot| + |basisOfMiddleNucleus| |incrementKthElement| |genericRightTrace| + |compiledFunction| |quadratic?| |entry?| |computeBasis| |label| + |extractIndex| |sumSquares| |internalDecompose| |patternMatch| |int| + |topFortranOutputStack| |flagFactor| |stoseInvertibleSet| |units| + |pile| |eigenvectors| |outputMeasure| |cubic| |epilogue| + |mapMatrixIfCan| |getRef| |getMeasure| |gethi| + |removeRoughlyRedundantFactorsInContents| |decompose| + |monomialIntegrate| |reducedSystem| |bivariatePolynomials| |moduleSum| + |asechIfCan| |s17acf| |indicialEquation| |leftMinimalPolynomial| + |positiveRemainder| |totalDegree| |square?| |mesh?| + |multiEuclideanTree| |pascalTriangle| |fortranCarriageReturn| + |sequences| |scaleRoots| |monomRDE| |quasiMonicPolynomials| |d01akf| + |monomials| |next| |clipParametric| |useEisensteinCriterion| |orbits| + |eigenvalues| |Is| |largest| |GospersMethod| |primitivePart!| |code| + |safetyMargin| |exptMod| |c05pbf| |someBasis| |times!| |charClass| + |optAttributes| |normalDenom| |mapdiv| |graphStates| |head| + |OMputEndError| |conditionP| |overbar| |dmpToHdmp| |jordanAdmissible?| + |second| |rightTrace| |sign| |saturate| |startTableGcd!| F2FG + |invertibleSet| |karatsuba| |anticoord| |s19aaf| |ptree| |resultant| + |third| |shiftRoots| |dAndcExp| |toseInvertible?| GE |terms| + |createLowComplexityNormalBasis| |OMgetVariable| |maxint| + |createRandomElement| |factorOfDegree| |leftTrace| |imagE| + |colorFunction| GT |option| |lazy?| |fortranComplex| |c06fqf| + |explogs2trigs| |f04atf| |rightExtendedGcd| |normalElement| |lyndon?| + |outputArgs| |stirling1| LE |iiatan| |selectPolynomials| |repeating| + |generic?| |multiplyExponents| |sturmVariationsOf| |rightTrim| + |complexIntegrate| |f02bbf| |subNodeOf?| LT |hostPlatform| + |sparsityIF| |perspective| |octon| |primes| |computeInt| |leftTrim| + |convergents| |numerator| |lSpaceBasis| |erf| |pushdterm| + |symmetricPower| |showAll?| |iiabs| |resetNew| |algebraicSort| + |OMputVariable| |setEpilogue!| |aspFilename| |karatsubaOnce| + |inRadical?| |members| |parabolic| |startStats!| |minset| |swapRows!| + |f01rcf| |isPlus| |OMunhandledSymbol| |jacobian| |f07fef| |baseRDE| + |bipolarCylindrical| |integralRepresents| |accuracyIF| |lp| |exists?| + |derivative| |f01brf| |pointSizeDefault| |dilog| |listLoops| + |bezoutDiscriminant| |toseInvertibleSet| |trigs2explogs| + |semiResultantEuclideannaif| |quotientByP| |host| + |radicalEigenvectors| |resize| |sin| |iitan| |imaginary| |character?| + |edf2fi| |genericPosition| LODO2FUN |getIdentifier| |anfactor| + |ignore?| |cos| |stop| |OMputFloat| |bytes| |and?| |cylindrical| + |choosemon| |mapExponents| |nextPrime| |csubst| |OMgetType| |delta| + |tan| |zero| |eyeDistance| |domainOf| |ord| |complexNumericIfCan| + |getBadValues| |modularFactor| |bandedHessian| |composite| + |numberOfComputedEntries| |cot| |printCode| |makeSeries| |push!| + |numberOfHues| |countRealRootsMultiple| |s21bbf| + |rationalApproximation| |OMUnknownSymbol?| |f04mcf| |And| |sec| + |concat!| |divisor| |showTheRoutinesTable| |approximants| |e01bef| + |belong?| |toseLastSubResultant| |transcendenceDegree| |zeroVector| + |Or| |csc| |permanent| |redPo| |quasiComponent| |f01ref| |node?| + |localReal?| |var2Steps| |iiacot| |getMultiplicationTable| |pattern| + |Not| |asin| |clearFortranOutputStack| |setValue!| |tan2trig| + |binarySearchTree| |isobaric?| |derivationCoordinates| + |removeIrreducibleRedundantFactors| |complexElementary| |groebner?| + |physicalLength!| |acos| |setMaxPoints3D| |height| |enterInCache| + |tanh2trigh| |factorSFBRlcUnit| |loadNativeModule| |conjug| + |deepExpand| |shade| |rightDivide| |atan| |setrest!| |bat| + |collectQuasiMonic| |getProperty| |mainContent| |ranges| |ratPoly| + |boundOfCauchy| |lambda| |squareMatrix| |acot| |functionIsOscillatory| + |modulus| |graphState| |mergeDifference| |closedCurve| |drawStyle| + |inverseLaplace| |selectAndPolynomials| |function| |floor| |message| + |asec| |wholeRadix| |integralBasisAtInfinity| |integer?| |permutation| + |multiplyCoefficients| |weight| |basisOfRightAnnihilator| + |rowEchLocal| |sup| |acsc| |rootRadius| |fractRagits| + |monicRightFactorIfCan| |d02gbf| |mainVariable?| |typeList| + |integerBound| |prepareSubResAlgo| |trailingCoefficient| |eval| |sinh| + |consnewpol| |setColumn!| |tanNa| |frst| |addPointLast| |yellow| + |normalizedDivide| |addiag| |log| |cAcoth| |cosh| |deepestTail| |xor| + |overset?| |radicalRoots| |rootOfIrreduciblePoly| |abelianGroup| + |OMputBVar| |innerSolve1| |cTan| |infix| |setAttributeButtonStep| + |tanh| |dn| |supersub| |cycleTail| |listOfLists| |viewpoint| |cons| + |separant| |ratpart| |reduceLODE| |callForm?| |polygamma| |coth| + |OMputEndAttr| |combineFeatureCompatibility| |loopPoints| |innerSolve| + |curve?| |logical?| |mapDown!| |s14baf| |inf| |level| |sech| + |doubleComplex?| |rightRank| |nthRoot| |close!| |fullPartialFraction| + |rank| |exactQuotient| |isTimes| |findCycle| |reverseLex| |csch| + |leader| |cardinality| |nullary| |c06ebf| |f04mbf| |moduloP| + |diagonal| |createLowComplexityTable| |minimumDegree| |printTypes| + |asinh| |setStatus| |makeop| |updateStatus!| |listConjugateBases| + |crest| |extractIfCan| |conical| |hspace| |c06fuf| |acosh| |separate| + |leftDivide| |generalLambert| |leastPower| |c05nbf| |qelt| + |simpleBounds?| |semiDegreeSubResultantEuclidean| |var1StepsDefault| + |li| |bernoulliB| |atanh| |rootProduct| |c05adf| |iiacsc| |corrPoly| + |palginfieldint| |e04ycf| |qsetelt| |source| |prem| |central?| + |exprToUPS| |pr2dmp| |highCommonTerms| |genericRightMinimalPolynomial| + |hyperelliptic| |wholeRagits| |submod| |isOpen?| |xRange| + |doubleResultant| |iisinh| |logGamma| |f04arf| |lcm| |completeSmith| + |baseRDEsys| |knownInfBasis| |extractTop!| |finiteBasis| |lowerCase!| + |lists| |yRange| |list| |f01rdf| |dfRange| |deleteRoutine!| + |primitiveElement| |subPolSet?| |f02axf| |pointData| |alternative?| + |palglimint0| |zRange| |car| |bottom!| |makeUnit| |triangularSystems| + |append| |routines| |top!| |close| |viewWriteDefault| + |viewWriteAvailable| |clipPointsDefault| |nextItem| |map!| |cdr| + |removeSuperfluousCases| |lastSubResultantEuclidean| |difference| + |gcd| |SturmHabichtCoefficients| |expintegrate| |elementary| + |primeFactor| |OMlistCDs| |pade| |qsetelt!| |setDifference| |ravel| + |OMputEndAtp| |vspace| |internalAugment| |operators| |false| |critT| + |display| |s18def| |interpolate| |pointPlot| |subresultantVector| + |setIntersection| |copyInto!| |reshape| |minimumExponent| |cross| + |besselJ| |oddlambert| |multinomial| |harmonic| |balancedBinaryTree| + |pseudoRemainder| |setUnion| |pmComplexintegrate| |hMonic| + |univariatePolynomials| |prod| |decrease| |enterPointData| + |firstSubsetGray| |e02ddf| |apply| |e01sff| |eq?| |dmpToP| |imagk| + |clipWithRanges| |leftCharacteristicPolynomial| |d02cjf| + |cyclotomicFactorization| UTS2UP |schema| |element?| |limitPlus| + |semiDiscriminantEuclidean| |#| |initials| |test| |makeGraphImage| + |middle| |tubePlot| |f04jgf| |acsch| |size| |alphabetic?| + |nthRootIfCan| |normal?| |remove| |shrinkable| |unravel| |key| + |coth2trigh| |divideExponents| |gramschmidt| |ceiling| + |leftExtendedGcd| |randomR| |cothIfCan| |cycleLength| |objectOf| + |standardBasisOfCyclicSubmodule| |primlimitedint| |viewPosDefault| + |showRegion| |nand| |leftTraceMatrix| |last| |perfectNthRoot| + |filename| |position!| |iitanh| |binomThmExpt| |extendedIntegrate| + |intcompBasis| |fullDisplay| |first| |assoc| |palgextint0| |moebiusMu| + |assign| |prefix| |satisfy?| |not?| |trapezoidal| |iteratedInitials| + |s20acf| |symmetricGroup| |att2Result| |rest| |f01mcf| |OMreadStr| + |cosSinInfo| |equiv?| |parse| |internalIntegrate| |roughUnitIdeal?| + |besselY| |decimal| |substitute| |curveColorPalette| |Nul| |iroot| + |externalList| |leviCivitaSymbol| |primPartElseUnitCanonical!| |box| + |showClipRegion| |setleft!| |insert!| |coerceS| |removeDuplicates| + |selectPDERoutines| |f04faf| |round| |stiffnessAndStabilityFactor| + |lift| |fortranCharacter| |forLoop| |selectOrPolynomials| |rspace| + |bumprow| |iiacos| |drawComplexVectorField| |cSinh| |extractClosed| + |e02akf| |reduce| |recur| |partialNumerators| |complementaryBasis| + |returns| |readable?| |hasSolution?| |euler| |eq| |acschIfCan| + |semiIndiceSubResultantEuclidean| |mapUp!| |quotient| |factorList| + |coHeight| |iter| |irreducibleFactors| |lazyVariations| |rules| + |physicalLength| |mainPrimitivePart| |extendedSubResultantGcd| + |unknown| |lagrange| |packageCall| |LagrangeInterpolation| + |setButtonValue| |qroot| |generic| |rootSimp| |setErrorBound| + |insertBottom!| |pomopo!| |leadingCoefficientRicDE| |iicoth| + |generalizedInverse| |spherical| |replace| |exponent| |alphabetic| + |varList| |f02adf| |variable?| |internalSubPolSet?| |infinityNorm| + |toseSquareFreePart| |powern| |getOperator| |sturmSequence| |iiGamma| + |univariatePolynomial| |realElementary| |reseed| |retract| + |squareFree| |outputSpacing| |pointColorDefault| |bag| |quadratic| + |goto| |curry| |c02agf| |identitySquareMatrix| |sh| |rotatez| |module| + |s18aff| |dequeue| |sincos| |points| |showAllElements| + |fortranCompilerName| |localAbs| |imagK| |reducedContinuedFraction| + |e04mbf| |categoryFrame| |expint| |iicot| |f2df| |validExponential| + |index| |discriminantEuclidean| |precision| |implies?| + |balancedFactorisation| |setOrder| |diagonals| |OMgetApp| |exp| + |iipow| |symmetricDifference| |comparison| |e02dcf| |f01maf| + |optimize| |createPrimitivePoly| |wholePart| |lazyPseudoRemainder| + |sinhIfCan| |e02ajf| |dmp2rfi| |algSplitSimple| |leftUnit| + |powerAssociative?| |argumentListOf| |denominators| |extendIfCan| + |diag| |colorDef| |rightNorm| |compile| |f04asf| |associatedEquations| + |sorted?| |interReduce| |e04jaf| |signatureAst| |pair| |tanhIfCan| + |noLinearFactor?| |rombergo| |nthCoef| |fixedPoints| |readBytes!| + |seriesSolve| |groebnerIdeal| |e04naf| |s15adf| |clip| |minimize| + |mathieu24| |hash| |critB| |tan2cot| |hessian| + |genericLeftDiscriminant| |eulerE| |readIfCan!| |tubePointsDefault| + |numberOfPrimitivePoly| |HenselLift| |count| |negative?| + |subscriptedVariables| |overlabel| |minIndex| |d01bbf| |sqfree| + |sumOfSquares| |characteristicSerie| |constantOperator| + |basisOfCommutingElements| |iiasec| |e02bbf| |sechIfCan| |bitCoef| + |e01bff| |trapezoidalo| |twist| |characteristicSet| |currentScope| + |nthFlag| |component| |f02wef| |evaluate| |yCoordinates| |value| + |selectOptimizationRoutines| |aLinear| |unary?| |tanIfCan| |not| + |integralBasis| |c06frf| |setMinPoints| |linearPart| |minGbasis| + |plus| |OMencodingXML| |twoFactor| |monicCompleteDecompose| + |rightUnit| |An| |integralMatrix| + |generalizedContinuumHypothesisAssumed?| |associator| |universe| + |stoseLastSubResultant| |explimitedint| |bivariateSLPEBR| |Lazard| + |multiset| |slash| |resetVariableOrder| |cLog| |setAdaptive| |rootsOf| + |s17aef| |badNum| |alphanumeric?| |coordinates| |neglist| |s14aaf| + |fill!| |double?| |children| |printingInfo?| |vectorise| |divideIfCan| + |useEisensteinCriterion?| |enqueue!| |s18dcf| |collectUpper| |sum| + |cRationalPower| |sPol| |inputBinaryFile| |rightZero| + |removeDuplicates!| |light| |OMsupportsCD?| |recoverAfterFail| + |writable?| |makeViewport2D| |any| |OMread| |quadraticNorm| |expt| + |gcdcofact| |setvalue!| |subst| |hitherPlane| |lazyPquo| + |nextPartition| |Vectorise| |e04dgf| |iisqrt3| |matrixDimensions| + |OMgetEndError| |mapCoef| |basicSet| |totalfract| + |setScreenResolution3D| |move| |OMputInteger| |prefixRagits| |initial| + |powers| |selectODEIVPRoutines| |numberOfVariables| |infinite?| + |bivariate?| |partitions| |constDsolve| |setchildren!| |subtractIfCan| + |antiCommutative?| |tube| |digit| |oblateSpheroidal| |check| + |scripted?| |gderiv| |scalarTypeOf| |OMopenString| |trace2PowMod| + |lifting| |rootKerSimp| |normalise| |lowerCase| |legendre| + |removeCoshSq| |datalist| |setLabelValue| |nextNormalPoly| + |fortranLiteral| |option?| |finiteBound| |f02agf| |bipolar| + |mainMonomials| |extendedEuclidean| |clearTheSymbolTable| + |clipSurface| |OMbindTCP| |fixedDivisor| |charthRoot| + |createGenericMatrix| |nthExponent| |generalizedEigenvector| + |singular?| |constantIfCan| |mainValue| |objects| |extract!| + |getButtonValue| |s13aaf| |OMputEndBind| |generators| + |nonSingularModel| |select!| |testDim| |basisOfRightNucloid| + |maxIndex| |base| |expenseOfEvaluationIF| |rootNormalize| + |univariatePolynomialsGcds| |color| |front| ~ |red| |setprevious!| + |order| |stirling2| |elseBranch| |escape| |search| |parametersOf| + |coerceListOfPairs| |acoshIfCan| |rischDE| |imagi| |minus!| + |factorSquareFreePolynomial| |complete| |expextendedint| |recip| + |createIrreduciblePoly| |open| |paren| |symmetric?| |coth2tanh| + |withPredicates| |digits| |sort| |weights| |rightAlternative?| + |f02fjf| |presub| |symbolTableOf| |leadingExponent| + |intermediateResultsIF| |shiftRight| + |removeSuperfluousQuasiComponents| |discriminant| |interpretString| + |reify| |nativeModuleExtension| |iiasinh| |imagJ| |orOperands| + |d01fcf| |subResultantChain| |expintfldpoly| |LiePolyIfCan| + |leftRecip| |generalizedContinuumHypothesisAssumed| + |solveLinearPolynomialEquation| |f02bjf| |showScalarValues| |find| + |factorials| |uniform| |headAst| |tableau| |selectIntegrationRoutines| + |getZechTable| |cCsch| |copies| |cyclicCopy| |OMputBind| + |generateIrredPoly| |completeEchelonBasis| |shuffle| |bubbleSort!| + |random| |s18aef| |OMgetEndAtp| |real?| |perfectNthPower?| + |explicitEntries?| |integralMatrixAtInfinity| |froot| |besselI| + |beauzamyBound| |c06fpf| |completeEval| |psolve| |computePowers| + |tree| |multiEuclidean| |repeatUntilLoop| |getSyntaxFormsFromFile| + |zCoord| |changeThreshhold| |e04ucf| |hdmpToDmp| |readLine!| + |groebSolve| |cCosh| |directSum| |partition| |bindings| + |factorSquareFreeByRecursion| |midpoints| |shallowCopy| |sub| |or| + |semicolonSeparate| |leftQuotient| |univariateSolve| + |limitedIntegrate| |fixedPoint| |eigenvector| |setleaves!| + |rationalPoints| |totalDifferential| |viewSizeDefault| |comp| |mkPrim| + |rischNormalize| |purelyAlgebraicLeadingMonomial?| |insertRoot!| + |atanhIfCan| |tab| |isConnected?| |nodeOf?| |iprint| |roman| + |mkAnswer| |elColumn2!| |product| |newTypeLists| |extend| |depth| + |cschIfCan| |changeName| |dictionary| |iterationVar| |legendreP| ~= + |exactQuotient!| |decreasePrecision| |e02zaf| |push| |OMconnInDevice| + |nextPrimitiveNormalPoly| |lllip| |mappingAst| F |style| |isExpt| + |numerators| |lazyIntegrate| |coerce| |nthFactor| + |wordInStrongGenerators| |eigenMatrix| |reset| |symbol?| |testModulus| + |rectangularMatrix| |genus| |prime?| |byteBuffer| |construct| + |discreteLog| |makeYoungTableau| |const| |polygon?| |unvectorise| + |cycles| |lazyPremWithDefault| |basisOfLeftNucloid| |viewport2D| + |read!| |matrixGcd| |primaryDecomp| |OMencodingUnknown| + |getExplanations| |write| |cSech| |headReduce| |subspace| |getCode| + |dimensionsOf| |save| |sylvesterSequence| |integral| + |possiblyInfinite?| |changeVar| |patternVariable| + |fortranDoubleComplex| |normalizeAtInfinity| + |rewriteIdealWithQuasiMonicGenerators| |linears| |expandLog| + |rightDiscriminant| |totalLex| |closeComponent| |d02raf| |sinIfCan| + |halfExtendedResultant1| |aromberg| |merge| |denominator| |low| |dec| + |modularGcdPrimitive| |prime| |pushuconst| |nodes| |id| |alternating| + |rootPoly| |pointColorPalette| |write!| |e02adf| |OMclose| + |denomRicDE| |semiSubResultantGcdEuclidean2| + |tryFunctionalDecomposition?| |d01anf| |dihedral| |null| |vedf2vef| + |lazyGintegrate| |leftFactor| |invertibleElseSplit?| |cCos| + |irreducibleFactor| |s18adf| |stopTableGcd!| |mirror| |table| |pdf2ef| + |case| |differentialVariables| |linearAssociatedOrder| + |useSingleFactorBound| |pop!| |atom?| |mapBivariate| |conjugate| + |prevPrime| |monicDivide| |new| |rightRankPolynomial| |OMmakeConn| + |OMwrite| |child| |rangeIsFinite| |normalize| |nextSublist| + |singRicDE| |intensity| |inverseIntegralMatrixAtInfinity| |overlap| ** + |scan| |OMgetEndAttr| |purelyTranscendental?| |setStatus!| + |createMultiplicationMatrix| |pow| |endSubProgram| |empty| + |maxColIndex| |SturmHabichtSequence| |viewDeltaYDefault| |sdf2lst| + |mindeg| |traverse| FG2F |decomposeFunc| |delete!| |acothIfCan| + |tower| |subresultantSequence| |char| |leftDiscriminant| + |gcdPolynomial| |term| |reverse| |s13acf| |setClipValue| + |setImagSteps| |e01saf| EQ |trunc| |rename!| |zeroSetSplit| + |genericLeftMinimalPolynomial| |upDateBranches| |FormatRoman| + |indiceSubResultantEuclidean| |cAsin| |OMputObject| |andOperands| + |makeViewport3D| |entry| |oddInfiniteProduct| |showTypeInOutput| + |f01qdf| |iiasin| |rightMinimalPolynomial| |quoByVar| |mathieu23| + |nextsubResultant2| |cAcos| |trigs| |monicLeftDivide| + |impliesOperands| |term?| |halfExtendedSubResultantGcd1| + |axesColorDefault| |pointLists| |outputFixed| |cPower| + |associatedSystem| |headReduced?| |companionBlocks| |category| + |complexExpand| |headRemainder| |cup| |smith| |autoReduced?| + |genericLeftTrace| |qinterval| |reindex| |complexNumeric| |pointColor| + |lflimitedint| |domain| |f04qaf| |orthonormalBasis| |float| |lprop| + |modTree| |any?| |partialQuotients| |setVariableOrder| + |mainExpression| |numberOfFractionalTerms| |pseudoQuotient| |package| + |reduceBasisAtInfinity| |relativeApprox| |fglmIfCan| |elliptic| + |noncommutativeJordanAlgebra?| |tablePow| |ScanArabic| |kernels| + |comment| |magnitude| |left| |df2st| |e02def| + |wordsForStrongGenerators| |coshIfCan| |ptFunc| |factorFraction| + |monicDecomposeIfCan| |rightQuotient| |univariate| |right| + |showArrayValues| |point?| |qfactor| |Si| |exponents| |zerosOf| + |extractSplittingLeaf| |lexTriangular| |mainSquareFreePart| + |showTheSymbolTable| |s21bcf| |leftLcm| |e02agf| |splitNodeOf!| + |palgLODE0| |lexGroebner| |solveLinearlyOverQ| |every?| |reduced?| + |top| |mat| |finite?| UP2UTS |elRow1!| |e02bef| |pToHdmp| |groebgen| + |linearlyDependentOverZ?| |constantCoefficientRicDE| |quatern| + |matrixConcat3D| |factor| |dihedralGroup| |setlast!| |totalGroebner| + |basisOfLeftAnnihilator| |f01qef| |setRealSteps| + |semiResultantEuclidean2| |innerint| |clearTheIFTable| |sqrt| + |safeCeiling| |d02ejf| |union| |create3Space| |arity| |redmat| + |initTable!| |groebnerFactorize| |getOrder| |real| |unmakeSUP| |isOp| + |or?| |c06ecf| |internalZeroSetSplit| |modifyPoint| + |exprHasWeightCosWXorSinWX| |ip4Address| |euclideanSize| |lexico| + |kmax| |imag| |clipBoolean| |rightFactorCandidate| |duplicates| |hclf| + |copy!| |hasoln| |matrix| |karatsubaDivide| |exprex| |solveInField| + |directProduct| |viewThetaDefault| |palgintegrate| |duplicates?| + |kovacic| |normalForm| |isAbsolutelyIrreducible?| |powmod| |integrate| + |createNormalElement| |allRootsOf| |pleskenSplit| + |irreducibleRepresentation| |deriv| |powerSum| |chiSquare| |iilog| + |contract| |permutationGroup| |newReduc| |plenaryPower| + |fortranLinkerArgs| |brace| |plus!| |rightScalarTimes!| + |restorePrecision| |mdeg| |paraboloidal| |polynomialZeros| |quartic| + |bumptab1| |heap| |rowEch| |destruct| |branchIfCan| |cAsec| |rk4a| + |reflect| |f02awf| |numberOfFactors| |ScanRoman| |prinb| |regime| + |e02bcf| |OMgetBind| |certainlySubVariety?| |symbol| |thenBranch| + |split| |radicalSimplify| |radicalSolve| |mkIntegral| |rightUnits| + |asecIfCan| |linearDependenceOverZ| |palgextint| |mainCoefficients| + |enumerate| |expression| |removeRoughlyRedundantFactorsInPols| + |rationalIfCan| |perfectSqrt| |OMgetString| |represents| |leftUnits| + |cos2sec| |pseudoDivide| |radicalEigenvector| |abs| |d01apf| |integer| + |cartesian| |setAdaptive3D| |processTemplate| |setTopPredicate| + |solid?| |leftExactQuotient| |repSq| |stoseInternalLastSubResultant| + |roughBasicSet| |hue| |directory| |cyclicGroup| |monomial| |d02bbf| + |changeMeasure| |factorsOfCyclicGroupSize| |pack!| |cap| |f2st| + |approxNthRoot| |hasHi| |factorGroebnerBasis| |solveid| |newLine| + |multivariate| |cExp| |removeRedundantFactors| |increasePrecision| + |lazyPseudoQuotient| |principal?| |degreePartition| |s17adf| |pastel| + |isQuotient| |polyRDE| |crushedSet| |indicialEquationAtInfinity| + |variables| |rroot| |zeroSetSplitIntoTriangularSystems| + |measure2Result| |minRowIndex| |rootPower| |s17dhf| + |innerEigenvectors| |degreeSubResultant| |subNode?| |simpsono| + |generalPosition| |quickSort| |factorSquareFree| |constantKernel| + |complexLimit| |setLegalFortranSourceExtensions| |signAround| + |checkRur| |thetaCoord| |maxPoints| |whatInfinity| + |removeRedundantFactorsInPols| |listexp| |setref| |drawComplex| + |leadingIndex| |computeCycleLength| |commaSeparate| |d03edf| |Beta| + |OMputEndApp| |triangular?| |rationalFunction| |linearAssociatedLog| + |adaptive?| |outputFloating| |startTable!| |equality| |chvar| |updatD| + |characteristicPolynomial| |scanOneDimSubspaces| |axes| |upperCase?| + |cscIfCan| |composites| |makeVariable| |HermiteIntegrate| + |tableForDiscreteLogarithm| |bits| |f02aff| |distance| + |roughEqualIdeals?| |norm| |makeprod| |taylor| |invmod| + |sumOfDivisors| |squareFreeLexTriangular| |OMgetEndApp| |doubleRank| + |minimalPolynomial| |s19adf| |resultantEuclideannaif| |controlPanel| + |ricDsolve| |digit?| |leftRankPolynomial| |laurent| |OMputString| + RF2UTS |c06ekf| |f04adf| |tubeRadius| |ode2| |UnVectorise| + |FormatArabic| |mathieu11| |deref| |empty?| |puiseux| + |sumOfKthPowerDivisors| |mapGen| |setClosed| |revert| |nullary?| + |algintegrate| |index?| |Gamma| |maxrow| |printStats!| |obj| |stFunc2| + |iCompose| |s18acf| |identification| |equiv| |hypergeometric0F1| + |errorInfo| |drawCurves| |cAcsch| |ParCondList| + |inverseIntegralMatrix| |inv| |modifyPointData| |redPol| + |exponential1| |factor1| |cache| |normalizeIfCan| |countable?| + |printInfo!| |resultantnaif| |lambert| |nothing| |curveColor| + |ground?| |prinpolINFO| |denomLODE| |primextintfrac| |surface| + |cAsech| |lepol| |lazyPseudoDivide| |prepareDecompose| + |commonDenominator| |ground| |rdregime| |fi2df| |hdmpToP| |primitive?| + |leastAffineMultiple| |rowEchelon| |high| |constant?| |hex| |c06eaf| + |leadingMonomial| |llprop| |getProperties| |unrankImproperPartitions0| + |isMult| |viewZoomDefault| |bandedJacobian| |alphanumeric| |po| + |doublyTransitive?| |youngGroup| |leadingCoefficient| + |stoseIntegralLastSubResultant| |trueEqual| |SturmHabichtMultiple| + |aCubic| |airyBi| |elements| |power!| |internalSubQuasiComponent?| + |iicsch| |symmetricSquare| |rubiksGroup| |primitiveMonomials| + |reduction| |resetBadValues| |generalTwoFactor| |RemainderList| + |bezoutResultant| |mapUnivariateIfCan| |resultantReduit| |curryRight| + |s17dcf| |PollardSmallFactor| |reductum| |d02bhf| |secIfCan| + |complexSolve| |setOfMinN| |reorder| |palgint0| |OMgetAtp| |df2fi| + |palgRDE0| |writeBytes!| |e02dff| |logIfCan| |mainDefiningPolynomial| + |lineColorDefault| |cot2tan| |bit?| |outputBinaryFile| |critMTonD1| + |mapSolve| |leaves| |homogeneous?| |goodPoint| |subResultantsChain| + |s21bdf| |more?| |fortranTypeOf| |lllp| |output| |tab1| |dflist| + |palgint| |say| |setLength!| |movedPoints| |factors| |minordet| |true| + |quasiRegular?| |radPoly| |cAcsc| |OMgetError| GF2FG |collectUnder| + |branchPoint?| |meatAxe| |pmintegrate| |hermiteH| |and| + |stoseInvertibleSetreg| |OMputError| |keys| |minrank| |lighting| + |back| |simplify| |replaceKthElement| |opeval| |conjugates| |critBonD| + |sech2cosh| |expPot| |number?| |e02baf| |ParCond| |child?| |var1Steps| + |nextSubsetGray| |currentEnv| |scalarMatrix| |swap| |triangulate| + |f07aef| |ScanFloatIgnoreSpacesIfCan| |cyclicSubmodule| |contains?| + |pToDmp| |iisqrt2| |lieAdmissible?| |factorial| |squareFreePrim| + |iflist2Result| |rootDirectory| |heapSort| |solveLinear| + |gcdcofactprim| |solveLinearPolynomialEquationByFractions| + |lfextlimint| |buildSyntax| |linearDependence| |normDeriv2| |zero?| + |d02gaf| |realEigenvalues| |iiacoth| |numericalIntegration| |pdf2df| + |notelem| |makeFloatFunction| |f02abf| |e01bgf| |mainMonomial| |acoth| + |even?| |ratDsolve| |outputForm| |relationsIdeal| |fractionPart| + |less?| |simplifyPower| |lazyPrem| |createNormalPoly| |setMaxPoints| + |asech| |listBranches| |iiexp| |branchPointAtInfinity?| |summation| + |lookup| |gcdPrimitive| |c06gsf| |setEmpty!| |torsion?| |clikeUniv| + |inc| |complexRoots| |OMcloseConn| |laguerre| |nextIrreduciblePoly| + |s14abf| |rischDEsys| |extractPoint| |exprToXXP| |external?| + |multiple| |drawToScale| |divideIfCan!| |region| |s19abf| + |stoseInvertible?| |cot2trig| |definingInequation| |sample| |mapExpon| + |lazyEvaluate| |applyQuote| |iExquo| |diophantineSystem| + |normalizedAssociate| |OMputApp| |tanSum| |script| |completeHensel| + |infLex?| |port| |addPoint| |rightCharacteristicPolynomial| + |predicates| |structuralConstants| |csch2sinh| |algebraicVariables| + |s19acf| |rk4qc| |bitLength| |imagj| |quoted?| |rur| |complement| + |polyRicDE| |OMgetObject| |supRittWu?| |laplacian| |setfirst!| + |string?| |OMconnectTCP| |currentCategoryFrame| |numberOfOperations| + |getVariableOrder| |incrementBy| |ruleset| |infix?| |makingStats?| + |exteriorDifferential| |calcRanges| |leaf?| |alternatingGroup| |tex| + |iicosh| |iisech| |ef2edf| |c06gcf| |factorsOfDegree| |condition| + |mask| |degree| |expand| |rightTraceMatrix| |rightGcd| + |prolateSpheroidal| |csc2sin| |integralDerivationMatrix| |constant| + |e02daf| |expandTrigProducts| |quote| |radicalEigenvalues| |relerror| + |filterWhile| |d01alf| |simplifyExp| |extension| |cAsinh| |seed| + |idealiser| |listRepresentation| |suchThat| |row| |filterUntil| + |radicalOfLeftTraceForm| |separateFactors| |OMputAttr| |polygon| + |atoms| |exponential| |rk4f| |primPartElseUnitCanonical| |rootSplit| + |select| |rootOf| |stripCommentsAndBlanks| |unit| |create| + |countRealRoots| |getPickedPoints| |elliptic?| |upperCase| |s17agf| + |bfKeys| |stoseSquareFreePart| |OMParseError?| |Lazard2| |options| + |nary?| |compBound| |constantOpIfCan| |writeLine!| |setRow!| + |ramifiedAtInfinity?| |ReduceOrder| |predicate| |argument| |exquo| + |exQuo| |readByteIfCan!| |e04fdf| |dom| |rightFactorIfCan| + |mainVariables| |delay| |basisOfLeftNucleus| |useNagFunctions| + |monic?| |symbolTable| |div| |invmultisect| |ran| |coerceL| |split!| + |biRank| |functionIsContinuousAtEndPoints| |brillhartIrreducible?| + |antiAssociative?| |string| |createNormalPrimitivePoly| |quo| + |wronskianMatrix| |goodnessOfFit| |phiCoord| |eof?| |shallowExpand| + |f07adf| |lfinfieldint| |numericIfCan| |pushFortranOutputStack| + |LyndonCoordinates| |numer| |resultantReduitEuclidean| |setPosition| + |makeRecord| |rationalPoint?| |upperCase!| |makeSketch| + |popFortranOutputStack| |stopTableInvSet!| |limitedint| |rem| |denom| + |showIntensityFunctions| |s17ahf| |adjoint| NOT |iidsum| |polyPart| + |subTriSet?| |fortranLogical| |lyndon| |cyclicParents| |reopen!| + |remove!| |coefficients| OR |traceMatrix| |title| |nilFactor| + |constantRight| |palglimint| |atanIfCan| |makeCrit| |pi| + |strongGenerators| |ldf2lst| |ramified?| AND |iisec| |deepestInitial| + |cfirst| |algebraicOf| |outputAsFortran| |freeOf?| |infinity| |pole?| + |localIntegralBasis| |center| |outputGeneral| |leftRank| + |problemPoints| |absolutelyIrreducible?| |hconcat| |parameters| + |s17dgf| |status| |Aleph| |integralAtInfinity?| |compound?| |e| + |cAcot| |coefChoose| |fixedPointExquo| |has?| |f02aaf| |addmod| + |bringDown| |width| |putColorInfo| |divide| + |createMultiplicationTable| |linearMatrix| |OMsetEncoding| + |linearAssociatedExp| |exp1| |explicitlyEmpty?| |shellSort| |kernel| + |LiePoly| |readLineIfCan!| |extensionDegree| |palgRDE| |pushup| + |complexZeros| |inHallBasis?| |subset?| |deleteProperty!| + |subResultantGcdEuclidean| |draw| |adaptive3D?| |categories| + |padicallyExpand| |log10| |sequence| |clearTheFTable| |birth| + |primintfldpoly| |d01ajf| |tracePowMod| |c06gqf| + |rewriteIdealWithRemainder| |solve1| |cCoth| |bitand| |musserTrials| + |gcdprim| |complexForm| |interval| |subQuasiComponent?| |d01asf| + |linear?| |setelt!| |s17dlf| |continue| |bitior| |pushdown| |gradient| + |initiallyReduce| |dimensions| |changeWeightLevel| |d03eef| + |integralCoordinates| |sinh2csch| |iomode| |optional?| + |numberOfCycles| |lintgcd| |s17ajf| |makeFR| |poisson| |generator| + |plotPolar| |extractProperty| |makeObject| |setTex!| |insertTop!| + |null?| * |interpret| |lazyResidueClass| |f02xef| |mathieu22| + |algDsolve| |removeZeroes| |firstUncouplingMatrix| |lieAlgebra?| + |optional| |eisensteinIrreducible?| |graphs| |arguments| |sqfrFactor| + |arrayStack| |stFunc1| |minColIndex| |completeHermite| |fracPart| + |splitConstant| |coef| |stFuncN| |e01bhf| |connectTo| |basis| |refine| + |tubeRadiusDefault| |iibinom| |leftRegularRepresentation| + |factorAndSplit| |augment| |setPoly| |coord| + |initializeGroupForWordProblem| |getOperands| |coordinate| + |setPrologue!| |hasTopPredicate?| |nthr| |jordanAlgebra?| |failed| + |reducedForm| |orbit| |quasiRegular| |bfEntry| |makeSin| |vark| + |c02aff| |OMgetBVar| |s20adf| |internal?| |specialTrigs| |endOfFile?| + |node| |makeMulti| |ScanFloatIgnoreSpaces| |ode| + |solveLinearPolynomialEquationByRecursion| |fractRadix| |geometric| + |complexEigenvalues| |linkToFortran| |rewriteIdealWithHeadRemainder| + |d03faf| |idealSimplify| |nsqfree| |pureLex| |meshPar1Var| + |generalInfiniteProduct| |monicRightDivide| |optpair| |rotate!| + |antisymmetric?| |reducedQPowers| |limit| |numFunEvals| + |chainSubResultants| |edf2efi| |pair?| |lo| |operator| + |LazardQuotient| |sncndn| |mapUnivariate| |makeEq| |kroneckerDelta| + |graeffe| |genericRightNorm| |fibonacci| |incr| |factorByRecursion| + |internalLastSubResultant| |pdct| |diagonalProduct| |cn| + |internalIntegrate0| |linear| |makeCos| |content| |rightMult| |se2rfi| + |hi| |d01gbf| |rdHack1| |droot| |imports| |lfintegrate| + |rowEchelonLocal| |numberOfNormalPoly| |subSet| |subCase?| + |cyclicEqual?| |formula| |variationOfParameters| |SturmHabicht| + |associative?| |mainForm| |realSolve| |createPrimitiveNormalPoly| + |polynomial| |binaryTree| |medialSet| |applyRules| |algebraic?| + |s21baf| |SFunction| |localUnquote| |symmetricRemainder| + |chineseRemainder| |iicsc| |build| |realRoots| |regularRepresentation| + |laplace| |plot| |cosIfCan| |univcase| |rename| |dark| |swapColumns!| + |maxrank| |eulerPhi| |rst| |ocf2ocdf| |selectNonFiniteRoutines| + |uniform01| |logpart| |lastSubResultant| |increase| |solid| + |OMgetSymbol| |cycleElt| |pol| |nrows| |cyclotomicDecomposition| + |stoseInvertibleSetsqfreg| |scopes| |root| |addMatchRestricted| + |npcoef| SEGMENT |zeroDimPrimary?| |nextsousResultant2| |cycleRagits| + |halfExtendedSubResultantGcd2| |ncols| |normalDeriv| + |selectMultiDimensionalRoutines| |maximumExponent| |debug3D| + |positive?| |fortran| |padecf| |curryLeft| |power| |maxRowIndex| + |simplifyLog| |algint| |viewport3D| |cyclePartition| |getStream| + |subscript| |f02aef| |polar| |prindINFO| |fractionFreeGauss!| + |meshFun2Var| |setProperty| |s13adf| |nil| |removeZero| + |degreeSubResultantEuclidean| |semiLastSubResultantEuclidean| + |declare| |fixPredicate| |OMputAtp| |OMUnknownCD?| |mindegTerm| |name| + |initiallyReduced?| |inrootof| |weakBiRank| |pquo| + |internalInfRittWu?| |equation| |sylvesterMatrix| |multMonom| + |infieldIntegrate| |hcrf| |LyndonWordsList| |body| |flexible?| |xn| + |super| |adaptive| |showTheFTable| |genericRightDiscriminant| + |doubleFloatFormat| |graphImage| |in?| |splitDenominator| |cycleEntry| + |mulmod| |rational?| |substring?| |concat| |rotatey| |approximate| + |iiacosh| |showTheIFTable| |unaryFunction| |zag| |frobenius| + |mainCharacterization| |t| |contours| |elem?| |generate| |OMreceive| + |complex| |gbasis| |lfunc| |zoom| |normal01| |OMgetEndObject| + |rewriteSetWithReduction| |UP2ifCan| |shufflein| |computeCycleEntry| + |sizeLess?| |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#1| |t#1| |t#1|) $ $)) (-15 -1478 ($ (-1 |t#1| |t#1| |t#1|) $ $ |t#1|)))) -(((-34) . T) ((-101) |has| |#1| (-1079)) ((-600 (-845)) -4028 (|has| |#1| (-1079)) (|has| |#1| (-600 (-845)))) ((-303 |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079))) ((-482 |#1|) . T) ((-507 |#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1079))) ((-1079) |has| |#1| (-1079)) ((-1192) . T)) -((-3108 (((-58 |#2|) (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|) 16)) (-3883 ((|#2| (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|) 18)) (-1478 (((-58 |#2|) (-1 |#2| |#1|) (-58 |#1|)) 13))) -(((-57 |#1| |#2|) (-10 -7 (-15 -3108 ((-58 |#2|) (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|)) (-15 -3883 (|#2| (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|)) (-15 -1478 ((-58 |#2|) (-1 |#2| |#1|) (-58 |#1|)))) (-1192) (-1192)) (T -57)) -((-1478 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1192)) (-4 *6 (-1192)) (-5 *2 (-58 *6)) (-5 *1 (-57 *5 *6)))) (-3883 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1192)) (-4 *2 (-1192)) (-5 *1 (-57 *5 *2)))) (-3108 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *6 *5)) (-5 *4 (-58 *6)) (-4 *6 (-1192)) (-4 *5 (-1192)) (-5 *2 (-58 *5)) (-5 *1 (-57 *6 *5))))) -(-10 -7 (-15 -3108 ((-58 |#2|) (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|)) (-15 -3883 (|#2| (-1 |#2| |#1| |#2|) (-58 |#1|) |#2|)) (-15 -1478 ((-58 |#2|) (-1 |#2| |#1|) (-58 |#1|)))) -((-3200 (((-111) $ $) NIL 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-401 (-553))) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-38 |#1|) . T) ((-38 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-35) |has| |#1| (-1177)) ((-94) |has| |#1| (-1177)) ((-101) . T) ((-110 #0# #0#) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-110 |#1| |#1|) . T) ((-110 $ $) . T) ((-129) . T) ((-142) -3988 (|has| |#1| (-343)) (|has| |#1| (-142))) ((-144) |has| |#1| (-144)) ((-603 #0#) -3988 (|has| |#1| (-1020 (-401 (-553)))) (|has| |#1| (-343)) (|has| |#1| (-357))) ((-603 (-553)) . T) ((-603 |#1|) . T) ((-603 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-600 (-845)) . T) ((-169) . T) ((-601 (-166 (-220))) |has| |#1| (-1004)) ((-601 (-166 (-373))) |has| |#1| (-1004)) ((-601 (-529)) |has| |#1| (-601 (-529))) ((-601 (-874 (-373))) |has| |#1| (-601 (-874 (-373)))) ((-601 (-874 (-553))) |has| |#1| (-601 (-874 (-553)))) ((-601 #1=(-1151 |#1|)) . T) ((-226 |#1|) . T) ((-228) -3988 (|has| |#1| (-343)) (|has| |#1| (-228))) ((-238) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-278) |has| |#1| (-1177)) ((-280 |#1| $) |has| |#1| (-280 |#1| |#1|)) ((-284) -3988 (|has| |#1| (-545)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-301) -3988 (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-303 |#1|) |has| |#1| (-303 |#1|)) ((-357) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-396) |has| |#1| (-343)) ((-362) -3988 (|has| |#1| (-362)) (|has| |#1| (-343))) ((-343) |has| |#1| (-343)) ((-364 |#1| #1#) . T) ((-403 |#1| #1#) . T) ((-332 |#1|) . T) ((-371 |#1|) . T) ((-394 |#1|) . T) ((-405 |#1|) . T) ((-445) -3988 (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-486) |has| |#1| (-1177)) ((-507 (-1155) |#1|) |has| |#1| (-507 (-1155) |#1|)) ((-507 |#1| |#1|) |has| |#1| (-303 |#1|)) ((-545) -3988 (|has| |#1| (-545)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-633 #0#) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-633 |#1|) . T) ((-633 $) . T) ((-626 (-553)) |has| |#1| (-626 (-553))) ((-626 |#1|) . T) ((-703 #0#) -3988 (|has| |#1| (-343)) (|has| |#1| (-357))) ((-703 |#1|) . T) ((-703 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-343)) (|has| |#1| (-357)) (|has| |#1| (-301))) ((-710 |#1| #1#) . T) ((-712) . T) ((-833) |has| |#1| (-833)) ((-882 (-1155)) |has| |#1| (-882 (-1155))) ((-868 (-373)) |has| |#1| (-868 (-373))) ((-868 (-553)) |has| |#1| (-868 (-553))) ((-866 |#1|) . 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T) ((-169) |has| |#2| (-169)) ((-226 |#2|) |has| |#2| (-1031)) ((-228) -12 (|has| |#2| (-228)) (|has| |#2| (-1031))) ((-280 #2=(-553) |#2|) . T) ((-282 #2# |#2|) . T) ((-303 |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((-362) |has| |#2| (-362)) ((-371 |#2|) |has| |#2| (-1031)) ((-405 |#2|) |has| |#2| (-1079)) ((-482 |#2|) . T) ((-591 #2# |#2|) . T) ((-507 |#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((-633 |#2|) -4028 (|has| |#2| (-1031)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-633 $) -4028 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-626 (-553)) -12 (|has| |#2| (-626 (-553))) (|has| |#2| (-1031))) ((-626 |#2|) |has| |#2| (-1031)) ((-703 |#2|) -4028 (|has| |#2| (-357)) (|has| |#2| (-169))) ((-712) -4028 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-712)) (|has| |#2| (-169))) ((-777) |has| |#2| (-831)) ((-778) -4028 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-779) |has| |#2| (-779)) ((-780) -4028 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-781) -4028 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-831) |has| |#2| (-831)) ((-833) -4028 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-882 (-1155)) -12 (|has| |#2| (-882 (-1155))) (|has| |#2| (-1031))) ((-1020 #0#) -12 (|has| |#2| (-1020 (-401 (-553)))) (|has| |#2| (-1079))) ((-1020 #1#) -12 (|has| |#2| (-1020 (-553))) (|has| |#2| (-1079))) ((-1020 |#2|) |has| |#2| (-1079)) ((-1037 |#2|) -4028 (|has| |#2| (-1031)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-1037 $) |has| |#2| (-169)) ((-1031) -4028 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-1038) -4028 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-1091) -4028 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-712)) (|has| |#2| (-169))) ((-1079) -4028 (|has| |#2| (-1079)) (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-779)) (|has| |#2| (-712)) (|has| |#2| (-362)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-129)) (|has| |#2| (-25))) ((-1192) . T) ((-1245 |#2|) |has| |#2| (-357))) -((-3108 (((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 21)) (-3883 ((|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 23)) (-1478 (((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)) 18))) -(((-234 |#1| |#2| |#3|) (-10 -7 (-15 -3108 ((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -3883 (|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -1478 ((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)))) (-757) (-1192) (-1192)) (T -234)) -((-1478 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-235 *5 *6)) (-14 *5 (-757)) (-4 *6 (-1192)) (-4 *7 (-1192)) (-5 *2 (-235 *5 *7)) (-5 *1 (-234 *5 *6 *7)))) (-3883 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-235 *5 *6)) (-14 *5 (-757)) (-4 *6 (-1192)) (-4 *2 (-1192)) (-5 *1 (-234 *5 *6 *2)))) (-3108 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-235 *6 *7)) (-14 *6 (-757)) (-4 *7 (-1192)) (-4 *5 (-1192)) (-5 *2 (-235 *6 *5)) (-5 *1 (-234 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-169)) ((-101) -3988 (|has| |#2| (-1079)) (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-779)) (|has| |#2| (-712)) (|has| |#2| (-362)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-129)) (|has| |#2| (-25))) ((-110 |#2| |#2|) -3988 (|has| |#2| (-1031)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-110 $ $) |has| |#2| (-169)) ((-129) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-779)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-129))) ((-603 #0=(-401 (-553))) -12 (|has| |#2| (-1020 (-401 (-553)))) (|has| |#2| (-1079))) ((-603 (-553)) -3988 (|has| |#2| (-1031)) (-12 (|has| |#2| (-1020 (-553))) (|has| |#2| (-1079))) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-603 |#2|) -3988 (|has| |#2| (-1079)) (|has| |#2| (-169))) ((-600 (-845)) -3988 (|has| |#2| (-1079)) (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-779)) (|has| |#2| (-712)) (|has| |#2| (-362)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-600 (-845))) (|has| |#2| (-129)) (|has| |#2| (-25))) ((-600 (-1238 |#2|)) . T) ((-169) |has| |#2| (-169)) ((-226 |#2|) |has| |#2| (-1031)) ((-228) -12 (|has| |#2| (-228)) (|has| |#2| (-1031))) ((-280 #1=(-553) |#2|) . T) ((-282 #1# |#2|) . T) ((-303 |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((-362) |has| |#2| (-362)) ((-371 |#2|) |has| |#2| (-1031)) ((-405 |#2|) |has| |#2| (-1079)) ((-482 |#2|) . T) ((-591 #1# |#2|) . T) ((-507 |#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1079))) ((-633 |#2|) -3988 (|has| |#2| (-1031)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-633 $) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-626 (-553)) -12 (|has| |#2| (-626 (-553))) (|has| |#2| (-1031))) ((-626 |#2|) |has| |#2| (-1031)) ((-703 |#2|) -3988 (|has| |#2| (-357)) (|has| |#2| (-169))) ((-712) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-712)) (|has| |#2| (-169))) ((-777) |has| |#2| (-831)) ((-778) -3988 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-779) |has| |#2| (-779)) ((-780) -3988 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-781) -3988 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-831) |has| |#2| (-831)) ((-833) -3988 (|has| |#2| (-831)) (|has| |#2| (-779))) ((-882 (-1155)) -12 (|has| |#2| (-882 (-1155))) (|has| |#2| (-1031))) ((-1020 #0#) -12 (|has| |#2| (-1020 (-401 (-553)))) (|has| |#2| (-1079))) ((-1020 (-553)) -12 (|has| |#2| (-1020 (-553))) (|has| |#2| (-1079))) ((-1020 |#2|) |has| |#2| (-1079)) ((-1037 |#2|) -3988 (|has| |#2| (-1031)) (|has| |#2| (-357)) (|has| |#2| (-169))) ((-1037 $) |has| |#2| (-169)) ((-1031) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-1038) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-169))) ((-1091) -3988 (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-712)) (|has| |#2| (-169))) ((-1079) -3988 (|has| |#2| (-1079)) (|has| |#2| (-1031)) (|has| |#2| (-831)) (|has| |#2| (-779)) (|has| |#2| (-712)) (|has| |#2| (-362)) (|has| |#2| (-357)) (|has| |#2| (-169)) (|has| |#2| (-129)) (|has| |#2| (-25))) ((-1192) . T) ((-1245 |#2|) |has| |#2| (-357))) +((-3215 (((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 21)) (-2654 ((|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|) 23)) (-1482 (((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)) 18))) +(((-234 |#1| |#2| |#3|) (-10 -7 (-15 -3215 ((-235 |#1| |#3|) (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -2654 (|#3| (-1 |#3| |#2| |#3|) (-235 |#1| |#2|) |#3|)) (-15 -1482 ((-235 |#1| |#3|) (-1 |#3| |#2|) (-235 |#1| |#2|)))) (-757) (-1192) (-1192)) (T -234)) +((-1482 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-235 *5 *6)) (-14 *5 (-757)) (-4 *6 (-1192)) (-4 *7 (-1192)) (-5 *2 (-235 *5 *7)) (-5 *1 (-234 *5 *6 *7)))) (-2654 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-235 *5 *6)) (-14 *5 (-757)) (-4 *6 (-1192)) (-4 *2 (-1192)) (-5 *1 (-234 *5 *6 *2)))) (-3215 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-235 *6 *7)) (-14 *6 (-757)) (-4 *7 (-1192)) (-4 *5 (-1192)) (-5 *2 (-235 *6 *5)) (-5 *1 (-234 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-401 (-553))) |has| |#1| (-38 (-401 (-553)))) ((-38 |#1|) |has| |#1| (-169)) ((-38 $) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445))) ((-101) . T) ((-110 #0# #0#) |has| |#1| (-38 (-401 (-553)))) ((-110 |#1| |#1|) . T) ((-110 $ $) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445)) (|has| |#1| (-169))) ((-129) . T) ((-142) |has| |#1| (-142)) ((-144) |has| |#1| (-144)) ((-603 #0#) -3988 (|has| |#1| (-1020 (-401 (-553)))) (|has| |#1| (-38 (-401 (-553))))) ((-603 (-553)) . T) ((-603 |#1|) . T) ((-603 |#2|) . T) ((-603 |#3|) . T) ((-603 $) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445))) ((-600 (-845)) . T) ((-169) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445)) (|has| |#1| (-169))) ((-601 (-529)) -12 (|has| |#1| (-601 (-529))) (|has| |#3| (-601 (-529)))) ((-601 (-874 (-373))) -12 (|has| |#1| (-601 (-874 (-373)))) (|has| |#3| (-601 (-874 (-373))))) ((-601 (-874 (-553))) -12 (|has| |#1| (-601 (-874 (-553)))) (|has| |#3| (-601 (-874 (-553))))) ((-226 |#1|) . T) ((-228) |has| |#1| (-228)) ((-284) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445))) ((-303 $) . T) ((-320 |#1| |#4|) . T) ((-371 |#1|) . T) ((-405 |#1|) . T) ((-445) -3988 (|has| |#1| (-891)) (|has| |#1| (-445))) ((-507 |#2| |#1|) |has| |#1| (-228)) ((-507 |#2| $) |has| |#1| (-228)) ((-507 |#3| |#1|) . T) ((-507 |#3| $) . T) ((-507 $ $) . T) ((-545) -3988 (|has| |#1| (-891)) (|has| |#1| (-545)) (|has| |#1| (-445))) ((-633 #0#) |has| |#1| (-38 (-401 (-553)))) ((-633 |#1|) . T) ((-633 $) . T) ((-626 (-553)) |has| |#1| (-626 (-553))) ((-626 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-553)) . T) ((-25) . T) ((-38 #1=(-401 (-553))) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-357)) ((-38 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-357))) ((-35) |has| |#1| (-38 (-401 (-553)))) ((-94) |has| |#1| (-38 (-401 (-553)))) ((-101) . T) ((-110 #1# #1#) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-110 |#1| |#1|) . T) ((-110 |#2| |#2|) |has| |#1| (-357)) ((-110 $ $) -3988 (|has| |#1| (-545)) (|has| |#1| (-357)) (|has| |#1| (-169))) ((-129) . T) ((-142) -3988 (-12 (|has| |#1| (-357)) (|has| |#2| (-142))) (|has| |#1| (-142))) ((-144) -3988 (-12 (|has| |#1| (-357)) (|has| |#2| (-144))) (|has| |#1| (-144))) ((-603 #1#) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-603 (-553)) . T) ((-603 #2=(-1155)) -12 (|has| |#1| (-357)) (|has| |#2| (-1020 (-1155)))) ((-603 |#1|) |has| |#1| (-169)) ((-603 |#2|) . T) ((-603 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-357))) ((-600 (-845)) . T) ((-169) -3988 (|has| |#1| (-545)) (|has| |#1| (-357)) (|has| |#1| (-169))) ((-601 (-220)) -12 (|has| |#1| (-357)) (|has| |#2| (-1004))) ((-601 (-373)) -12 (|has| |#1| (-357)) (|has| |#2| (-1004))) ((-601 (-529)) -12 (|has| |#1| (-357)) (|has| |#2| (-601 (-529)))) ((-601 (-874 (-373))) -12 (|has| |#1| (-357)) (|has| |#2| (-601 (-874 (-373))))) ((-601 (-874 (-553))) -12 (|has| |#1| (-357)) (|has| |#2| (-601 (-874 (-553))))) ((-226 |#2|) |has| |#1| (-357)) ((-228) -3988 (-12 (|has| |#1| (-357)) (|has| |#2| (-228))) (|has| |#1| (-15 * (|#1| (-553) |#1|)))) ((-238) |has| |#1| (-357)) ((-278) |has| |#1| (-38 (-401 (-553)))) ((-280 |#2| $) -12 (|has| |#1| (-357)) (|has| |#2| (-280 |#2| |#2|))) ((-280 $ $) |has| (-553) (-1091)) ((-284) -3988 (|has| |#1| (-545)) (|has| |#1| (-357))) ((-301) |has| |#1| (-357)) ((-303 |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-303 |#2|))) ((-357) |has| |#1| (-357)) ((-332 |#2|) |has| |#1| (-357)) ((-371 |#2|) |has| |#1| (-357)) ((-394 |#2|) |has| |#1| (-357)) ((-445) |has| |#1| (-357)) ((-486) |has| |#1| (-38 (-401 (-553)))) ((-507 (-1155) |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-507 (-1155) |#2|))) ((-507 |#2| |#2|) -12 (|has| |#1| (-357)) (|has| |#2| (-303 |#2|))) ((-545) -3988 (|has| |#1| (-545)) (|has| |#1| (-357))) ((-633 #1#) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-633 |#1|) . T) ((-633 |#2|) |has| |#1| (-357)) ((-633 $) . T) ((-626 (-553)) -12 (|has| |#1| (-357)) (|has| |#2| (-626 (-553)))) ((-626 |#2|) |has| |#1| (-357)) ((-703 #1#) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-703 |#1|) |has| |#1| (-169)) ((-703 |#2|) |has| |#1| (-357)) ((-703 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-357))) ((-712) . T) ((-777) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-778) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-780) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-781) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-806) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-831) -12 (|has| |#1| (-357)) (|has| |#2| (-806))) ((-833) -3988 (-12 (|has| |#1| (-357)) (|has| |#2| (-833))) (-12 (|has| |#1| (-357)) (|has| |#2| (-806)))) ((-882 (-1155)) -3988 (-12 (|has| |#1| (-357)) (|has| |#2| (-882 (-1155)))) (-12 (|has| |#1| (-15 * (|#1| (-553) |#1|))) (|has| |#1| (-882 (-1155))))) ((-868 (-373)) -12 (|has| |#1| (-357)) (|has| |#2| (-868 (-373)))) ((-868 (-553)) -12 (|has| |#1| (-357)) (|has| |#2| (-868 (-553)))) ((-866 |#2|) |has| |#1| (-357)) ((-891) -12 (|has| |#1| (-357)) (|has| |#2| (-891))) ((-955 |#1| #0# (-1061)) . T) ((-902) |has| |#1| (-357)) ((-974 |#2|) |has| |#1| (-357)) ((-984) |has| |#1| (-38 (-401 (-553)))) ((-1004) -12 (|has| |#1| (-357)) (|has| |#2| (-1004))) ((-1020 (-401 (-553))) -12 (|has| |#1| (-357)) (|has| |#2| (-1020 (-553)))) ((-1020 (-553)) -12 (|has| |#1| (-357)) (|has| |#2| (-1020 (-553)))) ((-1020 #2#) -12 (|has| |#1| (-357)) (|has| |#2| (-1020 (-1155)))) ((-1020 |#2|) . T) ((-1037 #1#) -3988 (|has| |#1| (-357)) (|has| |#1| (-38 (-401 (-553))))) ((-1037 |#1|) . T) ((-1037 |#2|) |has| |#1| (-357)) ((-1037 $) -3988 (|has| |#1| (-545)) (|has| |#1| (-357)) (|has| |#1| (-169))) ((-1031) . T) ((-1038) . T) ((-1091) . T) ((-1079) . T) ((-1130) -12 (|has| |#1| (-357)) (|has| |#2| (-1130))) ((-1177) |has| |#1| (-38 (-401 (-553)))) ((-1180) |has| |#1| (-38 (-401 (-553)))) ((-1192) |has| |#1| (-357)) ((-1196) |has| |#1| (-357)) ((-1198 |#1|) . T) ((-1216 |#1| #0#) . 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2866584 2867098 2867536 "TEX" 2868303 T TEX (NIL) -8 NIL NIL) (-1171 2866365 2866396 2866468 "TEX1" 2866547 NIL TEX1 (NIL T) -7 NIL NIL) (-1170 2866013 2866076 2866166 "TEMUTL" 2866297 T TEMUTL (NIL) -7 NIL NIL) (-1169 2864167 2864447 2864772 "TBCMPPK" 2865736 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1168 2856055 2862327 2862383 "TBAGG" 2862783 NIL TBAGG (NIL T T) -9 NIL 2862994) (-1167 2851125 2852613 2854367 "TBAGG-" 2854372 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1166 2850509 2850616 2850761 "TANEXP" 2851014 NIL TANEXP (NIL T) -7 NIL NIL) (-1165 2844010 2850366 2850459 "TABLE" 2850464 NIL TABLE (NIL T T) -8 NIL NIL) (-1164 2843422 2843521 2843659 "TABLEAU" 2843907 NIL TABLEAU (NIL T) -8 NIL NIL) (-1163 2838030 2839250 2840498 "TABLBUMP" 2842208 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1162 2837458 2837558 2837686 "SYSTEM" 2837924 T SYSTEM (NIL) -7 NIL NIL) (-1161 2833921 2834616 2835399 "SYSSOLP" 2836709 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1160 2830299 2831210 2831912 "SYNTAX" 2833241 T SYNTAX (NIL) -8 NIL NIL) (-1159 2827457 2828059 2828691 "SYMTAB" 2829689 T SYMTAB (NIL) -8 NIL NIL) (-1158 2822706 2823608 2824591 "SYMS" 2826496 T SYMS (NIL) -8 NIL NIL) (-1157 2819978 2822164 2822394 "SYMPOLY" 2822511 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1156 2819495 2819570 2819693 "SYMFUNC" 2819890 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1155 2815472 2816732 2817554 "SYMBOL" 2818695 T SYMBOL (NIL) -8 NIL NIL) (-1154 2809011 2810700 2812420 "SWITCH" 2813774 T SWITCH (NIL) -8 NIL NIL) (-1153 2802281 2807832 2808135 "SUTS" 2808766 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1152 2794250 2801396 2801678 "SUPXS" 2802057 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1151 2785779 2793868 2793994 "SUP" 2794159 NIL SUP (NIL T) -8 NIL NIL) (-1150 2784938 2785065 2785282 "SUPFRACF" 2785647 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1149 2784559 2784618 2784731 "SUP2" 2784873 NIL SUP2 (NIL T T) -7 NIL NIL) (-1148 2782972 2783246 2783609 "SUMRF" 2784258 NIL SUMRF (NIL T) -7 NIL NIL) (-1147 2782286 2782352 2782551 "SUMFS" 2782893 NIL SUMFS (NIL T T) -7 NIL NIL) (-1146 2766293 2781463 2781714 "SULS" 2782093 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1145 2765922 2766115 2766185 "SUCHTAST" 2766245 T SUCHTAST (NIL) -8 NIL NIL) (-1144 2765244 2765447 2765587 "SUCH" 2765830 NIL SUCH (NIL T T) -8 NIL NIL) (-1143 2759138 2760150 2761109 "SUBSPACE" 2764332 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1142 2758568 2758658 2758822 "SUBRESP" 2759026 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1141 2751937 2753233 2754544 "STTF" 2757304 NIL STTF (NIL T) -7 NIL NIL) (-1140 2746110 2747230 2748377 "STTFNC" 2750837 NIL STTFNC (NIL T) -7 NIL NIL) (-1139 2737425 2739292 2741086 "STTAYLOR" 2744351 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1138 2730669 2737289 2737372 "STRTBL" 2737377 NIL STRTBL (NIL T) -8 NIL NIL) (-1137 2726060 2730624 2730655 "STRING" 2730660 T STRING (NIL) -8 NIL NIL) (-1136 2720948 2725433 2725463 "STRICAT" 2725522 T STRICAT (NIL) -9 NIL 2725584) (-1135 2713661 2718471 2719091 "STREAM" 2720363 NIL STREAM (NIL T) -8 NIL NIL) (-1134 2713171 2713248 2713392 "STREAM3" 2713578 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1133 2712153 2712336 2712571 "STREAM2" 2712984 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1132 2711841 2711893 2711986 "STREAM1" 2712095 NIL STREAM1 (NIL T) -7 NIL NIL) (-1131 2710857 2711038 2711269 "STINPROD" 2711657 NIL STINPROD (NIL T) -7 NIL NIL) (-1130 2710435 2710619 2710649 "STEP" 2710729 T STEP (NIL) -9 NIL 2710807) (-1129 2703978 2710334 2710411 "STBL" 2710416 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1128 2699153 2703200 2703243 "STAGG" 2703396 NIL STAGG (NIL T) -9 NIL 2703485) (-1127 2696855 2697457 2698329 "STAGG-" 2698334 NIL STAGG- (NIL T T) -8 NIL NIL) (-1126 2695050 2696625 2696717 "STACK" 2696798 NIL STACK (NIL T) -8 NIL NIL) (-1125 2687775 2693191 2693647 "SREGSET" 2694680 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1124 2680201 2681569 2683082 "SRDCMPK" 2686381 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1123 2673168 2677641 2677671 "SRAGG" 2678974 T SRAGG (NIL) -9 NIL 2679582) (-1122 2672185 2672440 2672819 "SRAGG-" 2672824 NIL SRAGG- (NIL T) -8 NIL NIL) (-1121 2666680 2671132 2671553 "SQMATRIX" 2671811 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1120 2660432 2663400 2664126 "SPLTREE" 2666026 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1119 2656422 2657088 2657734 "SPLNODE" 2659858 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1118 2655469 2655702 2655732 "SPFCAT" 2656176 T SPFCAT (NIL) -9 NIL NIL) (-1117 2654206 2654416 2654680 "SPECOUT" 2655227 T SPECOUT (NIL) -7 NIL NIL) (-1116 2645895 2647639 2647669 "SPADXPT" 2652061 T SPADXPT (NIL) -9 NIL 2654095) (-1115 2645656 2645696 2645765 "SPADPRSR" 2645848 T SPADPRSR (NIL) -7 NIL NIL) (-1114 2643839 2645611 2645642 "SPADAST" 2645647 T SPADAST (NIL) -8 NIL NIL) (-1113 2635810 2637557 2637600 "SPACEC" 2641973 NIL SPACEC (NIL T) -9 NIL 2643789) (-1112 2633981 2635742 2635791 "SPACE3" 2635796 NIL SPACE3 (NIL T) -8 NIL NIL) (-1111 2632733 2632904 2633195 "SORTPAK" 2633786 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1110 2630783 2631086 2631505 "SOLVETRA" 2632397 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1109 2629794 2630016 2630290 "SOLVESER" 2630556 NIL SOLVESER (NIL T) -7 NIL NIL) (-1108 2625014 2625895 2626897 "SOLVERAD" 2628846 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1107 2620829 2621438 2622167 "SOLVEFOR" 2624381 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1106 2615126 2620178 2620275 "SNTSCAT" 2620280 NIL SNTSCAT (NIL T T T T) -9 NIL 2620350) (-1105 2609269 2613449 2613840 "SMTS" 2614816 NIL SMTS (NIL T T T) -8 NIL NIL) (-1104 2603719 2609157 2609234 "SMP" 2609239 NIL SMP (NIL T T) -8 NIL NIL) (-1103 2601878 2602179 2602577 "SMITH" 2603416 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1102 2594752 2598907 2599010 "SMATCAT" 2600361 NIL SMATCAT (NIL NIL T T T) -9 NIL 2600911) (-1101 2591692 2592515 2593693 "SMATCAT-" 2593698 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1100 2589405 2590928 2590971 "SKAGG" 2591232 NIL SKAGG (NIL T) -9 NIL 2591367) (-1099 2585521 2588509 2588787 "SINT" 2589149 T SINT (NIL) -8 NIL NIL) (-1098 2585293 2585331 2585397 "SIMPAN" 2585477 T SIMPAN (NIL) -7 NIL NIL) (-1097 2584600 2584828 2584968 "SIG" 2585175 T SIG (NIL) -8 NIL NIL) (-1096 2583438 2583659 2583934 "SIGNRF" 2584359 NIL SIGNRF (NIL T) -7 NIL NIL) (-1095 2582243 2582394 2582685 "SIGNEF" 2583267 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1094 2581576 2581826 2581950 "SIGAST" 2582141 T SIGAST (NIL) -8 NIL NIL) (-1093 2579266 2579720 2580226 "SHP" 2581117 NIL SHP (NIL T NIL) -7 NIL NIL) (-1092 2573172 2579167 2579243 "SHDP" 2579248 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1091 2572771 2572937 2572967 "SGROUP" 2573060 T SGROUP (NIL) -9 NIL 2573122) (-1090 2572629 2572655 2572728 "SGROUP-" 2572733 NIL SGROUP- (NIL T) -8 NIL NIL) (-1089 2569465 2570162 2570885 "SGCF" 2571928 T SGCF (NIL) -7 NIL NIL) (-1088 2563860 2568912 2569009 "SFRTCAT" 2569014 NIL SFRTCAT (NIL T T T T) -9 NIL 2569053) (-1087 2557284 2558299 2559435 "SFRGCD" 2562843 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1086 2550412 2551483 2552669 "SFQCMPK" 2556217 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1085 2550034 2550123 2550233 "SFORT" 2550353 NIL SFORT (NIL T T) -8 NIL NIL) (-1084 2549179 2549874 2549995 "SEXOF" 2550000 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1083 2548313 2549060 2549128 "SEX" 2549133 T SEX (NIL) -8 NIL NIL) (-1082 2543089 2543778 2543873 "SEXCAT" 2547644 NIL SEXCAT (NIL T T T T T) -9 NIL 2548263) (-1081 2540269 2543023 2543071 "SET" 2543076 NIL SET (NIL T) -8 NIL NIL) (-1080 2538520 2538982 2539287 "SETMN" 2540010 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1079 2538126 2538252 2538282 "SETCAT" 2538399 T SETCAT (NIL) -9 NIL 2538484) (-1078 2537906 2537958 2538057 "SETCAT-" 2538062 NIL SETCAT- (NIL T) -8 NIL NIL) (-1077 2534293 2536367 2536410 "SETAGG" 2537280 NIL SETAGG (NIL T) -9 NIL 2537620) (-1076 2533751 2533867 2534104 "SETAGG-" 2534109 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1075 2533221 2533447 2533548 "SEQAST" 2533672 T SEQAST (NIL) -8 NIL NIL) (-1074 2532425 2532718 2532779 "SEGXCAT" 2533065 NIL SEGXCAT (NIL T T) -9 NIL 2533185) (-1073 2531481 2532091 2532273 "SEG" 2532278 NIL SEG (NIL T) -8 NIL NIL) (-1072 2530388 2530601 2530644 "SEGCAT" 2531226 NIL SEGCAT (NIL T) -9 NIL 2531464) (-1071 2529437 2529767 2529967 "SEGBIND" 2530223 NIL SEGBIND (NIL T) -8 NIL NIL) (-1070 2529058 2529117 2529230 "SEGBIND2" 2529372 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1069 2528659 2528859 2528936 "SEGAST" 2529003 T SEGAST (NIL) -8 NIL NIL) (-1068 2527878 2528004 2528208 "SEG2" 2528503 NIL SEG2 (NIL T T) -7 NIL NIL) (-1067 2527315 2527813 2527860 "SDVAR" 2527865 NIL SDVAR (NIL T) -8 NIL NIL) (-1066 2519605 2527085 2527215 "SDPOL" 2527220 NIL SDPOL (NIL T) -8 NIL NIL) (-1065 2518198 2518464 2518783 "SCPKG" 2519320 NIL SCPKG (NIL T) -7 NIL NIL) (-1064 2517334 2517514 2517714 "SCOPE" 2518020 T SCOPE (NIL) -8 NIL NIL) (-1063 2516555 2516688 2516867 "SCACHE" 2517189 NIL SCACHE (NIL T) -7 NIL NIL) (-1062 2516264 2516424 2516454 "SASTCAT" 2516459 T SASTCAT (NIL) -9 NIL 2516472) (-1061 2515703 2516024 2516109 "SAOS" 2516201 T SAOS (NIL) -8 NIL NIL) (-1060 2515268 2515303 2515476 "SAERFFC" 2515662 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1059 2509242 2515165 2515245 "SAE" 2515250 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1058 2508835 2508870 2509029 "SAEFACT" 2509201 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1057 2507156 2507470 2507871 "RURPK" 2508501 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1056 2505792 2506071 2506383 "RULESET" 2506990 NIL RULESET (NIL T T T) -8 NIL NIL) (-1055 2502979 2503482 2503947 "RULE" 2505473 NIL RULE (NIL T T T) -8 NIL NIL) (-1054 2502618 2502773 2502856 "RULECOLD" 2502931 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1053 2502116 2502335 2502429 "RSTRCAST" 2502546 T RSTRCAST (NIL) -8 NIL NIL) (-1052 2496965 2497759 2498679 "RSETGCD" 2501315 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1051 2486222 2491274 2491371 "RSETCAT" 2495490 NIL RSETCAT (NIL T T T T) -9 NIL 2496587) (-1050 2484149 2484688 2485512 "RSETCAT-" 2485517 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1049 2476536 2477911 2479431 "RSDCMPK" 2482748 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1048 2474541 2474982 2475056 "RRCC" 2476142 NIL RRCC (NIL T T) -9 NIL 2476486) (-1047 2473892 2474066 2474345 "RRCC-" 2474350 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1046 2473362 2473588 2473689 "RPTAST" 2473813 T RPTAST (NIL) -8 NIL NIL) (-1045 2447463 2457048 2457115 "RPOLCAT" 2467779 NIL RPOLCAT (NIL T T T) -9 NIL 2470938) (-1044 2438963 2441301 2444423 "RPOLCAT-" 2444428 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1043 2430010 2437174 2437656 "ROUTINE" 2438503 T ROUTINE (NIL) -8 NIL NIL) (-1042 2426768 2429561 2429710 "ROMAN" 2429883 T ROMAN (NIL) -8 NIL NIL) (-1041 2425043 2425628 2425888 "ROIRC" 2426573 NIL ROIRC (NIL T T) -8 NIL NIL) (-1040 2421452 2423691 2423721 "RNS" 2424025 T RNS (NIL) -9 NIL 2424298) (-1039 2419961 2420344 2420878 "RNS-" 2420953 NIL RNS- (NIL T) -8 NIL NIL) (-1038 2419410 2419792 2419822 "RNG" 2419827 T RNG (NIL) -9 NIL 2419848) (-1037 2418802 2419164 2419207 "RMODULE" 2419269 NIL RMODULE (NIL T) -9 NIL 2419311) (-1036 2417638 2417732 2418068 "RMCAT2" 2418703 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1035 2414343 2416812 2417137 "RMATRIX" 2417372 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1034 2407285 2409519 2409634 "RMATCAT" 2412993 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2413975) (-1033 2406660 2406807 2407114 "RMATCAT-" 2407119 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1032 2406227 2406302 2406430 "RINTERP" 2406579 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1031 2405315 2405835 2405865 "RING" 2405977 T RING (NIL) -9 NIL 2406072) (-1030 2405107 2405151 2405248 "RING-" 2405253 NIL RING- (NIL T) -8 NIL NIL) (-1029 2403948 2404185 2404443 "RIDIST" 2404871 T RIDIST (NIL) -7 NIL NIL) (-1028 2395264 2403416 2403622 "RGCHAIN" 2403796 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1027 2394640 2395020 2395061 "RGBCSPC" 2395119 NIL RGBCSPC (NIL T) -9 NIL 2395171) (-1026 2393824 2394179 2394220 "RGBCMDL" 2394452 NIL RGBCMDL (NIL T) -9 NIL 2394566) (-1025 2390818 2391432 2392102 "RF" 2393188 NIL RF (NIL T) -7 NIL NIL) (-1024 2390464 2390527 2390630 "RFFACTOR" 2390749 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1023 2390189 2390224 2390321 "RFFACT" 2390423 NIL RFFACT (NIL T) -7 NIL NIL) (-1022 2388306 2388670 2389052 "RFDIST" 2389829 T RFDIST (NIL) -7 NIL NIL) (-1021 2387759 2387851 2388014 "RETSOL" 2388208 NIL RETSOL (NIL T T) -7 NIL NIL) (-1020 2387395 2387475 2387518 "RETRACT" 2387651 NIL RETRACT (NIL T) -9 NIL 2387738) (-1019 2387244 2387269 2387356 "RETRACT-" 2387361 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1018 2386873 2387066 2387136 "RETAST" 2387196 T RETAST (NIL) -8 NIL NIL) (-1017 2379727 2386526 2386653 "RESULT" 2386768 T RESULT (NIL) -8 NIL NIL) (-1016 2378353 2378996 2379195 "RESRING" 2379630 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1015 2377989 2378038 2378136 "RESLATC" 2378290 NIL RESLATC (NIL T) -7 NIL NIL) (-1014 2377695 2377729 2377836 "REPSQ" 2377948 NIL REPSQ (NIL T) -7 NIL NIL) (-1013 2375117 2375697 2376299 "REP" 2377115 T REP (NIL) -7 NIL NIL) (-1012 2374815 2374849 2374960 "REPDB" 2375076 NIL REPDB (NIL T) -7 NIL NIL) (-1011 2368725 2370104 2371327 "REP2" 2373627 NIL REP2 (NIL T) -7 NIL NIL) (-1010 2365102 2365783 2366591 "REP1" 2367952 NIL REP1 (NIL T) -7 NIL NIL) (-1009 2357828 2363243 2363699 "REGSET" 2364732 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1008 2356641 2356976 2357226 "REF" 2357613 NIL REF (NIL T) -8 NIL NIL) (-1007 2356018 2356121 2356288 "REDORDER" 2356525 NIL REDORDER (NIL T T) -7 NIL NIL) (-1006 2352025 2355233 2355459 "RECLOS" 2355847 NIL RECLOS (NIL T) -8 NIL NIL) (-1005 2351077 2351258 2351473 "REALSOLV" 2351832 T REALSOLV (NIL) -7 NIL NIL) (-1004 2350923 2350964 2350994 "REAL" 2350999 T REAL (NIL) -9 NIL 2351034) (-1003 2347406 2348208 2349092 "REAL0Q" 2350088 NIL REAL0Q (NIL T) -7 NIL NIL) (-1002 2343007 2343995 2345056 "REAL0" 2346387 NIL REAL0 (NIL T) -7 NIL NIL) (-1001 2342505 2342724 2342818 "RDUCEAST" 2342935 T RDUCEAST (NIL) -8 NIL NIL) (-1000 2341910 2341982 2342189 "RDIV" 2342427 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-999 2340983 2341157 2341368 "RDIST" 2341732 NIL RDIST (NIL T) -7 NIL NIL) (-998 2339584 2339871 2340241 "RDETRS" 2340691 NIL RDETRS (NIL T T) -7 NIL NIL) (-997 2337401 2337855 2338391 "RDETR" 2339126 NIL RDETR (NIL T T) -7 NIL NIL) (-996 2336015 2336293 2336695 "RDEEFS" 2337117 NIL RDEEFS (NIL T T) -7 NIL NIL) (-995 2334513 2334819 2335249 "RDEEF" 2335703 NIL RDEEF (NIL T T) -7 NIL NIL) (-994 2328779 2331650 2331678 "RCFIELD" 2332955 T RCFIELD (NIL) -9 NIL 2333685) (-993 2326848 2327352 2328045 "RCFIELD-" 2328118 NIL RCFIELD- (NIL T) -8 NIL NIL) (-992 2323179 2324964 2325005 "RCAGG" 2326076 NIL RCAGG (NIL T) -9 NIL 2326541) (-991 2322810 2322904 2323064 "RCAGG-" 2323069 NIL RCAGG- (NIL T T) -8 NIL NIL) (-990 2322150 2322262 2322425 "RATRET" 2322694 NIL RATRET (NIL T) -7 NIL NIL) (-989 2321707 2321774 2321893 "RATFACT" 2322078 NIL RATFACT (NIL T) -7 NIL NIL) (-988 2321022 2321142 2321292 "RANDSRC" 2321577 T RANDSRC (NIL) -7 NIL NIL) (-987 2320759 2320803 2320874 "RADUTIL" 2320971 T RADUTIL (NIL) -7 NIL NIL) (-986 2313822 2319502 2319819 "RADIX" 2320474 NIL RADIX (NIL NIL) -8 NIL NIL) (-985 2305479 2313666 2313794 "RADFF" 2313799 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-984 2305131 2305206 2305234 "RADCAT" 2305391 T RADCAT (NIL) -9 NIL NIL) (-983 2304916 2304964 2305061 "RADCAT-" 2305066 NIL RADCAT- (NIL T) -8 NIL NIL) (-982 2303067 2304691 2304780 "QUEUE" 2304860 NIL QUEUE (NIL T) -8 NIL NIL) (-981 2299643 2303004 2303049 "QUAT" 2303054 NIL QUAT (NIL T) -8 NIL NIL) (-980 2299281 2299324 2299451 "QUATCT2" 2299594 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-979 2293032 2296333 2296373 "QUATCAT" 2297153 NIL QUATCAT (NIL T) -9 NIL 2297919) (-978 2289176 2290213 2291600 "QUATCAT-" 2291694 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-977 2286696 2288260 2288301 "QUAGG" 2288676 NIL QUAGG (NIL T) -9 NIL 2288851) (-976 2286328 2286521 2286589 "QQUTAST" 2286648 T QQUTAST (NIL) -8 NIL NIL) (-975 2285253 2285726 2285898 "QFORM" 2286200 NIL QFORM (NIL NIL T) -8 NIL NIL) (-974 2276433 2281638 2281678 "QFCAT" 2282336 NIL QFCAT (NIL T) -9 NIL 2283337) (-973 2272005 2273206 2274797 "QFCAT-" 2274891 NIL QFCAT- (NIL T T) -8 NIL NIL) (-972 2271643 2271686 2271813 "QFCAT2" 2271956 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-971 2271103 2271213 2271343 "QEQUAT" 2271533 T QEQUAT (NIL) -8 NIL NIL) (-970 2264251 2265322 2266506 "QCMPACK" 2270036 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-969 2261827 2262248 2262676 "QALGSET" 2263906 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-968 2261072 2261246 2261478 "QALGSET2" 2261647 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-967 2259763 2259986 2260303 "PWFFINTB" 2260845 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-966 2257945 2258113 2258467 "PUSHVAR" 2259577 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-965 2253863 2254917 2254958 "PTRANFN" 2256842 NIL PTRANFN (NIL T) -9 NIL NIL) (-964 2252265 2252556 2252878 "PTPACK" 2253574 NIL PTPACK (NIL T) -7 NIL NIL) (-963 2251897 2251954 2252063 "PTFUNC2" 2252202 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-962 2246363 2250708 2250749 "PTCAT" 2251122 NIL PTCAT (NIL T) -9 NIL 2251284) (-961 2246021 2246056 2246180 "PSQFR" 2246322 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-960 2244616 2244914 2245248 "PSEUDLIN" 2245719 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-959 2231385 2233750 2236074 "PSETPK" 2242376 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-958 2224429 2227143 2227239 "PSETCAT" 2230260 NIL PSETCAT (NIL T T T T) -9 NIL 2231074) (-957 2222265 2222899 2223720 "PSETCAT-" 2223725 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-956 2221614 2221779 2221807 "PSCURVE" 2222075 T PSCURVE (NIL) -9 NIL 2222242) (-955 2218095 2219577 2219642 "PSCAT" 2220486 NIL PSCAT (NIL T T T) -9 NIL 2220726) (-954 2217158 2217374 2217774 "PSCAT-" 2217779 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-953 2215810 2216443 2216657 "PRTITION" 2216964 T PRTITION (NIL) -8 NIL NIL) (-952 2215312 2215531 2215623 "PRTDAST" 2215738 T PRTDAST (NIL) -8 NIL NIL) (-951 2204410 2206616 2208804 "PRS" 2213174 NIL PRS (NIL T T) -7 NIL NIL) (-950 2202268 2203760 2203800 "PRQAGG" 2203983 NIL PRQAGG (NIL T) -9 NIL 2204085) (-949 2201654 2201883 2201911 "PROPLOG" 2202096 T PROPLOG (NIL) -9 NIL 2202218) (-948 2198824 2199468 2199932 "PROPFRML" 2201222 NIL PROPFRML (NIL T) -8 NIL NIL) (-947 2198284 2198394 2198524 "PROPERTY" 2198714 T PROPERTY (NIL) -8 NIL NIL) (-946 2192369 2196450 2197270 "PRODUCT" 2197510 NIL PRODUCT (NIL T T) -8 NIL NIL) (-945 2189682 2191827 2192061 "PR" 2192180 NIL PR (NIL T T) -8 NIL NIL) (-944 2189478 2189510 2189569 "PRINT" 2189643 T PRINT (NIL) -7 NIL NIL) (-943 2188818 2188935 2189087 "PRIMES" 2189358 NIL PRIMES (NIL T) -7 NIL NIL) (-942 2186883 2187284 2187750 "PRIMELT" 2188397 NIL PRIMELT (NIL T) -7 NIL NIL) (-941 2186612 2186661 2186689 "PRIMCAT" 2186813 T PRIMCAT (NIL) -9 NIL NIL) (-940 2182773 2186550 2186595 "PRIMARR" 2186600 NIL PRIMARR (NIL T) -8 NIL NIL) (-939 2181780 2181958 2182186 "PRIMARR2" 2182591 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-938 2181423 2181479 2181590 "PREASSOC" 2181718 NIL PREASSOC (NIL T T) -7 NIL NIL) (-937 2180898 2181031 2181059 "PPCURVE" 2181264 T PPCURVE (NIL) -9 NIL 2181400) (-936 2180520 2180693 2180776 "PORTNUM" 2180835 T PORTNUM (NIL) -8 NIL NIL) (-935 2177879 2178278 2178870 "POLYROOT" 2180101 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-934 2171824 2177483 2177643 "POLY" 2177752 NIL POLY (NIL T) -8 NIL NIL) (-933 2171207 2171265 2171499 "POLYLIFT" 2171760 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-932 2167482 2167931 2168560 "POLYCATQ" 2170752 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-931 2154394 2159750 2159815 "POLYCAT" 2163329 NIL POLYCAT (NIL T T T) -9 NIL 2165257) (-930 2147844 2149705 2152089 "POLYCAT-" 2152094 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-929 2147431 2147499 2147619 "POLY2UP" 2147770 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-928 2147063 2147120 2147229 "POLY2" 2147368 NIL POLY2 (NIL T T) -7 NIL NIL) (-927 2145748 2145987 2146263 "POLUTIL" 2146837 NIL POLUTIL (NIL T T) -7 NIL NIL) (-926 2144103 2144380 2144711 "POLTOPOL" 2145470 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-925 2139621 2144039 2144085 "POINT" 2144090 NIL POINT (NIL T) -8 NIL NIL) (-924 2137808 2138165 2138540 "PNTHEORY" 2139266 T PNTHEORY (NIL) -7 NIL NIL) (-923 2136227 2136524 2136936 "PMTOOLS" 2137506 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-922 2135820 2135898 2136015 "PMSYM" 2136143 NIL PMSYM (NIL T) -7 NIL NIL) (-921 2135330 2135399 2135573 "PMQFCAT" 2135745 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-920 2134685 2134795 2134951 "PMPRED" 2135207 NIL PMPRED (NIL T) -7 NIL NIL) (-919 2134081 2134167 2134328 "PMPREDFS" 2134586 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-918 2132724 2132932 2133317 "PMPLCAT" 2133843 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-917 2132256 2132335 2132487 "PMLSAGG" 2132639 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-916 2131731 2131807 2131988 "PMKERNEL" 2132174 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-915 2131348 2131423 2131536 "PMINS" 2131650 NIL PMINS (NIL T) -7 NIL NIL) (-914 2130776 2130845 2131061 "PMFS" 2131273 NIL PMFS (NIL T T T) -7 NIL NIL) (-913 2130004 2130122 2130327 "PMDOWN" 2130653 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-912 2129167 2129326 2129508 "PMASS" 2129842 T PMASS (NIL) -7 NIL NIL) (-911 2128441 2128552 2128715 "PMASSFS" 2129053 NIL PMASSFS (NIL T T) -7 NIL NIL) (-910 2128096 2128164 2128258 "PLOTTOOL" 2128367 T PLOTTOOL (NIL) -7 NIL NIL) (-909 2122718 2123907 2125055 "PLOT" 2126968 T PLOT (NIL) -8 NIL NIL) (-908 2118532 2119566 2120487 "PLOT3D" 2121817 T PLOT3D (NIL) -8 NIL NIL) (-907 2117444 2117621 2117856 "PLOT1" 2118336 NIL PLOT1 (NIL T) -7 NIL NIL) (-906 2092838 2097510 2102361 "PLEQN" 2112710 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-905 2092156 2092278 2092458 "PINTERP" 2092703 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-904 2091849 2091896 2091999 "PINTERPA" 2092103 NIL PINTERPA (NIL T T) -7 NIL NIL) (-903 2091134 2091655 2091742 "PI" 2091782 T PI (NIL) -8 NIL NIL) (-902 2089566 2090507 2090535 "PID" 2090717 T PID (NIL) -9 NIL 2090851) (-901 2089291 2089328 2089416 "PICOERCE" 2089523 NIL PICOERCE (NIL T) -7 NIL NIL) (-900 2088611 2088750 2088926 "PGROEB" 2089147 NIL PGROEB (NIL T) -7 NIL NIL) (-899 2084198 2085012 2085917 "PGE" 2087726 T PGE (NIL) -7 NIL NIL) (-898 2082322 2082568 2082934 "PGCD" 2083915 NIL PGCD (NIL T T T T) -7 NIL NIL) (-897 2081660 2081763 2081924 "PFRPAC" 2082206 NIL PFRPAC (NIL T) -7 NIL NIL) (-896 2078340 2080208 2080561 "PFR" 2081339 NIL PFR (NIL T) -8 NIL NIL) (-895 2076729 2076973 2077298 "PFOTOOLS" 2078087 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-894 2075262 2075501 2075852 "PFOQ" 2076486 NIL PFOQ (NIL T T T) -7 NIL NIL) (-893 2073735 2073947 2074310 "PFO" 2075046 NIL PFO (NIL T T T T T) -7 NIL NIL) (-892 2070323 2073624 2073693 "PF" 2073698 NIL PF (NIL NIL) -8 NIL NIL) (-891 2067792 2069029 2069057 "PFECAT" 2069642 T PFECAT (NIL) -9 NIL 2070026) (-890 2067237 2067391 2067605 "PFECAT-" 2067610 NIL PFECAT- (NIL T) -8 NIL NIL) (-889 2065841 2066092 2066393 "PFBRU" 2066986 NIL PFBRU (NIL T T) -7 NIL NIL) (-888 2063708 2064059 2064491 "PFBR" 2065492 NIL PFBR (NIL T T T T) -7 NIL NIL) (-887 2059624 2061084 2061760 "PERM" 2063065 NIL PERM (NIL T) -8 NIL NIL) (-886 2054890 2055831 2056701 "PERMGRP" 2058787 NIL PERMGRP (NIL T) -8 NIL NIL) (-885 2053022 2053953 2053994 "PERMCAT" 2054440 NIL PERMCAT (NIL T) -9 NIL 2054745) (-884 2052675 2052716 2052840 "PERMAN" 2052975 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-883 2050115 2052244 2052375 "PENDTREE" 2052577 NIL PENDTREE (NIL T) -8 NIL NIL) (-882 2048228 2048962 2049003 "PDRING" 2049660 NIL PDRING (NIL T) -9 NIL 2049946) (-881 2047331 2047549 2047911 "PDRING-" 2047916 NIL PDRING- (NIL T T) -8 NIL NIL) (-880 2044472 2045223 2045914 "PDEPROB" 2046660 T PDEPROB (NIL) -8 NIL NIL) (-879 2042019 2042521 2043076 "PDEPACK" 2043937 T PDEPACK (NIL) -7 NIL NIL) (-878 2040931 2041121 2041372 "PDECOMP" 2041818 NIL PDECOMP (NIL T T) -7 NIL NIL) (-877 2038536 2039353 2039381 "PDECAT" 2040168 T PDECAT (NIL) -9 NIL 2040881) (-876 2038287 2038320 2038410 "PCOMP" 2038497 NIL PCOMP (NIL T T) -7 NIL NIL) (-875 2036492 2037088 2037385 "PBWLB" 2038016 NIL PBWLB (NIL T) -8 NIL NIL) (-874 2028996 2030565 2031903 "PATTERN" 2035175 NIL PATTERN (NIL T) -8 NIL NIL) (-873 2028628 2028685 2028794 "PATTERN2" 2028933 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-872 2026385 2026773 2027230 "PATTERN1" 2028217 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-871 2023780 2024334 2024815 "PATRES" 2025950 NIL PATRES (NIL T T) -8 NIL NIL) (-870 2023344 2023411 2023543 "PATRES2" 2023707 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-869 2021227 2021632 2022039 "PATMATCH" 2023011 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-868 2020763 2020946 2020987 "PATMAB" 2021094 NIL PATMAB (NIL T) -9 NIL 2021177) (-867 2019308 2019617 2019875 "PATLRES" 2020568 NIL PATLRES (NIL T T T) -8 NIL NIL) (-866 2018854 2018977 2019018 "PATAB" 2019023 NIL PATAB (NIL T) -9 NIL 2019195) (-865 2016335 2016867 2017440 "PARTPERM" 2018301 T PARTPERM (NIL) -7 NIL NIL) (-864 2015956 2016019 2016121 "PARSURF" 2016266 NIL PARSURF (NIL T) -8 NIL NIL) (-863 2015588 2015645 2015754 "PARSU2" 2015893 NIL PARSU2 (NIL T T) -7 NIL NIL) (-862 2015352 2015392 2015459 "PARSER" 2015541 T PARSER (NIL) -7 NIL NIL) (-861 2014973 2015036 2015138 "PARSCURV" 2015283 NIL PARSCURV (NIL T) -8 NIL NIL) (-860 2014605 2014662 2014771 "PARSC2" 2014910 NIL PARSC2 (NIL T T) -7 NIL NIL) (-859 2014244 2014302 2014399 "PARPCURV" 2014541 NIL PARPCURV (NIL T) -8 NIL NIL) (-858 2013876 2013933 2014042 "PARPC2" 2014181 NIL PARPC2 (NIL T T) -7 NIL NIL) (-857 2013396 2013482 2013601 "PAN2EXPR" 2013777 T PAN2EXPR (NIL) -7 NIL NIL) (-856 2012202 2012517 2012745 "PALETTE" 2013188 T PALETTE (NIL) -8 NIL NIL) (-855 2010670 2011207 2011567 "PAIR" 2011888 NIL PAIR (NIL T T) -8 NIL NIL) (-854 2004576 2009929 2010123 "PADICRC" 2010525 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-853 1997840 2003922 2004106 "PADICRAT" 2004424 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-852 1996190 1997777 1997822 "PADIC" 1997827 NIL PADIC (NIL NIL) -8 NIL NIL) (-851 1993435 1994965 1995005 "PADICCT" 1995586 NIL PADICCT (NIL NIL) -9 NIL 1995868) (-850 1992392 1992592 1992860 "PADEPAC" 1993222 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-849 1991604 1991737 1991943 "PADE" 1992254 NIL PADE (NIL T T T) -7 NIL NIL) (-848 1989654 1990440 1990757 "OWP" 1991371 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-847 1988763 1989259 1989431 "OVAR" 1989522 NIL OVAR (NIL NIL) -8 NIL NIL) (-846 1988027 1988148 1988309 "OUT" 1988622 T OUT (NIL) -7 NIL NIL) (-845 1976934 1979136 1981336 "OUTFORM" 1985847 T OUTFORM (NIL) -8 NIL NIL) (-844 1976355 1976531 1976658 "OUTBFILE" 1976827 T OUTBFILE (NIL) -8 NIL NIL) (-843 1975992 1976075 1976103 "OUTBCON" 1976254 T OUTBCON (NIL) -9 NIL 1976339) (-842 1975832 1975867 1975943 "OUTBCON-" 1975948 NIL OUTBCON- (NIL T) -8 NIL NIL) (-841 1975240 1975561 1975650 "OSI" 1975763 T OSI (NIL) -8 NIL NIL) (-840 1974796 1975108 1975136 "OSGROUP" 1975141 T OSGROUP (NIL) -9 NIL 1975163) (-839 1973541 1973768 1974053 "ORTHPOL" 1974543 NIL ORTHPOL (NIL T) -7 NIL NIL) (-838 1970951 1973200 1973339 "OREUP" 1973484 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-837 1968389 1970642 1970769 "ORESUP" 1970893 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-836 1965917 1966417 1966978 "OREPCTO" 1967878 NIL OREPCTO (NIL T T) -7 NIL NIL) (-835 1959719 1961886 1961927 "OREPCAT" 1964275 NIL OREPCAT (NIL T) -9 NIL 1965379) (-834 1956866 1957648 1958706 "OREPCAT-" 1958711 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-833 1956043 1956315 1956343 "ORDSET" 1956652 T ORDSET (NIL) -9 NIL 1956816) (-832 1955562 1955684 1955877 "ORDSET-" 1955882 NIL ORDSET- (NIL T) -8 NIL NIL) (-831 1954216 1954973 1955001 "ORDRING" 1955203 T ORDRING (NIL) -9 NIL 1955328) (-830 1953861 1953955 1954099 "ORDRING-" 1954104 NIL ORDRING- (NIL T) -8 NIL NIL) (-829 1953267 1953704 1953732 "ORDMON" 1953737 T ORDMON (NIL) -9 NIL 1953758) (-828 1952429 1952576 1952771 "ORDFUNS" 1953116 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-827 1951940 1952299 1952327 "ORDFIN" 1952332 T ORDFIN (NIL) -9 NIL 1952353) (-826 1948532 1950526 1950935 "ORDCOMP" 1951564 NIL ORDCOMP (NIL T) -8 NIL NIL) (-825 1947798 1947925 1948111 "ORDCOMP2" 1948392 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-824 1944305 1945188 1946025 "OPTPROB" 1946981 T OPTPROB (NIL) -8 NIL NIL) (-823 1941107 1941746 1942450 "OPTPACK" 1943621 T OPTPACK (NIL) -7 NIL NIL) (-822 1938820 1939560 1939588 "OPTCAT" 1940407 T OPTCAT (NIL) -9 NIL 1941057) (-821 1938588 1938627 1938693 "OPQUERY" 1938774 T OPQUERY (NIL) -7 NIL NIL) (-820 1935754 1936899 1937403 "OP" 1938117 NIL OP (NIL T) -8 NIL NIL) (-819 1932599 1934551 1934920 "ONECOMP" 1935418 NIL ONECOMP (NIL T) -8 NIL NIL) (-818 1931904 1932019 1932193 "ONECOMP2" 1932471 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-817 1931323 1931429 1931559 "OMSERVER" 1931794 T OMSERVER (NIL) -7 NIL NIL) (-816 1928211 1930763 1930803 "OMSAGG" 1930864 NIL OMSAGG (NIL T) -9 NIL 1930928) (-815 1926834 1927097 1927379 "OMPKG" 1927949 T OMPKG (NIL) -7 NIL NIL) (-814 1926264 1926367 1926395 "OM" 1926694 T OM (NIL) -9 NIL NIL) (-813 1924846 1925813 1925982 "OMLO" 1926145 NIL OMLO (NIL T T) -8 NIL NIL) (-812 1923771 1923918 1924145 "OMEXPR" 1924672 NIL OMEXPR (NIL T) -7 NIL NIL) (-811 1923089 1923317 1923453 "OMERR" 1923655 T OMERR (NIL) -8 NIL NIL) (-810 1922267 1922510 1922670 "OMERRK" 1922949 T OMERRK (NIL) -8 NIL NIL) (-809 1921745 1921944 1922052 "OMENC" 1922179 T OMENC (NIL) -8 NIL NIL) (-808 1915640 1916825 1917996 "OMDEV" 1920594 T OMDEV (NIL) -8 NIL NIL) (-807 1914709 1914880 1915074 "OMCONN" 1915466 T OMCONN (NIL) -8 NIL NIL) (-806 1913365 1914307 1914335 "OINTDOM" 1914340 T OINTDOM (NIL) -9 NIL 1914361) (-805 1909171 1910355 1911071 "OFMONOID" 1912681 NIL OFMONOID (NIL T) -8 NIL NIL) (-804 1908609 1909108 1909153 "ODVAR" 1909158 NIL ODVAR (NIL T) -8 NIL NIL) (-803 1905819 1908106 1908291 "ODR" 1908484 NIL ODR (NIL T T NIL) -8 NIL NIL) (-802 1898163 1905595 1905721 "ODPOL" 1905726 NIL ODPOL (NIL T) -8 NIL NIL) (-801 1892039 1898035 1898140 "ODP" 1898145 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-800 1890805 1891020 1891295 "ODETOOLS" 1891813 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-799 1887774 1888430 1889146 "ODESYS" 1890138 NIL ODESYS (NIL T T) -7 NIL NIL) (-798 1882656 1883564 1884589 "ODERTRIC" 1886849 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-797 1882082 1882164 1882358 "ODERED" 1882568 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-796 1878970 1879518 1880195 "ODERAT" 1881505 NIL ODERAT (NIL T T) -7 NIL NIL) (-795 1875930 1876394 1876991 "ODEPRRIC" 1878499 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-794 1873799 1874368 1874877 "ODEPROB" 1875441 T ODEPROB (NIL) -8 NIL NIL) (-793 1870321 1870804 1871451 "ODEPRIM" 1873278 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-792 1869570 1869672 1869932 "ODEPAL" 1870213 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-791 1865732 1866523 1867387 "ODEPACK" 1868726 T ODEPACK (NIL) -7 NIL NIL) (-790 1864765 1864872 1865101 "ODEINT" 1865621 NIL ODEINT (NIL T T) -7 NIL NIL) (-789 1858866 1860291 1861738 "ODEIFTBL" 1863338 T ODEIFTBL (NIL) -8 NIL NIL) (-788 1854201 1854987 1855946 "ODEEF" 1858025 NIL ODEEF (NIL T T) -7 NIL NIL) (-787 1853536 1853625 1853855 "ODECONST" 1854106 NIL ODECONST (NIL T T T) -7 NIL NIL) (-786 1851687 1852322 1852350 "ODECAT" 1852955 T ODECAT (NIL) -9 NIL 1853486) (-785 1848594 1851399 1851518 "OCT" 1851600 NIL OCT (NIL T) -8 NIL NIL) (-784 1848232 1848275 1848402 "OCTCT2" 1848545 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-783 1842984 1845384 1845424 "OC" 1846521 NIL OC (NIL T) -9 NIL 1847379) (-782 1840211 1840959 1841949 "OC-" 1842043 NIL OC- (NIL T T) -8 NIL NIL) (-781 1839589 1840031 1840059 "OCAMON" 1840064 T OCAMON (NIL) -9 NIL 1840085) (-780 1839146 1839461 1839489 "OASGP" 1839494 T OASGP (NIL) -9 NIL 1839514) (-779 1838433 1838896 1838924 "OAMONS" 1838964 T OAMONS (NIL) -9 NIL 1839007) (-778 1837873 1838280 1838308 "OAMON" 1838313 T OAMON (NIL) -9 NIL 1838333) (-777 1837177 1837669 1837697 "OAGROUP" 1837702 T OAGROUP (NIL) -9 NIL 1837722) (-776 1836867 1836917 1837005 "NUMTUBE" 1837121 NIL NUMTUBE (NIL T) -7 NIL NIL) (-775 1830440 1831958 1833494 "NUMQUAD" 1835351 T NUMQUAD (NIL) -7 NIL NIL) (-774 1826196 1827184 1828209 "NUMODE" 1829435 T NUMODE (NIL) -7 NIL NIL) (-773 1823577 1824431 1824459 "NUMINT" 1825382 T NUMINT (NIL) -9 NIL 1826146) (-772 1822525 1822722 1822940 "NUMFMT" 1823379 T NUMFMT (NIL) -7 NIL NIL) (-771 1808884 1811829 1814361 "NUMERIC" 1820032 NIL NUMERIC (NIL T) -7 NIL NIL) (-770 1803281 1808333 1808428 "NTSCAT" 1808433 NIL NTSCAT (NIL T T T T) -9 NIL 1808472) (-769 1802475 1802640 1802833 "NTPOLFN" 1803120 NIL NTPOLFN (NIL T) -7 NIL NIL) (-768 1790315 1799300 1800112 "NSUP" 1801696 NIL NSUP (NIL T) -8 NIL NIL) (-767 1789947 1790004 1790113 "NSUP2" 1790252 NIL NSUP2 (NIL T T) -7 NIL NIL) (-766 1779944 1789721 1789854 "NSMP" 1789859 NIL NSMP (NIL T T) -8 NIL NIL) (-765 1778376 1778677 1779034 "NREP" 1779632 NIL NREP (NIL T) -7 NIL NIL) (-764 1776967 1777219 1777577 "NPCOEF" 1778119 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-763 1776033 1776148 1776364 "NORMRETR" 1776848 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-762 1774074 1774364 1774773 "NORMPK" 1775741 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-761 1773759 1773787 1773911 "NORMMA" 1774040 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-760 1773586 1773716 1773745 "NONE" 1773750 T NONE (NIL) -8 NIL NIL) (-759 1773375 1773404 1773473 "NONE1" 1773550 NIL NONE1 (NIL T) -7 NIL NIL) (-758 1772858 1772920 1773106 "NODE1" 1773307 NIL NODE1 (NIL T T) -7 NIL NIL) (-757 1771198 1772021 1772276 "NNI" 1772623 T NNI (NIL) -8 NIL NIL) (-756 1769618 1769931 1770295 "NLINSOL" 1770866 NIL NLINSOL (NIL T) -7 NIL NIL) (-755 1765785 1766753 1767675 "NIPROB" 1768716 T NIPROB (NIL) -8 NIL NIL) (-754 1764542 1764776 1765078 "NFINTBAS" 1765547 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-753 1763986 1764193 1764234 "NETCLT" 1764398 NIL NETCLT (NIL T) -9 NIL 1764487) (-752 1762694 1762925 1763206 "NCODIV" 1763754 NIL NCODIV (NIL T T) -7 NIL NIL) (-751 1762456 1762493 1762568 "NCNTFRAC" 1762651 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-750 1760636 1761000 1761420 "NCEP" 1762081 NIL NCEP (NIL T) -7 NIL NIL) (-749 1759547 1760286 1760314 "NASRING" 1760424 T NASRING (NIL) -9 NIL 1760498) (-748 1759342 1759386 1759480 "NASRING-" 1759485 NIL NASRING- (NIL T) -8 NIL NIL) (-747 1758495 1758994 1759022 "NARNG" 1759139 T NARNG (NIL) -9 NIL 1759230) (-746 1758187 1758254 1758388 "NARNG-" 1758393 NIL NARNG- (NIL T) -8 NIL NIL) (-745 1757066 1757273 1757508 "NAGSP" 1757972 T NAGSP (NIL) -7 NIL NIL) (-744 1748338 1750022 1751695 "NAGS" 1755413 T NAGS (NIL) -7 NIL NIL) (-743 1746886 1747194 1747525 "NAGF07" 1748027 T NAGF07 (NIL) -7 NIL NIL) (-742 1741424 1742715 1744022 "NAGF04" 1745599 T NAGF04 (NIL) -7 NIL NIL) (-741 1734392 1736006 1737639 "NAGF02" 1739811 T NAGF02 (NIL) -7 NIL NIL) (-740 1729616 1730716 1731833 "NAGF01" 1733295 T NAGF01 (NIL) -7 NIL NIL) (-739 1723244 1724810 1726395 "NAGE04" 1728051 T NAGE04 (NIL) -7 NIL NIL) (-738 1714413 1716534 1718664 "NAGE02" 1721134 T NAGE02 (NIL) -7 NIL NIL) (-737 1710366 1711313 1712277 "NAGE01" 1713469 T NAGE01 (NIL) -7 NIL NIL) (-736 1708161 1708695 1709253 "NAGD03" 1709828 T NAGD03 (NIL) -7 NIL NIL) (-735 1699911 1701839 1703793 "NAGD02" 1706227 T NAGD02 (NIL) -7 NIL NIL) (-734 1693722 1695147 1696587 "NAGD01" 1698491 T NAGD01 (NIL) -7 NIL NIL) (-733 1689931 1690753 1691590 "NAGC06" 1692905 T NAGC06 (NIL) -7 NIL NIL) (-732 1688396 1688728 1689084 "NAGC05" 1689595 T NAGC05 (NIL) -7 NIL NIL) (-731 1687772 1687891 1688035 "NAGC02" 1688272 T NAGC02 (NIL) -7 NIL NIL) (-730 1686832 1687389 1687429 "NAALG" 1687508 NIL NAALG (NIL T) -9 NIL 1687569) (-729 1686667 1686696 1686786 "NAALG-" 1686791 NIL NAALG- (NIL T T) -8 NIL NIL) (-728 1680617 1681725 1682912 "MULTSQFR" 1685563 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-727 1679936 1680011 1680195 "MULTFACT" 1680529 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-726 1673159 1677024 1677077 "MTSCAT" 1678147 NIL MTSCAT (NIL T T) -9 NIL 1678661) (-725 1672871 1672925 1673017 "MTHING" 1673099 NIL MTHING (NIL T) -7 NIL NIL) (-724 1672663 1672696 1672756 "MSYSCMD" 1672831 T MSYSCMD (NIL) -7 NIL NIL) (-723 1668775 1671418 1671738 "MSET" 1672376 NIL MSET (NIL T) -8 NIL NIL) (-722 1665870 1668336 1668377 "MSETAGG" 1668382 NIL MSETAGG (NIL T) -9 NIL 1668416) (-721 1661753 1663249 1663994 "MRING" 1665170 NIL MRING (NIL T T) -8 NIL NIL) (-720 1661319 1661386 1661517 "MRF2" 1661680 NIL MRF2 (NIL T T T) -7 NIL NIL) (-719 1660937 1660972 1661116 "MRATFAC" 1661278 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-718 1658549 1658844 1659275 "MPRFF" 1660642 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-717 1652609 1658403 1658500 "MPOLY" 1658505 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-716 1652099 1652134 1652342 "MPCPF" 1652568 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-715 1651613 1651656 1651840 "MPC3" 1652050 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-714 1650808 1650889 1651110 "MPC2" 1651528 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-713 1649109 1649446 1649836 "MONOTOOL" 1650468 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-712 1648360 1648651 1648679 "MONOID" 1648898 T MONOID (NIL) -9 NIL 1649045) (-711 1647906 1648025 1648206 "MONOID-" 1648211 NIL MONOID- (NIL T) -8 NIL NIL) (-710 1638847 1644753 1644812 "MONOGEN" 1645486 NIL MONOGEN (NIL T T) -9 NIL 1645942) (-709 1636065 1636800 1637800 "MONOGEN-" 1637919 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-708 1634924 1635344 1635372 "MONADWU" 1635764 T MONADWU (NIL) -9 NIL 1636002) (-707 1634296 1634455 1634703 "MONADWU-" 1634708 NIL MONADWU- (NIL T) -8 NIL NIL) (-706 1633681 1633899 1633927 "MONAD" 1634134 T MONAD (NIL) -9 NIL 1634246) (-705 1633366 1633444 1633576 "MONAD-" 1633581 NIL MONAD- (NIL T) -8 NIL NIL) (-704 1631682 1632279 1632558 "MOEBIUS" 1633119 NIL MOEBIUS (NIL T) -8 NIL NIL) (-703 1631074 1631452 1631492 "MODULE" 1631497 NIL MODULE (NIL T) -9 NIL 1631523) (-702 1630642 1630738 1630928 "MODULE-" 1630933 NIL MODULE- (NIL T T) -8 NIL NIL) (-701 1628357 1629006 1629333 "MODRING" 1630466 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-700 1625343 1626462 1626983 "MODOP" 1627886 NIL MODOP (NIL T T) -8 NIL NIL) (-699 1623530 1623982 1624323 "MODMONOM" 1625142 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-698 1613238 1621722 1622145 "MODMON" 1623158 NIL MODMON (NIL T T) -8 NIL NIL) (-697 1610429 1612082 1612358 "MODFIELD" 1613113 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-696 1609433 1609710 1609900 "MMLFORM" 1610259 T MMLFORM (NIL) -8 NIL NIL) (-695 1608959 1609002 1609181 "MMAP" 1609384 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-694 1607228 1607961 1608002 "MLO" 1608425 NIL MLO (NIL T) -9 NIL 1608667) (-693 1604595 1605110 1605712 "MLIFT" 1606709 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-692 1603986 1604070 1604224 "MKUCFUNC" 1604506 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-691 1603585 1603655 1603778 "MKRECORD" 1603909 NIL MKRECORD (NIL T T) -7 NIL NIL) (-690 1602633 1602794 1603022 "MKFUNC" 1603396 NIL MKFUNC (NIL T) -7 NIL NIL) (-689 1602021 1602125 1602281 "MKFLCFN" 1602516 NIL MKFLCFN (NIL T) -7 NIL NIL) (-688 1601447 1601814 1601903 "MKCHSET" 1601965 NIL MKCHSET (NIL T) -8 NIL NIL) (-687 1600724 1600826 1601011 "MKBCFUNC" 1601340 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-686 1597466 1600278 1600414 "MINT" 1600608 T MINT (NIL) -8 NIL NIL) (-685 1596278 1596521 1596798 "MHROWRED" 1597221 NIL MHROWRED (NIL T) -7 NIL NIL) (-684 1591704 1594813 1595218 "MFLOAT" 1595893 T MFLOAT (NIL) -8 NIL NIL) (-683 1591061 1591137 1591308 "MFINFACT" 1591616 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-682 1587376 1588224 1589108 "MESH" 1590197 T MESH (NIL) -7 NIL NIL) (-681 1585766 1586078 1586431 "MDDFACT" 1587063 NIL MDDFACT (NIL T) -7 NIL NIL) (-680 1582608 1584925 1584966 "MDAGG" 1585221 NIL MDAGG (NIL T) -9 NIL 1585364) (-679 1572386 1581901 1582108 "MCMPLX" 1582421 T MCMPLX (NIL) -8 NIL NIL) (-678 1571527 1571673 1571873 "MCDEN" 1572235 NIL MCDEN (NIL T T) -7 NIL NIL) (-677 1569417 1569687 1570067 "MCALCFN" 1571257 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-676 1568328 1568501 1568742 "MAYBE" 1569215 NIL MAYBE (NIL T) -8 NIL NIL) (-675 1565940 1566463 1567025 "MATSTOR" 1567799 NIL MATSTOR (NIL T) -7 NIL NIL) (-674 1561946 1565312 1565560 "MATRIX" 1565725 NIL MATRIX (NIL T) -8 NIL NIL) (-673 1557715 1558419 1559155 "MATLIN" 1561303 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-672 1547869 1551007 1551084 "MATCAT" 1555964 NIL MATCAT (NIL T T T) -9 NIL 1557381) (-671 1544233 1545246 1546602 "MATCAT-" 1546607 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-670 1542827 1542980 1543313 "MATCAT2" 1544068 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-669 1540939 1541263 1541647 "MAPPKG3" 1542502 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-668 1539920 1540093 1540315 "MAPPKG2" 1540763 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-667 1538419 1538703 1539030 "MAPPKG1" 1539626 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-666 1537525 1537825 1538002 "MAPPAST" 1538262 T MAPPAST (NIL) -8 NIL NIL) (-665 1537136 1537194 1537317 "MAPHACK3" 1537461 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-664 1536728 1536789 1536903 "MAPHACK2" 1537068 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-663 1536166 1536269 1536411 "MAPHACK1" 1536619 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-662 1534272 1534866 1535170 "MAGMA" 1535894 NIL MAGMA (NIL T) -8 NIL NIL) (-661 1533778 1533996 1534087 "MACROAST" 1534201 T MACROAST (NIL) -8 NIL NIL) (-660 1530245 1532017 1532478 "M3D" 1533350 NIL M3D (NIL T) -8 NIL NIL) (-659 1524400 1528615 1528656 "LZSTAGG" 1529438 NIL LZSTAGG (NIL T) -9 NIL 1529733) (-658 1520373 1521531 1522988 "LZSTAGG-" 1522993 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-657 1517487 1518264 1518751 "LWORD" 1519918 NIL LWORD (NIL T) -8 NIL NIL) (-656 1517090 1517291 1517366 "LSTAST" 1517432 T LSTAST (NIL) -8 NIL NIL) (-655 1510291 1516861 1516995 "LSQM" 1517000 NIL LSQM (NIL NIL T) -8 NIL NIL) (-654 1509515 1509654 1509882 "LSPP" 1510146 NIL LSPP (NIL T T T T) -7 NIL NIL) (-653 1507327 1507628 1508084 "LSMP" 1509204 NIL LSMP (NIL T T T T) -7 NIL NIL) (-652 1504106 1504780 1505510 "LSMP1" 1506629 NIL LSMP1 (NIL T) -7 NIL NIL) (-651 1498032 1503274 1503315 "LSAGG" 1503377 NIL LSAGG (NIL T) -9 NIL 1503455) (-650 1494727 1495651 1496864 "LSAGG-" 1496869 NIL LSAGG- (NIL T T) -8 NIL NIL) (-649 1492353 1493871 1494120 "LPOLY" 1494522 NIL LPOLY (NIL T T) -8 NIL NIL) (-648 1491935 1492020 1492143 "LPEFRAC" 1492262 NIL LPEFRAC (NIL T) -7 NIL NIL) (-647 1490282 1491029 1491282 "LO" 1491767 NIL LO (NIL T T T) -8 NIL NIL) (-646 1489934 1490046 1490074 "LOGIC" 1490185 T LOGIC (NIL) -9 NIL 1490266) (-645 1489796 1489819 1489890 "LOGIC-" 1489895 NIL LOGIC- (NIL T) -8 NIL NIL) (-644 1488989 1489129 1489322 "LODOOPS" 1489652 NIL LODOOPS (NIL T T) -7 NIL NIL) (-643 1486447 1488905 1488971 "LODO" 1488976 NIL LODO (NIL T NIL) -8 NIL NIL) (-642 1484985 1485220 1485573 "LODOF" 1486194 NIL LODOF (NIL T T) -7 NIL NIL) (-641 1481319 1483716 1483757 "LODOCAT" 1484195 NIL LODOCAT (NIL T) -9 NIL 1484406) (-640 1481052 1481110 1481237 "LODOCAT-" 1481242 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-639 1478407 1480893 1481011 "LODO2" 1481016 NIL LODO2 (NIL T T) -8 NIL NIL) (-638 1475877 1478344 1478389 "LODO1" 1478394 NIL LODO1 (NIL T) -8 NIL NIL) (-637 1474737 1474902 1475214 "LODEEF" 1475700 NIL LODEEF (NIL T T T) -7 NIL NIL) (-636 1470023 1472867 1472908 "LNAGG" 1473855 NIL LNAGG (NIL T) -9 NIL 1474299) (-635 1469170 1469384 1469726 "LNAGG-" 1469731 NIL LNAGG- (NIL T T) -8 NIL NIL) (-634 1465333 1466095 1466734 "LMOPS" 1468585 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-633 1464728 1465090 1465131 "LMODULE" 1465192 NIL LMODULE (NIL T) -9 NIL 1465234) (-632 1461974 1464373 1464496 "LMDICT" 1464638 NIL LMDICT (NIL T) -8 NIL NIL) (-631 1461700 1461882 1461942 "LITERAL" 1461947 NIL LITERAL (NIL T) -8 NIL NIL) (-630 1454927 1460646 1460944 "LIST" 1461435 NIL LIST (NIL T) -8 NIL NIL) (-629 1454452 1454526 1454665 "LIST3" 1454847 NIL LIST3 (NIL T T T) -7 NIL NIL) (-628 1453459 1453637 1453865 "LIST2" 1454270 NIL LIST2 (NIL T T) -7 NIL NIL) (-627 1451593 1451905 1452304 "LIST2MAP" 1453106 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-626 1450343 1450979 1451020 "LINEXP" 1451275 NIL LINEXP (NIL T) -9 NIL 1451424) (-625 1448990 1449250 1449547 "LINDEP" 1450095 NIL LINDEP (NIL T T) -7 NIL NIL) (-624 1445757 1446476 1447253 "LIMITRF" 1448245 NIL LIMITRF (NIL T) -7 NIL NIL) (-623 1444033 1444328 1444744 "LIMITPS" 1445452 NIL LIMITPS (NIL T T) -7 NIL NIL) (-622 1438488 1443544 1443772 "LIE" 1443854 NIL LIE (NIL T T) -8 NIL NIL) (-621 1437537 1437980 1438020 "LIECAT" 1438160 NIL LIECAT (NIL T) -9 NIL 1438311) (-620 1437378 1437405 1437493 "LIECAT-" 1437498 NIL LIECAT- (NIL T T) -8 NIL NIL) (-619 1429990 1436827 1436992 "LIB" 1437233 T LIB (NIL) -8 NIL NIL) (-618 1425627 1426508 1427443 "LGROBP" 1429107 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-617 1423493 1423767 1424129 "LF" 1425348 NIL LF (NIL T T) -7 NIL NIL) (-616 1422333 1423025 1423053 "LFCAT" 1423260 T LFCAT (NIL) -9 NIL 1423399) (-615 1419237 1419865 1420553 "LEXTRIPK" 1421697 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-614 1416008 1416807 1417310 "LEXP" 1418817 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-613 1415511 1415729 1415821 "LETAST" 1415936 T LETAST (NIL) -8 NIL NIL) (-612 1413909 1414222 1414623 "LEADCDET" 1415193 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-611 1413099 1413173 1413402 "LAZM3PK" 1413830 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-610 1408055 1411176 1411714 "LAUPOL" 1412611 NIL LAUPOL (NIL T T) -8 NIL NIL) (-609 1407620 1407664 1407832 "LAPLACE" 1408005 NIL LAPLACE (NIL T T) -7 NIL NIL) (-608 1405594 1406721 1406972 "LA" 1407453 NIL LA (NIL T T T) -8 NIL NIL) (-607 1404695 1405245 1405286 "LALG" 1405348 NIL LALG (NIL T) -9 NIL 1405407) (-606 1404409 1404468 1404604 "LALG-" 1404609 NIL LALG- (NIL T T) -8 NIL NIL) (-605 1404244 1404268 1404309 "KVTFROM" 1404371 NIL KVTFROM (NIL T) -9 NIL NIL) (-604 1403044 1403461 1403690 "KTVLOGIC" 1404035 T KTVLOGIC (NIL) -8 NIL NIL) (-603 1402879 1402903 1402944 "KRCFROM" 1403006 NIL KRCFROM (NIL T) -9 NIL NIL) (-602 1401783 1401970 1402269 "KOVACIC" 1402679 NIL KOVACIC (NIL T T) -7 NIL NIL) (-601 1401618 1401642 1401683 "KONVERT" 1401745 NIL KONVERT (NIL T) -9 NIL NIL) (-600 1401453 1401477 1401518 "KOERCE" 1401580 NIL KOERCE (NIL T) -9 NIL NIL) (-599 1399187 1399947 1400340 "KERNEL" 1401092 NIL KERNEL (NIL T) -8 NIL NIL) (-598 1398689 1398770 1398900 "KERNEL2" 1399101 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-597 1392540 1397228 1397282 "KDAGG" 1397659 NIL KDAGG (NIL T T) -9 NIL 1397865) (-596 1392069 1392193 1392398 "KDAGG-" 1392403 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-595 1385244 1391730 1391885 "KAFILE" 1391947 NIL KAFILE (NIL T) -8 NIL NIL) (-594 1379699 1384755 1384983 "JORDAN" 1385065 NIL JORDAN (NIL T T) -8 NIL NIL) (-593 1379105 1379348 1379469 "JOINAST" 1379598 T JOINAST (NIL) -8 NIL NIL) (-592 1378834 1378893 1378980 "JAVACODE" 1379038 T JAVACODE (NIL) -8 NIL NIL) (-591 1375133 1377039 1377093 "IXAGG" 1378022 NIL IXAGG (NIL T T) -9 NIL 1378481) (-590 1374052 1374358 1374777 "IXAGG-" 1374782 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-589 1369632 1373974 1374033 "IVECTOR" 1374038 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-588 1368398 1368635 1368901 "ITUPLE" 1369399 NIL ITUPLE (NIL T) -8 NIL NIL) (-587 1366834 1367011 1367317 "ITRIGMNP" 1368220 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-586 1365579 1365783 1366066 "ITFUN3" 1366610 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-585 1365211 1365268 1365377 "ITFUN2" 1365516 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-584 1363048 1364073 1364372 "ITAYLOR" 1364945 NIL ITAYLOR (NIL T) -8 NIL NIL) (-583 1352030 1357185 1358348 "ISUPS" 1361918 NIL ISUPS (NIL T) -8 NIL NIL) (-582 1351134 1351274 1351510 "ISUMP" 1351877 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-581 1346398 1350935 1351014 "ISTRING" 1351087 NIL ISTRING (NIL NIL) -8 NIL NIL) (-580 1345901 1346119 1346211 "ISAST" 1346326 T ISAST (NIL) -8 NIL NIL) (-579 1345111 1345192 1345408 "IRURPK" 1345815 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-578 1344047 1344248 1344488 "IRSN" 1344891 T IRSN (NIL) -7 NIL NIL) (-577 1342076 1342431 1342867 "IRRF2F" 1343685 NIL IRRF2F (NIL T) -7 NIL NIL) (-576 1341823 1341861 1341937 "IRREDFFX" 1342032 NIL IRREDFFX (NIL T) -7 NIL NIL) (-575 1340438 1340697 1340996 "IROOT" 1341556 NIL IROOT (NIL T) -7 NIL NIL) (-574 1337070 1338122 1338814 "IR" 1339778 NIL IR (NIL T) -8 NIL NIL) (-573 1334683 1335178 1335744 "IR2" 1336548 NIL IR2 (NIL T T) -7 NIL NIL) (-572 1333755 1333868 1334089 "IR2F" 1334566 NIL IR2F (NIL T T) -7 NIL NIL) (-571 1333546 1333580 1333640 "IPRNTPK" 1333715 T IPRNTPK (NIL) -7 NIL NIL) (-570 1330165 1333435 1333504 "IPF" 1333509 NIL IPF (NIL NIL) -8 NIL NIL) (-569 1328528 1330090 1330147 "IPADIC" 1330152 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-568 1327859 1328086 1328223 "IP4ADDR" 1328411 T IP4ADDR (NIL) -8 NIL NIL) (-567 1327359 1327563 1327673 "IOMODE" 1327769 T IOMODE (NIL) -8 NIL NIL) (-566 1326717 1326956 1327083 "IOBFILE" 1327252 T IOBFILE (NIL) -8 NIL NIL) (-565 1326481 1326621 1326649 "IOBCON" 1326654 T IOBCON (NIL) -9 NIL 1326675) (-564 1325978 1326036 1326226 "INVLAPLA" 1326417 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-563 1315627 1317980 1320366 "INTTR" 1323642 NIL INTTR (NIL T T) -7 NIL NIL) (-562 1311971 1312713 1313577 "INTTOOLS" 1314812 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-561 1311557 1311648 1311765 "INTSLPE" 1311874 T INTSLPE (NIL) -7 NIL NIL) (-560 1309552 1311480 1311539 "INTRVL" 1311544 NIL INTRVL (NIL T) -8 NIL NIL) (-559 1307154 1307666 1308241 "INTRF" 1309037 NIL INTRF (NIL T) -7 NIL NIL) (-558 1306565 1306662 1306804 "INTRET" 1307052 NIL INTRET (NIL T) -7 NIL NIL) (-557 1304562 1304951 1305421 "INTRAT" 1306173 NIL INTRAT (NIL T T) -7 NIL NIL) (-556 1301790 1302373 1302999 "INTPM" 1304047 NIL INTPM (NIL T T) -7 NIL NIL) (-555 1298493 1299092 1299837 "INTPAF" 1301176 NIL INTPAF (NIL T T T) -7 NIL NIL) (-554 1293672 1294634 1295685 "INTPACK" 1297462 T INTPACK (NIL) -7 NIL NIL) (-553 1290584 1293401 1293528 "INT" 1293565 T INT (NIL) -8 NIL NIL) (-552 1289836 1289988 1290196 "INTHERTR" 1290426 NIL INTHERTR (NIL T T) -7 NIL NIL) (-551 1289275 1289355 1289543 "INTHERAL" 1289750 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-550 1287121 1287564 1288021 "INTHEORY" 1288838 T INTHEORY (NIL) -7 NIL NIL) (-549 1278429 1280050 1281829 "INTG0" 1285473 NIL INTG0 (NIL T T T) -7 NIL NIL) (-548 1259002 1263792 1268602 "INTFTBL" 1273639 T INTFTBL (NIL) -8 NIL NIL) (-547 1258251 1258389 1258562 "INTFACT" 1258861 NIL INTFACT (NIL T) -7 NIL NIL) (-546 1255636 1256082 1256646 "INTEF" 1257805 NIL INTEF (NIL T T) -7 NIL NIL) (-545 1254138 1254843 1254871 "INTDOM" 1255172 T INTDOM (NIL) -9 NIL 1255379) (-544 1253507 1253681 1253923 "INTDOM-" 1253928 NIL INTDOM- (NIL T) -8 NIL NIL) (-543 1250020 1251906 1251960 "INTCAT" 1252759 NIL INTCAT (NIL T) -9 NIL 1253079) (-542 1249493 1249595 1249723 "INTBIT" 1249912 T INTBIT (NIL) -7 NIL NIL) (-541 1248164 1248318 1248632 "INTALG" 1249338 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-540 1247621 1247711 1247881 "INTAF" 1248068 NIL INTAF (NIL T T) -7 NIL NIL) (-539 1241075 1247431 1247571 "INTABL" 1247576 NIL INTABL (NIL T T T) -8 NIL NIL) (-538 1236108 1238779 1238807 "INS" 1239741 T INS (NIL) -9 NIL 1240406) (-537 1233348 1234119 1235093 "INS-" 1235166 NIL INS- (NIL T) -8 NIL NIL) (-536 1232123 1232350 1232648 "INPSIGN" 1233101 NIL INPSIGN (NIL T T) -7 NIL NIL) (-535 1231241 1231358 1231555 "INPRODPF" 1232003 NIL INPRODPF (NIL T T) -7 NIL NIL) (-534 1230135 1230252 1230489 "INPRODFF" 1231121 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-533 1229135 1229287 1229547 "INNMFACT" 1229971 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-532 1228332 1228429 1228617 "INMODGCD" 1229034 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-531 1226841 1227085 1227409 "INFSP" 1228077 NIL INFSP (NIL T T T) -7 NIL NIL) (-530 1226025 1226142 1226325 "INFPROD0" 1226721 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-529 1222907 1224090 1224605 "INFORM" 1225518 T INFORM (NIL) -8 NIL NIL) (-528 1222517 1222577 1222675 "INFORM1" 1222842 NIL INFORM1 (NIL T) -7 NIL NIL) (-527 1222040 1222129 1222243 "INFINITY" 1222423 T INFINITY (NIL) -7 NIL NIL) (-526 1221485 1221758 1221866 "INETCLTS" 1221952 T INETCLTS (NIL) -8 NIL NIL) (-525 1220102 1220351 1220672 "INEP" 1221233 NIL INEP (NIL T T T) -7 NIL NIL) (-524 1219378 1219999 1220064 "INDE" 1220069 NIL INDE (NIL T) -8 NIL NIL) (-523 1218942 1219010 1219127 "INCRMAPS" 1219305 NIL INCRMAPS (NIL T) -7 NIL NIL) (-522 1217960 1218211 1218417 "INBFILE" 1218756 T INBFILE (NIL) -8 NIL NIL) (-521 1213271 1214196 1215140 "INBFF" 1217048 NIL INBFF (NIL T) -7 NIL NIL) (-520 1212940 1213016 1213044 "INBCON" 1213177 T INBCON (NIL) -9 NIL 1213255) (-519 1212780 1212815 1212891 "INBCON-" 1212896 NIL INBCON- (NIL T) -8 NIL NIL) (-518 1212282 1212501 1212593 "INAST" 1212708 T INAST (NIL) -8 NIL NIL) (-517 1211736 1211961 1212067 "IMPTAST" 1212196 T IMPTAST (NIL) -8 NIL NIL) (-516 1208230 1211580 1211684 "IMATRIX" 1211689 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-515 1206942 1207065 1207380 "IMATQF" 1208086 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-514 1205162 1205389 1205726 "IMATLIN" 1206698 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-513 1199788 1205086 1205144 "ILIST" 1205149 NIL ILIST (NIL T NIL) -8 NIL NIL) (-512 1197741 1199648 1199761 "IIARRAY2" 1199766 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-511 1193174 1197652 1197716 "IFF" 1197721 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-510 1192548 1192791 1192907 "IFAST" 1193078 T IFAST (NIL) -8 NIL NIL) (-509 1187591 1191840 1192028 "IFARRAY" 1192405 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-508 1186798 1187495 1187568 "IFAMON" 1187573 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-507 1186382 1186447 1186501 "IEVALAB" 1186708 NIL IEVALAB (NIL T T) -9 NIL NIL) (-506 1186057 1186125 1186285 "IEVALAB-" 1186290 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-505 1185715 1185971 1186034 "IDPO" 1186039 NIL IDPO (NIL T T) -8 NIL NIL) (-504 1184992 1185604 1185679 "IDPOAMS" 1185684 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-503 1184326 1184881 1184956 "IDPOAM" 1184961 NIL IDPOAM (NIL T T) -8 NIL NIL) (-502 1183411 1183661 1183714 "IDPC" 1184127 NIL IDPC (NIL T T) -9 NIL 1184276) (-501 1182907 1183303 1183376 "IDPAM" 1183381 NIL IDPAM (NIL T T) -8 NIL NIL) (-500 1182310 1182799 1182872 "IDPAG" 1182877 NIL IDPAG (NIL T T) -8 NIL NIL) (-499 1182040 1182225 1182275 "IDENT" 1182280 T IDENT (NIL) -8 NIL NIL) (-498 1178295 1179143 1180038 "IDECOMP" 1181197 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-497 1171168 1172218 1173265 "IDEAL" 1177331 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-496 1170332 1170444 1170643 "ICDEN" 1171052 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-495 1169431 1169812 1169959 "ICARD" 1170205 T ICARD (NIL) -8 NIL NIL) (-494 1167491 1167804 1168209 "IBPTOOLS" 1169108 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-493 1163125 1167111 1167224 "IBITS" 1167410 NIL IBITS (NIL NIL) -8 NIL NIL) (-492 1159848 1160424 1161119 "IBATOOL" 1162542 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-491 1157628 1158089 1158622 "IBACHIN" 1159383 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-490 1155505 1157474 1157577 "IARRAY2" 1157582 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-489 1151658 1155431 1155488 "IARRAY1" 1155493 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-488 1145651 1150070 1150551 "IAN" 1151197 T IAN (NIL) -8 NIL NIL) (-487 1145162 1145219 1145392 "IALGFACT" 1145588 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-486 1144690 1144803 1144831 "HYPCAT" 1145038 T HYPCAT (NIL) -9 NIL NIL) (-485 1144228 1144345 1144531 "HYPCAT-" 1144536 NIL HYPCAT- (NIL T) -8 NIL NIL) (-484 1143850 1144023 1144106 "HOSTNAME" 1144165 T HOSTNAME (NIL) -8 NIL NIL) (-483 1143695 1143732 1143773 "HOMOTOP" 1143778 NIL HOMOTOP (NIL T) -9 NIL 1143811) (-482 1140374 1141705 1141746 "HOAGG" 1142727 NIL HOAGG (NIL T) -9 NIL 1143406) (-481 1138968 1139367 1139893 "HOAGG-" 1139898 NIL HOAGG- (NIL T T) -8 NIL NIL) (-480 1132854 1138409 1138575 "HEXADEC" 1138822 T HEXADEC (NIL) -8 NIL NIL) (-479 1131602 1131824 1132087 "HEUGCD" 1132631 NIL HEUGCD (NIL T) -7 NIL NIL) (-478 1130705 1131439 1131569 "HELLFDIV" 1131574 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-477 1128933 1130482 1130570 "HEAP" 1130649 NIL HEAP (NIL T) -8 NIL NIL) (-476 1128224 1128485 1128619 "HEADAST" 1128819 T HEADAST (NIL) -8 NIL NIL) (-475 1122144 1128139 1128201 "HDP" 1128206 NIL HDP (NIL NIL T) -8 NIL NIL) (-474 1115895 1121779 1121931 "HDMP" 1122045 NIL HDMP (NIL NIL T) -8 NIL NIL) (-473 1115220 1115359 1115523 "HB" 1115751 T HB (NIL) -7 NIL NIL) (-472 1108717 1115066 1115170 "HASHTBL" 1115175 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-471 1108220 1108438 1108530 "HASAST" 1108645 T HASAST (NIL) -8 NIL NIL) (-470 1106032 1107842 1108024 "HACKPI" 1108058 T HACKPI (NIL) -8 NIL NIL) (-469 1101727 1105885 1105998 "GTSET" 1106003 NIL GTSET (NIL T T T T) -8 NIL NIL) (-468 1095253 1101605 1101703 "GSTBL" 1101708 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-467 1087566 1094284 1094549 "GSERIES" 1095044 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-466 1086733 1087124 1087152 "GROUP" 1087355 T GROUP (NIL) -9 NIL 1087489) (-465 1086099 1086258 1086509 "GROUP-" 1086514 NIL GROUP- (NIL T) -8 NIL NIL) (-464 1084468 1084787 1085174 "GROEBSOL" 1085776 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-463 1083408 1083670 1083721 "GRMOD" 1084250 NIL GRMOD (NIL T T) -9 NIL 1084418) (-462 1083176 1083212 1083340 "GRMOD-" 1083345 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-461 1078502 1079530 1080530 "GRIMAGE" 1082196 T GRIMAGE (NIL) -8 NIL NIL) (-460 1076969 1077229 1077553 "GRDEF" 1078198 T GRDEF (NIL) -7 NIL NIL) (-459 1076413 1076529 1076670 "GRAY" 1076848 T GRAY (NIL) -7 NIL NIL) (-458 1075626 1076006 1076057 "GRALG" 1076210 NIL GRALG (NIL T T) -9 NIL 1076303) (-457 1075287 1075360 1075523 "GRALG-" 1075528 NIL GRALG- (NIL T T T) -8 NIL NIL) (-456 1072091 1074872 1075050 "GPOLSET" 1075194 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-455 1071445 1071502 1071760 "GOSPER" 1072028 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-454 1067204 1067883 1068409 "GMODPOL" 1071144 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-453 1066209 1066393 1066631 "GHENSEL" 1067016 NIL GHENSEL (NIL T T) -7 NIL NIL) (-452 1060260 1061103 1062130 "GENUPS" 1065293 NIL GENUPS (NIL T T) -7 NIL NIL) (-451 1059957 1060008 1060097 "GENUFACT" 1060203 NIL GENUFACT (NIL T) -7 NIL NIL) (-450 1059369 1059446 1059611 "GENPGCD" 1059875 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-449 1058843 1058878 1059091 "GENMFACT" 1059328 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-448 1057411 1057666 1057973 "GENEEZ" 1058586 NIL GENEEZ (NIL T T) -7 NIL NIL) (-447 1051324 1057022 1057184 "GDMP" 1057334 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-446 1040701 1045095 1046201 "GCNAALG" 1050307 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-445 1039163 1039991 1040019 "GCDDOM" 1040274 T GCDDOM (NIL) -9 NIL 1040431) (-444 1038633 1038760 1038975 "GCDDOM-" 1038980 NIL GCDDOM- (NIL T) -8 NIL NIL) (-443 1037305 1037490 1037794 "GB" 1038412 NIL GB (NIL T T T T) -7 NIL NIL) (-442 1025925 1028251 1030643 "GBINTERN" 1034996 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1023762 1024054 1024475 "GBF" 1025600 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1022543 1022708 1022975 "GBEUCLID" 1023578 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1021892 1022017 1022166 "GAUSSFAC" 1022414 T GAUSSFAC (NIL) -7 NIL NIL) (-438 1020259 1020561 1020875 "GALUTIL" 1021611 NIL GALUTIL (NIL T) -7 NIL NIL) (-437 1018567 1018841 1019165 "GALPOLYU" 1019986 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-436 1015932 1016222 1016629 "GALFACTU" 1018264 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-435 1007738 1009237 1010845 "GALFACT" 1014364 NIL GALFACT (NIL T) -7 NIL NIL) (-434 1005126 1005784 1005812 "FVFUN" 1006968 T FVFUN (NIL) -9 NIL 1007688) (-433 1004392 1004574 1004602 "FVC" 1004893 T FVC (NIL) -9 NIL 1005076) (-432 1004034 1004189 1004270 "FUNCTION" 1004344 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-431 1001704 1002255 1002744 "FT" 1003565 T FT (NIL) -8 NIL NIL) (-430 1000522 1001005 1001208 "FTEM" 1001521 T FTEM (NIL) -8 NIL NIL) (-429 998778 999067 999471 "FSUPFACT" 1000213 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-428 997175 997464 997796 "FST" 998466 T FST (NIL) -8 NIL NIL) (-427 996346 996452 996647 "FSRED" 997057 NIL FSRED (NIL T T) -7 NIL NIL) (-426 995025 995280 995634 "FSPRMELT" 996061 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-425 992110 992548 993047 "FSPECF" 994588 NIL FSPECF (NIL T T) -7 NIL NIL) (-424 974272 982714 982754 "FS" 986602 NIL FS (NIL T) -9 NIL 988891) (-423 962922 965912 969968 "FS-" 970265 NIL FS- (NIL T T) -8 NIL NIL) (-422 962436 962490 962667 "FSINT" 962863 NIL FSINT (NIL T T) -7 NIL NIL) (-421 960763 961429 961732 "FSERIES" 962215 NIL FSERIES (NIL T T) -8 NIL NIL) (-420 959777 959893 960124 "FSCINT" 960643 NIL FSCINT (NIL T T) -7 NIL NIL) (-419 956011 958721 958762 "FSAGG" 959132 NIL FSAGG (NIL T) -9 NIL 959391) (-418 953773 954374 955170 "FSAGG-" 955265 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 952815 952958 953185 "FSAGG2" 953626 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-416 950470 950749 951303 "FS2UPS" 952533 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-415 950052 950095 950250 "FS2" 950421 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 948909 949080 949389 "FS2EXPXP" 949877 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-413 948335 948450 948602 "FRUTIL" 948789 NIL FRUTIL (NIL T) -7 NIL NIL) (-412 939790 943830 945188 "FR" 947009 NIL FR (NIL T) -8 NIL NIL) (-411 934865 937508 937548 "FRNAALG" 938944 NIL FRNAALG (NIL T) -9 NIL 939551) (-410 930543 931614 932889 "FRNAALG-" 933639 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 930181 930224 930351 "FRNAAF2" 930494 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 928588 929035 929330 "FRMOD" 929993 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 926367 926971 927288 "FRIDEAL" 928379 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-406 925562 925649 925938 "FRIDEAL2" 926274 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-405 924695 925109 925150 "FRETRCT" 925155 NIL FRETRCT (NIL T) -9 NIL 925331) (-404 923807 924038 924389 "FRETRCT-" 924394 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 921057 922233 922292 "FRAMALG" 923174 NIL FRAMALG (NIL T T) -9 NIL 923466) (-402 919191 919646 920276 "FRAMALG-" 920499 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 913149 918666 918942 "FRAC" 918947 NIL FRAC (NIL T) -8 NIL NIL) (-400 912785 912842 912949 "FRAC2" 913086 NIL FRAC2 (NIL T T) -7 NIL NIL) (-399 912421 912478 912585 "FR2" 912722 NIL FR2 (NIL T T) -7 NIL NIL) (-398 907110 909958 909986 "FPS" 911105 T FPS (NIL) -9 NIL 911662) (-397 906559 906668 906832 "FPS-" 906978 NIL FPS- (NIL T) -8 NIL NIL) (-396 904065 905700 905728 "FPC" 905953 T FPC (NIL) -9 NIL 906095) (-395 903858 903898 903995 "FPC-" 904000 NIL FPC- (NIL T) -8 NIL NIL) (-394 902736 903346 903387 "FPATMAB" 903392 NIL FPATMAB (NIL T) -9 NIL 903544) (-393 900436 900912 901338 "FPARFRAC" 902373 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-392 895829 896328 897010 "FORTRAN" 899868 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-391 893545 894045 894584 "FORT" 895310 T FORT (NIL) -7 NIL NIL) (-390 891221 891783 891811 "FORTFN" 892871 T FORTFN (NIL) -9 NIL 893495) (-389 890985 891035 891063 "FORTCAT" 891122 T FORTCAT (NIL) -9 NIL 891184) (-388 889045 889528 889927 "FORMULA" 890606 T FORMULA (NIL) -8 NIL NIL) (-387 888833 888863 888932 "FORMULA1" 889009 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 888356 888408 888581 "FORDER" 888775 NIL FORDER (NIL T T T T) -7 NIL NIL) (-385 887452 887616 887809 "FOP" 888183 T FOP (NIL) -7 NIL NIL) (-384 886060 886732 886906 "FNLA" 887334 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-383 884728 885117 885145 "FNCAT" 885717 T FNCAT (NIL) -9 NIL 886010) (-382 884294 884687 884715 "FNAME" 884720 T FNAME (NIL) -8 NIL NIL) (-381 882972 883901 883929 "FMTC" 883934 T FMTC (NIL) -9 NIL 883970) (-380 879334 880495 881124 "FMONOID" 882376 NIL FMONOID (NIL T) -8 NIL NIL) (-379 878553 879076 879225 "FM" 879230 NIL FM (NIL T T) -8 NIL NIL) (-378 875977 876623 876651 "FMFUN" 877795 T FMFUN (NIL) -9 NIL 878503) (-377 875246 875427 875455 "FMC" 875745 T FMC (NIL) -9 NIL 875927) (-376 872440 873274 873328 "FMCAT" 874523 NIL FMCAT (NIL T T) -9 NIL 875018) (-375 871333 872206 872306 "FM1" 872385 NIL FM1 (NIL T T) -8 NIL NIL) (-374 869107 869523 870017 "FLOATRP" 870884 NIL FLOATRP (NIL T) -7 NIL NIL) (-373 862658 866763 867393 "FLOAT" 868497 T FLOAT (NIL) -8 NIL NIL) (-372 860096 860596 861174 "FLOATCP" 862125 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 858925 859729 859770 "FLINEXP" 859775 NIL FLINEXP (NIL T) -9 NIL 859868) (-370 858079 858314 858642 "FLINEXP-" 858647 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-369 857155 857299 857523 "FLASORT" 857931 NIL FLASORT (NIL T T) -7 NIL NIL) (-368 854372 855214 855266 "FLALG" 856493 NIL FLALG (NIL T T) -9 NIL 856960) (-367 848156 851858 851899 "FLAGG" 853161 NIL FLAGG (NIL T) -9 NIL 853813) (-366 846882 847221 847711 "FLAGG-" 847716 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 845924 846067 846294 "FLAGG2" 846735 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-364 842937 843911 843970 "FINRALG" 845098 NIL FINRALG (NIL T T) -9 NIL 845606) (-363 842097 842326 842665 "FINRALG-" 842670 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-362 841503 841716 841744 "FINITE" 841940 T FINITE (NIL) -9 NIL 842047) (-361 833961 836122 836162 "FINAALG" 839829 NIL FINAALG (NIL T) -9 NIL 841282) (-360 829302 830343 831487 "FINAALG-" 832866 NIL FINAALG- (NIL T T) -8 NIL NIL) (-359 828697 829057 829160 "FILE" 829232 NIL FILE (NIL T) -8 NIL NIL) (-358 827381 827693 827747 "FILECAT" 828431 NIL FILECAT (NIL T T) -9 NIL 828647) (-357 825301 826795 826823 "FIELD" 826863 T FIELD (NIL) -9 NIL 826943) (-356 823921 824306 824817 "FIELD-" 824822 NIL FIELD- (NIL T) -8 NIL NIL) (-355 821799 822556 822903 "FGROUP" 823607 NIL FGROUP (NIL T) -8 NIL NIL) (-354 820889 821053 821273 "FGLMICPK" 821631 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-353 816756 820814 820871 "FFX" 820876 NIL FFX (NIL T NIL) -8 NIL NIL) (-352 816357 816418 816553 "FFSLPE" 816689 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-351 812350 813129 813925 "FFPOLY" 815593 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 811854 811890 812099 "FFPOLY2" 812308 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 807740 811773 811836 "FFP" 811841 NIL FFP (NIL T NIL) -8 NIL NIL) (-348 803173 807651 807715 "FF" 807720 NIL FF (NIL NIL NIL) -8 NIL NIL) (-347 798334 802516 802706 "FFNBX" 803027 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 793308 797469 797727 "FFNBP" 798188 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 787976 792592 792803 "FFNB" 793141 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 786808 787006 787321 "FFINTBAS" 787773 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 783092 785267 785295 "FFIELDC" 785915 T FFIELDC (NIL) -9 NIL 786291) (-342 781755 782125 782622 "FFIELDC-" 782627 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 781325 781370 781494 "FFHOM" 781697 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 779023 779507 780024 "FFF" 780840 NIL FFF (NIL T) -7 NIL NIL) (-339 774676 778765 778866 "FFCGX" 778966 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 770343 774408 774515 "FFCGP" 774619 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 765561 770070 770178 "FFCG" 770279 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 747497 756533 756619 "FFCAT" 761784 NIL FFCAT (NIL T T T) -9 NIL 763235) (-335 742695 743742 745056 "FFCAT-" 746286 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-334 742106 742149 742384 "FFCAT2" 742646 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-333 731318 735078 736298 "FEXPR" 740958 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-332 730318 730753 730794 "FEVALAB" 730878 NIL FEVALAB (NIL T) -9 NIL 731139) (-331 729477 729687 730025 "FEVALAB-" 730030 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-330 728070 728860 729063 "FDIV" 729376 NIL FDIV (NIL T T T T) -8 NIL NIL) (-329 725136 725851 725966 "FDIVCAT" 727534 NIL FDIVCAT (NIL T T T T) -9 NIL 727971) (-328 724898 724925 725095 "FDIVCAT-" 725100 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 724118 724205 724482 "FDIV2" 724805 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 722804 723063 723352 "FCPAK1" 723849 T FCPAK1 (NIL) -7 NIL NIL) (-325 721932 722304 722445 "FCOMP" 722695 NIL FCOMP (NIL T) -8 NIL NIL) (-324 705567 708981 712542 "FC" 718391 T FC (NIL) -8 NIL NIL) (-323 698202 702183 702223 "FAXF" 704025 NIL FAXF (NIL T) -9 NIL 704717) (-322 695481 696136 696961 "FAXF-" 697426 NIL FAXF- (NIL T T) -8 NIL NIL) (-321 690581 694857 695033 "FARRAY" 695338 NIL FARRAY (NIL T) -8 NIL NIL) (-320 685879 687911 687964 "FAMR" 688987 NIL FAMR (NIL T T) -9 NIL 689447) (-319 684769 685071 685506 "FAMR-" 685511 NIL FAMR- (NIL T T T) -8 NIL NIL) (-318 683965 684691 684744 "FAMONOID" 684749 NIL FAMONOID (NIL T) -8 NIL NIL) (-317 681777 682461 682514 "FAMONC" 683455 NIL FAMONC (NIL T T) -9 NIL 683841) (-316 680469 681531 681668 "FAGROUP" 681673 NIL FAGROUP (NIL T) -8 NIL NIL) (-315 678264 678583 678986 "FACUTIL" 680150 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-314 677363 677548 677770 "FACTFUNC" 678074 NIL FACTFUNC (NIL T) -7 NIL NIL) (-313 669768 676614 676826 "EXPUPXS" 677219 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-312 667251 667791 668377 "EXPRTUBE" 669202 T EXPRTUBE (NIL) -7 NIL NIL) (-311 663445 664037 664774 "EXPRODE" 666590 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 648819 662100 662528 "EXPR" 663049 NIL EXPR (NIL T) -8 NIL NIL) (-309 643226 643813 644626 "EXPR2UPS" 648117 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 642862 642919 643026 "EXPR2" 643163 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 634267 641994 642291 "EXPEXPAN" 642699 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 634094 634224 634253 "EXIT" 634258 T EXIT (NIL) -8 NIL NIL) (-305 633601 633818 633909 "EXITAST" 634023 T EXITAST (NIL) -8 NIL NIL) (-304 633228 633290 633403 "EVALCYC" 633533 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 632769 632887 632928 "EVALAB" 633098 NIL EVALAB (NIL T) -9 NIL 633202) (-302 632250 632372 632593 "EVALAB-" 632598 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 629753 631021 631049 "EUCDOM" 631604 T EUCDOM (NIL) -9 NIL 631954) (-300 628158 628600 629190 "EUCDOM-" 629195 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 615698 618456 621206 "ESTOOLS" 625428 T ESTOOLS (NIL) -7 NIL NIL) (-298 615330 615387 615496 "ESTOOLS2" 615635 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 615081 615123 615203 "ESTOOLS1" 615282 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 608986 610714 610742 "ES" 613510 T ES (NIL) -9 NIL 614919) (-295 603933 605220 607037 "ES-" 607201 NIL ES- (NIL T) -8 NIL NIL) (-294 600308 601068 601848 "ESCONT" 603173 T ESCONT (NIL) -7 NIL NIL) (-293 600053 600085 600167 "ESCONT1" 600270 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 599728 599778 599878 "ES2" 599997 NIL ES2 (NIL T T) -7 NIL NIL) (-291 599358 599416 599525 "ES1" 599664 NIL ES1 (NIL T T) -7 NIL NIL) (-290 598574 598703 598879 "ERROR" 599202 T ERROR (NIL) -7 NIL NIL) (-289 592077 598433 598524 "EQTBL" 598529 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 584634 587391 588840 "EQ" 590661 NIL -3356 (NIL T) -8 NIL NIL) (-287 584266 584323 584432 "EQ2" 584571 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 579558 580604 581697 "EP" 583205 NIL EP (NIL T) -7 NIL NIL) (-285 578140 578441 578758 "ENV" 579261 T ENV (NIL) -8 NIL NIL) (-284 577339 577859 577887 "ENTIRER" 577892 T ENTIRER (NIL) -9 NIL 577938) (-283 573841 575294 575664 "EMR" 577138 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-282 572985 573170 573224 "ELTAGG" 573604 NIL ELTAGG (NIL T T) -9 NIL 573815) (-281 572704 572766 572907 "ELTAGG-" 572912 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-280 572493 572522 572576 "ELTAB" 572660 NIL ELTAB (NIL T T) -9 NIL NIL) (-279 571619 571765 571964 "ELFUTS" 572344 NIL ELFUTS (NIL T T) -7 NIL NIL) (-278 571361 571417 571445 "ELEMFUN" 571550 T ELEMFUN (NIL) -9 NIL NIL) (-277 571231 571252 571320 "ELEMFUN-" 571325 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-276 566122 569331 569372 "ELAGG" 570312 NIL ELAGG (NIL T) -9 NIL 570775) (-275 564407 564841 565504 "ELAGG-" 565509 NIL ELAGG- (NIL T T) -8 NIL NIL) (-274 563064 563344 563639 "ELABEXPR" 564132 T ELABEXPR (NIL) -8 NIL NIL) (-273 555930 557731 558558 "EFUPXS" 562340 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-272 549380 551181 551991 "EFULS" 555206 NIL EFULS (NIL T T T) -8 NIL NIL) (-271 546802 547160 547639 "EFSTRUC" 549012 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-270 535874 537439 538999 "EF" 545317 NIL EF (NIL T T) -7 NIL NIL) (-269 534975 535359 535508 "EAB" 535745 T EAB (NIL) -8 NIL NIL) (-268 534184 534934 534962 "E04UCFA" 534967 T E04UCFA (NIL) -8 NIL NIL) (-267 533393 534143 534171 "E04NAFA" 534176 T E04NAFA (NIL) -8 NIL NIL) (-266 532602 533352 533380 "E04MBFA" 533385 T E04MBFA (NIL) -8 NIL NIL) (-265 531811 532561 532589 "E04JAFA" 532594 T E04JAFA (NIL) -8 NIL NIL) (-264 531022 531770 531798 "E04GCFA" 531803 T E04GCFA (NIL) -8 NIL NIL) (-263 530233 530981 531009 "E04FDFA" 531014 T E04FDFA (NIL) -8 NIL NIL) (-262 529442 530192 530220 "E04DGFA" 530225 T E04DGFA (NIL) -8 NIL NIL) (-261 523620 524967 526331 "E04AGNT" 528098 T E04AGNT (NIL) -7 NIL NIL) (-260 522326 522806 522846 "DVARCAT" 523321 NIL DVARCAT (NIL T) -9 NIL 523520) (-259 521530 521742 522056 "DVARCAT-" 522061 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-258 514430 521329 521458 "DSMP" 521463 NIL DSMP (NIL T T T) -8 NIL NIL) (-257 509240 510375 511443 "DROPT" 513382 T DROPT (NIL) -8 NIL NIL) (-256 508905 508964 509062 "DROPT1" 509175 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 504020 505146 506283 "DROPT0" 507788 T DROPT0 (NIL) -7 NIL NIL) (-254 502365 502690 503076 "DRAWPT" 503654 T DRAWPT (NIL) -7 NIL NIL) (-253 496952 497875 498954 "DRAW" 501339 NIL DRAW (NIL T) -7 NIL NIL) (-252 496585 496638 496756 "DRAWHACK" 496893 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 495316 495585 495876 "DRAWCX" 496314 T DRAWCX (NIL) -7 NIL NIL) (-250 494832 494900 495051 "DRAWCURV" 495242 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 485303 487262 489377 "DRAWCFUN" 492737 T DRAWCFUN (NIL) -7 NIL NIL) (-248 482116 483998 484039 "DQAGG" 484668 NIL DQAGG (NIL T) -9 NIL 484941) (-247 470490 477187 477270 "DPOLCAT" 479122 NIL DPOLCAT (NIL T T T T) -9 NIL 479667) (-246 465329 466675 468633 "DPOLCAT-" 468638 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-245 458484 465190 465288 "DPMO" 465293 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-244 451542 458264 458431 "DPMM" 458436 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-243 450962 451165 451279 "DOMAIN" 451448 T DOMAIN (NIL) -8 NIL NIL) (-242 444713 450597 450749 "DMP" 450863 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 444313 444369 444513 "DLP" 444651 NIL DLP (NIL T) -7 NIL NIL) (-240 437957 443414 443641 "DLIST" 444118 NIL DLIST (NIL T) -8 NIL NIL) (-239 434803 436812 436853 "DLAGG" 437403 NIL DLAGG (NIL T) -9 NIL 437632) (-238 433653 434283 434311 "DIVRING" 434403 T DIVRING (NIL) -9 NIL 434486) (-237 432890 433080 433380 "DIVRING-" 433385 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 430992 431349 431755 "DISPLAY" 432504 T DISPLAY (NIL) -7 NIL NIL) (-235 424934 430906 430969 "DIRPROD" 430974 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 423782 423985 424250 "DIRPROD2" 424727 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 413142 419094 419147 "DIRPCAT" 419557 NIL DIRPCAT (NIL NIL T) -9 NIL 420397) (-232 410468 411110 411991 "DIRPCAT-" 412328 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-231 409755 409915 410101 "DIOSP" 410302 T DIOSP (NIL) -7 NIL NIL) (-230 406457 408667 408708 "DIOPS" 409142 NIL DIOPS (NIL T) -9 NIL 409371) (-229 406006 406120 406311 "DIOPS-" 406316 NIL DIOPS- (NIL T T) -8 NIL NIL) (-228 404918 405512 405540 "DIFRING" 405727 T DIFRING (NIL) -9 NIL 405837) (-227 404564 404641 404793 "DIFRING-" 404798 NIL DIFRING- (NIL T) -8 NIL NIL) (-226 402389 403627 403668 "DIFEXT" 404031 NIL DIFEXT (NIL T) -9 NIL 404325) (-225 400674 401102 401768 "DIFEXT-" 401773 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-224 397996 400206 400247 "DIAGG" 400252 NIL DIAGG (NIL T) -9 NIL 400272) (-223 397380 397537 397789 "DIAGG-" 397794 NIL DIAGG- (NIL T T) -8 NIL NIL) (-222 392845 396339 396616 "DHMATRIX" 397149 NIL DHMATRIX (NIL T) -8 NIL NIL) (-221 388457 389366 390376 "DFSFUN" 391855 T DFSFUN (NIL) -7 NIL NIL) (-220 383573 387388 387700 "DFLOAT" 388165 T DFLOAT (NIL) -8 NIL NIL) (-219 381801 382082 382478 "DFINTTLS" 383281 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-218 378866 379822 380222 "DERHAM" 381467 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-217 376715 378641 378730 "DEQUEUE" 378810 NIL DEQUEUE (NIL T) -8 NIL NIL) (-216 375930 376063 376259 "DEGRED" 376577 NIL DEGRED (NIL T T) -7 NIL NIL) (-215 372325 373070 373923 "DEFINTRF" 375158 NIL DEFINTRF (NIL T) -7 NIL NIL) (-214 369852 370321 370920 "DEFINTEF" 371844 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-213 369229 369472 369587 "DEFAST" 369757 T DEFAST (NIL) -8 NIL NIL) (-212 363115 368670 368836 "DECIMAL" 369083 T DECIMAL (NIL) -8 NIL NIL) (-211 360627 361085 361591 "DDFACT" 362659 NIL DDFACT (NIL T T) -7 NIL NIL) (-210 360223 360266 360417 "DBLRESP" 360578 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-209 357933 358267 358636 "DBASE" 359981 NIL DBASE (NIL T) -8 NIL NIL) (-208 357202 357413 357559 "DATAARY" 357832 NIL DATAARY (NIL NIL T) -8 NIL NIL) (-207 356335 357161 357189 "D03FAFA" 357194 T D03FAFA (NIL) -8 NIL NIL) (-206 355469 356294 356322 "D03EEFA" 356327 T D03EEFA (NIL) -8 NIL NIL) (-205 353419 353885 354374 "D03AGNT" 355000 T D03AGNT (NIL) -7 NIL NIL) (-204 352735 353378 353406 "D02EJFA" 353411 T D02EJFA (NIL) -8 NIL NIL) (-203 352051 352694 352722 "D02CJFA" 352727 T D02CJFA (NIL) -8 NIL NIL) (-202 351367 352010 352038 "D02BHFA" 352043 T D02BHFA (NIL) -8 NIL NIL) (-201 350683 351326 351354 "D02BBFA" 351359 T D02BBFA (NIL) -8 NIL NIL) (-200 343881 345469 347075 "D02AGNT" 349097 T D02AGNT (NIL) -7 NIL NIL) (-199 341650 342172 342718 "D01WGTS" 343355 T D01WGTS (NIL) -7 NIL NIL) (-198 340745 341609 341637 "D01TRNS" 341642 T D01TRNS (NIL) -8 NIL NIL) (-197 339840 340704 340732 "D01GBFA" 340737 T D01GBFA (NIL) -8 NIL NIL) (-196 338935 339799 339827 "D01FCFA" 339832 T D01FCFA (NIL) -8 NIL NIL) (-195 338030 338894 338922 "D01ASFA" 338927 T D01ASFA (NIL) -8 NIL NIL) (-194 337125 337989 338017 "D01AQFA" 338022 T D01AQFA (NIL) -8 NIL NIL) (-193 336220 337084 337112 "D01APFA" 337117 T D01APFA (NIL) -8 NIL NIL) (-192 335315 336179 336207 "D01ANFA" 336212 T D01ANFA (NIL) -8 NIL NIL) (-191 334410 335274 335302 "D01AMFA" 335307 T D01AMFA (NIL) -8 NIL NIL) (-190 333505 334369 334397 "D01ALFA" 334402 T D01ALFA (NIL) -8 NIL NIL) (-189 332600 333464 333492 "D01AKFA" 333497 T D01AKFA (NIL) -8 NIL NIL) (-188 331695 332559 332587 "D01AJFA" 332592 T D01AJFA (NIL) -8 NIL NIL) (-187 324992 326543 328104 "D01AGNT" 330154 T D01AGNT (NIL) -7 NIL NIL) (-186 324329 324457 324609 "CYCLOTOM" 324860 T CYCLOTOM (NIL) -7 NIL NIL) (-185 321064 321777 322504 "CYCLES" 323622 T CYCLES (NIL) -7 NIL NIL) (-184 320376 320510 320681 "CVMP" 320925 NIL CVMP (NIL T) -7 NIL NIL) (-183 318147 318405 318781 "CTRIGMNP" 320104 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-182 317564 317770 317884 "CTOR" 318053 T CTOR (NIL) -8 NIL NIL) (-181 317100 317295 317396 "CTORKIND" 317483 T CTORKIND (NIL) -8 NIL NIL) (-180 316611 316800 316899 "CTORCALL" 317021 T CTORCALL (NIL) -8 NIL NIL) (-179 315985 316084 316237 "CSTTOOLS" 316508 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 311784 312441 313199 "CRFP" 315297 NIL CRFP (NIL T T) -7 NIL NIL) (-177 311286 311505 311597 "CRCEAST" 311712 T CRCEAST (NIL) -8 NIL NIL) (-176 310333 310518 310746 "CRAPACK" 311090 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 309717 309818 310022 "CPMATCH" 310209 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 309442 309470 309576 "CPIMA" 309683 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 305806 306478 307196 "COORDSYS" 308777 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 305190 305319 305469 "CONTOUR" 305676 T CONTOUR (NIL) -8 NIL NIL) (-171 301116 303193 303685 "CONTFRAC" 304730 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 300996 301017 301045 "CONDUIT" 301082 T CONDUIT (NIL) -9 NIL NIL) (-169 300189 300709 300737 "COMRING" 300742 T COMRING (NIL) -9 NIL 300794) (-168 299270 299547 299731 "COMPPROP" 300025 T COMPPROP (NIL) -8 NIL NIL) (-167 298931 298966 299094 "COMPLPAT" 299229 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 288988 298740 298849 "COMPLEX" 298854 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 288624 288681 288788 "COMPLEX2" 288925 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 288342 288377 288475 "COMPFACT" 288583 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 272637 282855 282895 "COMPCAT" 283899 NIL COMPCAT (NIL T) -9 NIL 285284) (-162 262152 265076 268703 "COMPCAT-" 269059 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 261881 261909 262012 "COMMUPC" 262118 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 261676 261709 261768 "COMMONOP" 261842 T COMMONOP (NIL) -7 NIL NIL) (-159 261259 261427 261514 "COMM" 261609 T COMM (NIL) -8 NIL NIL) (-158 260863 261063 261138 "COMMAAST" 261204 T COMMAAST (NIL) -8 NIL NIL) (-157 260112 260306 260334 "COMBOPC" 260672 T COMBOPC (NIL) -9 NIL 260847) (-156 259008 259218 259460 "COMBINAT" 259902 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 255206 255779 256419 "COMBF" 258430 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253992 254322 254557 "COLOR" 254991 T COLOR (NIL) -8 NIL NIL) (-153 253495 253713 253805 "COLONAST" 253920 T COLONAST (NIL) -8 NIL NIL) (-152 253135 253182 253307 "CMPLXRT" 253442 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 252610 252835 252934 "CLLCTAST" 253056 T CLLCTAST (NIL) -8 NIL NIL) (-150 248112 249140 250220 "CLIP" 251550 T CLIP (NIL) -7 NIL NIL) (-149 246494 247218 247457 "CLIF" 247939 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-148 242716 244640 244681 "CLAGG" 245610 NIL CLAGG (NIL T) -9 NIL 246146) (-147 241138 241595 242178 "CLAGG-" 242183 NIL CLAGG- (NIL T T) -8 NIL NIL) (-146 240682 240767 240907 "CINTSLPE" 241047 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-145 238183 238654 239202 "CHVAR" 240210 NIL CHVAR (NIL T T T) -7 NIL NIL) (-144 237446 237966 237994 "CHARZ" 237999 T CHARZ (NIL) -9 NIL 238014) (-143 237200 237240 237318 "CHARPOL" 237400 NIL CHARPOL (NIL T) -7 NIL NIL) (-142 236347 236900 236928 "CHARNZ" 236975 T CHARNZ (NIL) -9 NIL 237031) (-141 234372 235037 235372 "CHAR" 236032 T CHAR (NIL) -8 NIL NIL) (-140 234098 234159 234187 "CFCAT" 234298 T CFCAT (NIL) -9 NIL NIL) (-139 233343 233454 233636 "CDEN" 233982 NIL CDEN (NIL T T T) -7 NIL NIL) (-138 229335 232496 232776 "CCLASS" 233083 T CCLASS (NIL) -8 NIL NIL) (-137 229254 229280 229315 "CATEGORY" 229320 T -10 (NIL) -8 NIL NIL) (-136 228728 228954 229053 "CATAST" 229175 T CATAST (NIL) -8 NIL NIL) (-135 228231 228449 228541 "CASEAST" 228656 T CASEAST (NIL) -8 NIL NIL) (-134 223283 224260 225013 "CARTEN" 227534 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 222391 222539 222760 "CARTEN2" 223130 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-132 220733 221541 221798 "CARD" 222154 T CARD (NIL) -8 NIL NIL) (-131 220336 220537 220612 "CAPSLAST" 220678 T CAPSLAST (NIL) -8 NIL NIL) (-130 219708 220036 220064 "CACHSET" 220196 T CACHSET (NIL) -9 NIL 220273) (-129 219204 219500 219528 "CABMON" 219578 T CABMON (NIL) -9 NIL 219634) (-128 218131 218559 218755 "BYTE" 219028 T BYTE (NIL) -8 NIL NIL) (-127 213540 217599 217762 "BYTEBUF" 217988 T BYTEBUF (NIL) -8 NIL NIL) (-126 211097 213232 213339 "BTREE" 213466 NIL BTREE (NIL T) -8 NIL NIL) (-125 208595 210745 210867 "BTOURN" 211007 NIL BTOURN (NIL T) -8 NIL NIL) (-124 206013 208066 208107 "BTCAT" 208175 NIL BTCAT (NIL T) -9 NIL 208252) (-123 205680 205760 205909 "BTCAT-" 205914 NIL BTCAT- (NIL T T) -8 NIL NIL) (-122 200972 204823 204851 "BTAGG" 205073 T BTAGG (NIL) -9 NIL 205234) (-121 200462 200587 200793 "BTAGG-" 200798 NIL BTAGG- (NIL T) -8 NIL NIL) (-120 197506 199740 199955 "BSTREE" 200279 NIL BSTREE (NIL T) -8 NIL NIL) (-119 196644 196770 196954 "BRILL" 197362 NIL BRILL (NIL T) -7 NIL NIL) (-118 193345 195372 195413 "BRAGG" 196062 NIL BRAGG (NIL T) -9 NIL 196319) (-117 191874 192280 192835 "BRAGG-" 192840 NIL BRAGG- (NIL T T) -8 NIL NIL) (-116 185138 191220 191404 "BPADICRT" 191722 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-115 183488 185075 185120 "BPADIC" 185125 NIL BPADIC (NIL NIL) -8 NIL NIL) (-114 183186 183216 183330 "BOUNDZRO" 183452 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-113 178701 179792 180659 "BOP" 182339 T BOP (NIL) -8 NIL NIL) (-112 176322 176766 177286 "BOP1" 178214 NIL BOP1 (NIL T) -7 NIL NIL) (-111 175060 175746 175939 "BOOLEAN" 176149 T BOOLEAN (NIL) -8 NIL NIL) (-110 174422 174800 174854 "BMODULE" 174859 NIL BMODULE (NIL T T) -9 NIL 174924) (-109 170252 174220 174293 "BITS" 174369 T BITS (NIL) -8 NIL NIL) (-108 169664 169786 169928 "BINDING" 170130 T BINDING (NIL) -8 NIL NIL) (-107 163554 169108 169273 "BINARY" 169519 T BINARY (NIL) -8 NIL NIL) (-106 161381 162809 162850 "BGAGG" 163110 NIL BGAGG (NIL T) -9 NIL 163247) (-105 161212 161244 161335 "BGAGG-" 161340 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 160310 160596 160801 "BFUNCT" 161027 T BFUNCT (NIL) -8 NIL NIL) (-103 159000 159178 159466 "BEZOUT" 160134 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155517 157852 158182 "BBTREE" 158703 NIL BBTREE (NIL T) -8 NIL NIL) (-101 155251 155304 155332 "BASTYPE" 155451 T BASTYPE (NIL) -9 NIL NIL) (-100 155103 155132 155205 "BASTYPE-" 155210 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154541 154617 154767 "BALFACT" 155014 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 153424 153956 154142 "AUTOMOR" 154386 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 153150 153155 153181 "ATTREG" 153186 T ATTREG (NIL) -9 NIL NIL) (-96 151429 151847 152199 "ATTRBUT" 152816 T ATTRBUT (NIL) -8 NIL NIL) (-95 151064 151257 151323 "ATTRAST" 151381 T ATTRAST (NIL) -8 NIL NIL) (-94 150600 150713 150739 "ATRIG" 150940 T ATRIG (NIL) -9 NIL NIL) (-93 150409 150450 150537 "ATRIG-" 150542 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 150031 150191 150217 "ASTCAT" 150275 T ASTCAT (NIL) -9 NIL 150338) (-91 149758 149817 149936 "ASTCAT-" 149941 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147955 149534 149622 "ASTACK" 149701 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146460 146757 147122 "ASSOCEQ" 147637 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145492 146119 146243 "ASP9" 146367 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 145256 145440 145479 "ASP8" 145484 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 144125 144861 145003 "ASP80" 145145 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 143024 143760 143892 "ASP7" 144024 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141978 142701 142819 "ASP78" 142937 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140947 141658 141775 "ASP77" 141892 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 139859 140585 140716 "ASP74" 140847 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 138759 139494 139626 "ASP73" 139758 NIL ASP73 (NIL NIL) -8 NIL NIL) (-80 137714 138436 138554 "ASP6" 138672 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 136662 137391 137509 "ASP55" 137627 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 135612 136336 136455 "ASP50" 136574 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134700 135313 135423 "ASP4" 135533 NIL ASP4 (NIL NIL) -8 NIL NIL) (-76 133788 134401 134511 "ASP49" 134621 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 132573 133327 133495 "ASP42" 133677 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131350 132106 132276 "ASP41" 132460 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130300 131027 131145 "ASP35" 131263 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 130065 130248 130287 "ASP34" 130292 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129802 129869 129945 "ASP33" 130020 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128697 129437 129569 "ASP31" 129701 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128462 128645 128684 "ASP30" 128689 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 128197 128266 128342 "ASP29" 128417 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127962 128145 128184 "ASP28" 128189 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127727 127910 127949 "ASP27" 127954 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126811 127425 127536 "ASP24" 127647 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125727 126452 126582 "ASP20" 126712 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124815 125428 125538 "ASP1" 125648 NIL ASP1 (NIL NIL) -8 NIL NIL) (-62 123759 124489 124608 "ASP19" 124727 NIL ASP19 (NIL NIL) -8 NIL NIL) (-61 123496 123563 123639 "ASP12" 123714 NIL ASP12 (NIL NIL) -8 NIL NIL) (-60 122348 123095 123239 "ASP10" 123383 NIL ASP10 (NIL NIL) -8 NIL NIL) (-59 120247 122192 122283 "ARRAY2" 122288 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 116063 119895 120009 "ARRAY1" 120164 NIL ARRAY1 (NIL T) -8 NIL NIL) (-57 115095 115268 115489 "ARRAY12" 115886 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-56 109454 111325 111400 "ARR2CAT" 114030 NIL ARR2CAT (NIL T T T) -9 NIL 114788) (-55 106888 107632 108586 "ARR2CAT-" 108591 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105636 105788 106094 "APPRULE" 106724 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 105287 105335 105454 "APPLYORE" 105582 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104261 104552 104747 "ANY" 105110 T ANY (NIL) -8 NIL NIL) (-51 103539 103662 103819 "ANY1" 104135 NIL ANY1 (NIL T) -7 NIL NIL) (-50 101104 101976 102303 "ANTISYM" 103263 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100619 100808 100905 "ANON" 101025 T ANON (NIL) -8 NIL NIL) (-48 94751 99158 99612 "AN" 100183 T AN (NIL) -8 NIL NIL) (-47 91132 92486 92537 "AMR" 93285 NIL AMR (NIL T T) -9 NIL 93885) (-46 90244 90465 90828 "AMR-" 90833 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74794 90161 90222 "ALIST" 90227 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71631 74388 74557 "ALGSC" 74712 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 68187 68741 69348 "ALGPKG" 71071 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67464 67565 67749 "ALGMFACT" 68073 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 63203 63888 64543 "ALGMANIP" 66987 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54609 62829 62979 "ALGFF" 63136 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53805 53936 54115 "ALGFACT" 54467 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52835 53401 53439 "ALGEBRA" 53499 NIL ALGEBRA (NIL T) -9 NIL 53558) (-37 52553 52612 52744 "ALGEBRA-" 52749 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34813 50556 50608 "ALAGG" 50744 NIL ALAGG (NIL T T) -9 NIL 50905) (-35 34349 34462 34488 "AHYP" 34689 T AHYP (NIL) -9 NIL NIL) (-34 33280 33528 33554 "AGG" 34053 T AGG (NIL) -9 NIL 34332) (-33 32714 32876 33090 "AGG-" 33095 NIL AGG- (NIL T) -8 NIL NIL) (-32 30391 30813 31231 "AF" 32356 NIL AF (NIL T T) -7 NIL NIL) (-31 29898 30116 30206 "ADDAST" 30319 T ADDAST (NIL) -8 NIL NIL) (-30 29167 29425 29581 "ACPLOT" 29760 T ACPLOT (NIL) -8 NIL NIL) (-29 18358 26279 26330 "ACFS" 27041 NIL ACFS (NIL T) -9 NIL 27280) (-28 16372 16862 17637 "ACFS-" 17642 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3180784 3180789 3180794 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3180769 3180774 3180779 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3180754 3180759 3180764 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3180739 3180744 3180749 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1266 3179915 3180614 3180691 "ZMOD" 3180696 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1265 3179025 3179189 3179398 "ZLINDEP" 3179747 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1264 3168329 3170093 3172065 "ZDSOLVE" 3177155 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1263 3167575 3167716 3167905 "YSTREAM" 3168175 NIL YSTREAM (NIL T) -7 NIL NIL) (-1262 3165386 3166876 3167080 "XRPOLY" 3167418 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1261 3161974 3163257 3163832 "XPR" 3164858 NIL XPR (NIL T T) -8 NIL NIL) (-1260 3159730 3161305 3161509 "XPOLY" 3161805 NIL XPOLY (NIL T) -8 NIL NIL) (-1259 3157521 3158855 3158910 "XPOLYC" 3159198 NIL XPOLYC (NIL T T) -9 NIL 3159311) (-1258 3153939 3156038 3156426 "XPBWPOLY" 3157179 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1257 3149850 3152102 3152144 "XF" 3152765 NIL XF (NIL T) -9 NIL 3153165) (-1256 3149471 3149559 3149728 "XF-" 3149733 NIL XF- (NIL T T) -8 NIL NIL) (-1255 3144805 3146060 3146115 "XFALG" 3148287 NIL XFALG (NIL T T) -9 NIL 3149076) (-1254 3143938 3144042 3144247 "XEXPPKG" 3144697 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1253 3142082 3143788 3143884 "XDPOLY" 3143889 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1252 3141027 3141593 3141636 "XALG" 3141641 NIL XALG (NIL T) -9 NIL 3141752) (-1251 3134496 3139004 3139498 "WUTSET" 3140619 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1250 3132787 3133548 3133871 "WP" 3134307 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1249 3132416 3132609 3132679 "WHILEAST" 3132739 T WHILEAST (NIL) -8 NIL NIL) (-1248 3131915 3132133 3132227 "WHEREAST" 3132344 T WHEREAST (NIL) -8 NIL NIL) (-1247 3130801 3130999 3131294 "WFFINTBS" 3131712 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1246 3128705 3129132 3129594 "WEIER" 3130373 NIL WEIER (NIL T) -7 NIL NIL) (-1245 3127852 3128276 3128318 "VSPACE" 3128454 NIL VSPACE (NIL T) -9 NIL 3128528) (-1244 3127690 3127717 3127808 "VSPACE-" 3127813 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1243 3127498 3127541 3127609 "VOID" 3127644 T VOID (NIL) -8 NIL NIL) (-1242 3125634 3125993 3126399 "VIEW" 3127114 T VIEW (NIL) -7 NIL NIL) (-1241 3122059 3122697 3123434 "VIEWDEF" 3124919 T VIEWDEF (NIL) -7 NIL NIL) (-1240 3111397 3113607 3115780 "VIEW3D" 3119908 T VIEW3D (NIL) -8 NIL NIL) (-1239 3103679 3105308 3106887 "VIEW2D" 3109840 T VIEW2D (NIL) -8 NIL NIL) (-1238 3099083 3103449 3103541 "VECTOR" 3103622 NIL VECTOR (NIL T) -8 NIL NIL) (-1237 3097660 3097919 3098237 "VECTOR2" 3098813 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1236 3091187 3095444 3095487 "VECTCAT" 3096480 NIL VECTCAT (NIL T) -9 NIL 3097066) (-1235 3090201 3090455 3090845 "VECTCAT-" 3090850 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1234 3089682 3089852 3089972 "VARIABLE" 3090116 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1233 3089615 3089620 3089650 "UTYPE" 3089655 T UTYPE (NIL) -9 NIL NIL) (-1232 3088445 3088599 3088861 "UTSODETL" 3089441 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1231 3085885 3086345 3086869 "UTSODE" 3087986 NIL UTSODE (NIL T T) -7 NIL NIL) (-1230 3077761 3083511 3084000 "UTS" 3085454 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1229 3069004 3074328 3074371 "UTSCAT" 3075483 NIL UTSCAT (NIL T) -9 NIL 3076240) (-1228 3066358 3067074 3068063 "UTSCAT-" 3068068 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1227 3065985 3066028 3066161 "UTS2" 3066309 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1226 3060260 3062825 3062868 "URAGG" 3064938 NIL URAGG (NIL T) -9 NIL 3065660) (-1225 3057199 3058062 3059185 "URAGG-" 3059190 NIL URAGG- (NIL T T) -8 NIL NIL) (-1224 3052923 3055813 3056285 "UPXSSING" 3056863 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1223 3045025 3052170 3052443 "UPXS" 3052708 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1222 3038138 3044929 3045001 "UPXSCONS" 3045006 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1221 3028383 3035133 3035195 "UPXSCCA" 3035769 NIL UPXSCCA (NIL T T) -9 NIL 3036002) (-1220 3028021 3028106 3028280 "UPXSCCA-" 3028285 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1219 3018119 3024642 3024685 "UPXSCAT" 3025333 NIL UPXSCAT (NIL T) -9 NIL 3025941) (-1218 3017549 3017628 3017807 "UPXS2" 3018034 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1217 3016203 3016456 3016807 "UPSQFREE" 3017292 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1216 3009991 3013005 3013060 "UPSCAT" 3014221 NIL UPSCAT (NIL T T) -9 NIL 3014995) (-1215 3009195 3009402 3009729 "UPSCAT-" 3009734 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1214 2995045 3003043 3003086 "UPOLYC" 3005187 NIL UPOLYC (NIL T) -9 NIL 3006408) (-1213 2986374 2988799 2991946 "UPOLYC-" 2991951 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1212 2986001 2986044 2986177 "UPOLYC2" 2986325 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1211 2977575 2985684 2985813 "UP" 2985920 NIL UP (NIL NIL T) -8 NIL NIL) (-1210 2976914 2977021 2977185 "UPMP" 2977464 NIL UPMP (NIL T T) -7 NIL NIL) (-1209 2976467 2976548 2976687 "UPDIVP" 2976827 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1208 2975035 2975284 2975600 "UPDECOMP" 2976216 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1207 2974270 2974382 2974567 "UPCDEN" 2974919 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1206 2973789 2973858 2974007 "UP2" 2974195 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1205 2972306 2972993 2973270 "UNISEG" 2973547 NIL UNISEG (NIL T) -8 NIL NIL) (-1204 2971521 2971648 2971853 "UNISEG2" 2972149 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1203 2970581 2970761 2970987 "UNIFACT" 2971337 NIL UNIFACT (NIL T) -7 NIL NIL) (-1202 2954548 2969758 2970009 "ULS" 2970388 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1201 2942588 2954452 2954524 "ULSCONS" 2954529 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1200 2925204 2937146 2937208 "ULSCCAT" 2937846 NIL ULSCCAT (NIL T T) -9 NIL 2938134) (-1199 2924254 2924499 2924887 "ULSCCAT-" 2924892 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1198 2914129 2920566 2920609 "ULSCAT" 2921472 NIL ULSCAT (NIL T) -9 NIL 2922202) (-1197 2913559 2913638 2913817 "ULS2" 2914044 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1196 2911962 2912885 2912915 "UFD" 2913127 T UFD (NIL) -9 NIL 2913241) (-1195 2911756 2911802 2911897 "UFD-" 2911902 NIL UFD- (NIL T) -8 NIL NIL) (-1194 2910838 2911021 2911237 "UDVO" 2911562 T UDVO (NIL) -7 NIL NIL) (-1193 2908654 2909063 2909534 "UDPO" 2910402 NIL UDPO (NIL T) -7 NIL NIL) (-1192 2908587 2908592 2908622 "TYPE" 2908627 T TYPE (NIL) -9 NIL NIL) (-1191 2908374 2908542 2908573 "TYPEAST" 2908578 T TYPEAST (NIL) -8 NIL NIL) (-1190 2907345 2907547 2907787 "TWOFACT" 2908168 NIL TWOFACT (NIL T) -7 NIL NIL) (-1189 2906417 2906754 2906989 "TUPLE" 2907145 NIL TUPLE (NIL T) -8 NIL NIL) (-1188 2904108 2904627 2905166 "TUBETOOL" 2905900 T TUBETOOL (NIL) -7 NIL NIL) (-1187 2902957 2903162 2903403 "TUBE" 2903901 NIL TUBE (NIL T) -8 NIL NIL) (-1186 2897721 2901929 2902212 "TS" 2902709 NIL TS (NIL T) -8 NIL NIL) (-1185 2886388 2890480 2890577 "TSETCAT" 2895846 NIL TSETCAT (NIL T T T T) -9 NIL 2897377) (-1184 2881122 2882720 2884611 "TSETCAT-" 2884616 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1183 2875385 2876231 2877173 "TRMANIP" 2880258 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1182 2874826 2874889 2875052 "TRIMAT" 2875317 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1181 2872622 2872859 2873223 "TRIGMNIP" 2874575 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1180 2872142 2872255 2872285 "TRIGCAT" 2872498 T TRIGCAT (NIL) -9 NIL NIL) (-1179 2871811 2871890 2872031 "TRIGCAT-" 2872036 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1178 2868710 2870671 2870951 "TREE" 2871566 NIL TREE (NIL T) -8 NIL NIL) (-1177 2867984 2868512 2868542 "TRANFUN" 2868577 T TRANFUN (NIL) -9 NIL 2868643) (-1176 2867263 2867454 2867734 "TRANFUN-" 2867739 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1175 2867067 2867099 2867160 "TOPSP" 2867224 T TOPSP (NIL) -7 NIL NIL) (-1174 2866415 2866530 2866684 "TOOLSIGN" 2866948 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1173 2865076 2865592 2865831 "TEXTFILE" 2866198 T TEXTFILE (NIL) -8 NIL NIL) (-1172 2863015 2863529 2863958 "TEX" 2864669 T TEX (NIL) -8 NIL NIL) (-1171 2862796 2862827 2862899 "TEX1" 2862978 NIL TEX1 (NIL T) -7 NIL NIL) (-1170 2862444 2862507 2862597 "TEMUTL" 2862728 T TEMUTL (NIL) -7 NIL NIL) (-1169 2860598 2860878 2861203 "TBCMPPK" 2862167 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1168 2852486 2858758 2858814 "TBAGG" 2859214 NIL TBAGG (NIL T T) -9 NIL 2859425) (-1167 2847556 2849044 2850798 "TBAGG-" 2850803 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1166 2846940 2847047 2847192 "TANEXP" 2847445 NIL TANEXP (NIL T) -7 NIL NIL) (-1165 2840441 2846797 2846890 "TABLE" 2846895 NIL TABLE (NIL T T) -8 NIL NIL) (-1164 2839853 2839952 2840090 "TABLEAU" 2840338 NIL TABLEAU (NIL T) -8 NIL NIL) (-1163 2834461 2835681 2836929 "TABLBUMP" 2838639 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1162 2833889 2833989 2834117 "SYSTEM" 2834355 T SYSTEM (NIL) -7 NIL NIL) (-1161 2830352 2831047 2831830 "SYSSOLP" 2833140 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1160 2826730 2827641 2828343 "SYNTAX" 2829672 T SYNTAX (NIL) -8 NIL NIL) (-1159 2823888 2824490 2825122 "SYMTAB" 2826120 T SYMTAB (NIL) -8 NIL NIL) (-1158 2819137 2820039 2821022 "SYMS" 2822927 T SYMS (NIL) -8 NIL NIL) (-1157 2816409 2818595 2818825 "SYMPOLY" 2818942 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1156 2815926 2816001 2816124 "SYMFUNC" 2816321 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1155 2811978 2813238 2814051 "SYMBOL" 2815135 T SYMBOL (NIL) -8 NIL NIL) (-1154 2805517 2807206 2808926 "SWITCH" 2810280 T SWITCH (NIL) -8 NIL NIL) (-1153 2798787 2804338 2804641 "SUTS" 2805272 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1152 2790888 2798034 2798307 "SUPXS" 2798572 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1151 2782417 2790506 2790632 "SUP" 2790797 NIL SUP (NIL T) -8 NIL NIL) (-1150 2781576 2781703 2781920 "SUPFRACF" 2782285 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1149 2781197 2781256 2781369 "SUP2" 2781511 NIL SUP2 (NIL T T) -7 NIL NIL) (-1148 2779610 2779884 2780247 "SUMRF" 2780896 NIL SUMRF (NIL T) -7 NIL NIL) (-1147 2778924 2778990 2779189 "SUMFS" 2779531 NIL SUMFS (NIL T T) -7 NIL NIL) (-1146 2762931 2778101 2778352 "SULS" 2778731 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1145 2762560 2762753 2762823 "SUCHTAST" 2762883 T SUCHTAST (NIL) -8 NIL NIL) (-1144 2761882 2762085 2762225 "SUCH" 2762468 NIL SUCH (NIL T T) -8 NIL NIL) (-1143 2755776 2756788 2757747 "SUBSPACE" 2760970 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1142 2755206 2755296 2755460 "SUBRESP" 2755664 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1141 2748575 2749871 2751182 "STTF" 2753942 NIL STTF (NIL T) -7 NIL NIL) (-1140 2742748 2743868 2745015 "STTFNC" 2747475 NIL STTFNC (NIL T) -7 NIL NIL) (-1139 2734063 2735930 2737724 "STTAYLOR" 2740989 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1138 2727307 2733927 2734010 "STRTBL" 2734015 NIL STRTBL (NIL T) -8 NIL NIL) (-1137 2722698 2727262 2727293 "STRING" 2727298 T STRING (NIL) -8 NIL NIL) (-1136 2717586 2722071 2722101 "STRICAT" 2722160 T STRICAT (NIL) -9 NIL 2722222) (-1135 2710395 2715205 2715816 "STREAM" 2717010 NIL STREAM (NIL T) -8 NIL NIL) (-1134 2709905 2709982 2710126 "STREAM3" 2710312 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1133 2708887 2709070 2709305 "STREAM2" 2709718 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1132 2708575 2708627 2708720 "STREAM1" 2708829 NIL STREAM1 (NIL T) -7 NIL NIL) (-1131 2707591 2707772 2708003 "STINPROD" 2708391 NIL STINPROD (NIL T) -7 NIL NIL) (-1130 2707169 2707353 2707383 "STEP" 2707463 T STEP (NIL) -9 NIL 2707541) (-1129 2700712 2707068 2707145 "STBL" 2707150 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1128 2695887 2699934 2699977 "STAGG" 2700130 NIL STAGG (NIL T) -9 NIL 2700219) (-1127 2693589 2694191 2695063 "STAGG-" 2695068 NIL STAGG- (NIL T T) -8 NIL NIL) (-1126 2691784 2693359 2693451 "STACK" 2693532 NIL STACK (NIL T) -8 NIL NIL) (-1125 2684509 2689925 2690381 "SREGSET" 2691414 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1124 2676935 2678303 2679816 "SRDCMPK" 2683115 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1123 2669902 2674375 2674405 "SRAGG" 2675708 T SRAGG (NIL) -9 NIL 2676316) (-1122 2668919 2669174 2669553 "SRAGG-" 2669558 NIL SRAGG- (NIL T) -8 NIL NIL) (-1121 2663414 2667866 2668287 "SQMATRIX" 2668545 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1120 2657166 2660134 2660860 "SPLTREE" 2662760 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1119 2653156 2653822 2654468 "SPLNODE" 2656592 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1118 2652203 2652436 2652466 "SPFCAT" 2652910 T SPFCAT (NIL) -9 NIL NIL) (-1117 2650940 2651150 2651414 "SPECOUT" 2651961 T SPECOUT (NIL) -7 NIL NIL) (-1116 2642592 2644336 2644366 "SPADXPT" 2648758 T SPADXPT (NIL) -9 NIL 2650792) (-1115 2642353 2642393 2642462 "SPADPRSR" 2642545 T SPADPRSR (NIL) -7 NIL NIL) (-1114 2640536 2642308 2642339 "SPADAST" 2642344 T SPADAST (NIL) -8 NIL NIL) (-1113 2632507 2634254 2634297 "SPACEC" 2638670 NIL SPACEC (NIL T) -9 NIL 2640486) (-1112 2630678 2632439 2632488 "SPACE3" 2632493 NIL SPACE3 (NIL T) -8 NIL NIL) (-1111 2629430 2629601 2629892 "SORTPAK" 2630483 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1110 2627480 2627783 2628202 "SOLVETRA" 2629094 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1109 2626491 2626713 2626987 "SOLVESER" 2627253 NIL SOLVESER (NIL T) -7 NIL NIL) (-1108 2621711 2622592 2623594 "SOLVERAD" 2625543 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1107 2617526 2618135 2618864 "SOLVEFOR" 2621078 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1106 2611823 2616875 2616972 "SNTSCAT" 2616977 NIL SNTSCAT (NIL T T T T) -9 NIL 2617047) (-1105 2605966 2610146 2610537 "SMTS" 2611513 NIL SMTS (NIL T T T) -8 NIL NIL) (-1104 2600416 2605854 2605931 "SMP" 2605936 NIL SMP (NIL T T) -8 NIL NIL) (-1103 2598575 2598876 2599274 "SMITH" 2600113 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1102 2591470 2595626 2595729 "SMATCAT" 2597080 NIL SMATCAT (NIL NIL T T T) -9 NIL 2597630) (-1101 2588410 2589233 2590411 "SMATCAT-" 2590416 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1100 2586123 2587646 2587689 "SKAGG" 2587950 NIL SKAGG (NIL T) -9 NIL 2588085) (-1099 2582239 2585227 2585505 "SINT" 2585867 T SINT (NIL) -8 NIL NIL) (-1098 2582011 2582049 2582115 "SIMPAN" 2582195 T SIMPAN (NIL) -7 NIL NIL) (-1097 2581318 2581546 2581686 "SIG" 2581893 T SIG (NIL) -8 NIL NIL) (-1096 2580156 2580377 2580652 "SIGNRF" 2581077 NIL SIGNRF (NIL T) -7 NIL NIL) (-1095 2578961 2579112 2579403 "SIGNEF" 2579985 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1094 2578294 2578544 2578668 "SIGAST" 2578859 T SIGAST (NIL) -8 NIL NIL) (-1093 2575984 2576438 2576944 "SHP" 2577835 NIL SHP (NIL T NIL) -7 NIL NIL) (-1092 2569890 2575885 2575961 "SHDP" 2575966 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1091 2569489 2569655 2569685 "SGROUP" 2569778 T SGROUP (NIL) -9 NIL 2569840) (-1090 2569347 2569373 2569446 "SGROUP-" 2569451 NIL SGROUP- (NIL T) -8 NIL NIL) (-1089 2566183 2566880 2567603 "SGCF" 2568646 T SGCF (NIL) -7 NIL NIL) (-1088 2560578 2565630 2565727 "SFRTCAT" 2565732 NIL SFRTCAT (NIL T T T T) -9 NIL 2565771) (-1087 2554002 2555017 2556153 "SFRGCD" 2559561 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1086 2547130 2548201 2549387 "SFQCMPK" 2552935 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1085 2546752 2546841 2546951 "SFORT" 2547071 NIL SFORT (NIL T T) -8 NIL NIL) (-1084 2545897 2546592 2546713 "SEXOF" 2546718 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1083 2545031 2545778 2545846 "SEX" 2545851 T SEX (NIL) -8 NIL NIL) (-1082 2540570 2541259 2541354 "SEXCAT" 2544291 NIL SEXCAT (NIL T T T T T) -9 NIL 2544869) (-1081 2537750 2540504 2540552 "SET" 2540557 NIL SET (NIL T) -8 NIL NIL) (-1080 2536001 2536463 2536768 "SETMN" 2537491 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1079 2535607 2535733 2535763 "SETCAT" 2535880 T SETCAT (NIL) -9 NIL 2535965) (-1078 2535387 2535439 2535538 "SETCAT-" 2535543 NIL SETCAT- (NIL T) -8 NIL NIL) (-1077 2531774 2533848 2533891 "SETAGG" 2534761 NIL SETAGG (NIL T) -9 NIL 2535101) (-1076 2531232 2531348 2531585 "SETAGG-" 2531590 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1075 2530702 2530928 2531029 "SEQAST" 2531153 T SEQAST (NIL) -8 NIL NIL) (-1074 2529901 2530195 2530256 "SEGXCAT" 2530542 NIL SEGXCAT (NIL T T) -9 NIL 2530662) (-1073 2528957 2529567 2529749 "SEG" 2529754 NIL SEG (NIL T) -8 NIL NIL) (-1072 2527936 2528150 2528193 "SEGCAT" 2528715 NIL SEGCAT (NIL T) -9 NIL 2528936) (-1071 2526985 2527315 2527515 "SEGBIND" 2527771 NIL SEGBIND (NIL T) -8 NIL NIL) (-1070 2526606 2526665 2526778 "SEGBIND2" 2526920 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1069 2526207 2526407 2526484 "SEGAST" 2526551 T SEGAST (NIL) -8 NIL NIL) (-1068 2525426 2525552 2525756 "SEG2" 2526051 NIL SEG2 (NIL T T) -7 NIL NIL) (-1067 2524863 2525361 2525408 "SDVAR" 2525413 NIL SDVAR (NIL T) -8 NIL NIL) (-1066 2517153 2524633 2524763 "SDPOL" 2524768 NIL SDPOL (NIL T) -8 NIL NIL) (-1065 2515746 2516012 2516331 "SCPKG" 2516868 NIL SCPKG (NIL T) -7 NIL NIL) (-1064 2514882 2515062 2515262 "SCOPE" 2515568 T SCOPE (NIL) -8 NIL NIL) (-1063 2514103 2514236 2514415 "SCACHE" 2514737 NIL SCACHE (NIL T) -7 NIL NIL) (-1062 2513775 2513935 2513965 "SASTCAT" 2513970 T SASTCAT (NIL) -9 NIL 2513983) (-1061 2513289 2513610 2513686 "SAOS" 2513721 T SAOS (NIL) -8 NIL NIL) (-1060 2512854 2512889 2513062 "SAERFFC" 2513248 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1059 2506828 2512751 2512831 "SAE" 2512836 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1058 2506421 2506456 2506615 "SAEFACT" 2506787 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1057 2504742 2505056 2505457 "RURPK" 2506087 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1056 2503378 2503657 2503969 "RULESET" 2504576 NIL RULESET (NIL T T T) -8 NIL NIL) (-1055 2500565 2501068 2501533 "RULE" 2503059 NIL RULE (NIL T T T) -8 NIL NIL) (-1054 2500204 2500359 2500442 "RULECOLD" 2500517 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1053 2499702 2499921 2500015 "RSTRCAST" 2500132 T RSTRCAST (NIL) -8 NIL NIL) (-1052 2494551 2495345 2496265 "RSETGCD" 2498901 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1051 2483808 2488860 2488957 "RSETCAT" 2493076 NIL RSETCAT (NIL T T T T) -9 NIL 2494173) (-1050 2481735 2482274 2483098 "RSETCAT-" 2483103 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1049 2474122 2475497 2477017 "RSDCMPK" 2480334 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1048 2472127 2472568 2472642 "RRCC" 2473728 NIL RRCC (NIL T T) -9 NIL 2474072) (-1047 2471478 2471652 2471931 "RRCC-" 2471936 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1046 2470948 2471174 2471275 "RPTAST" 2471399 T RPTAST (NIL) -8 NIL NIL) (-1045 2444954 2454541 2454608 "RPOLCAT" 2465272 NIL RPOLCAT (NIL T T T) -9 NIL 2468431) (-1044 2436454 2438792 2441914 "RPOLCAT-" 2441919 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1043 2427501 2434665 2435147 "ROUTINE" 2435994 T ROUTINE (NIL) -8 NIL NIL) (-1042 2424334 2427127 2427267 "ROMAN" 2427383 T ROMAN (NIL) -8 NIL NIL) (-1041 2422609 2423194 2423454 "ROIRC" 2424139 NIL ROIRC (NIL T T) -8 NIL NIL) (-1040 2419002 2421245 2421275 "RNS" 2421579 T RNS (NIL) -9 NIL 2421852) (-1039 2417511 2417894 2418428 "RNS-" 2418503 NIL RNS- (NIL T) -8 NIL NIL) (-1038 2416960 2417342 2417372 "RNG" 2417377 T RNG (NIL) -9 NIL 2417398) (-1037 2416352 2416714 2416757 "RMODULE" 2416819 NIL RMODULE (NIL T) -9 NIL 2416861) (-1036 2415188 2415282 2415618 "RMCAT2" 2416253 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1035 2412065 2414534 2414831 "RMATRIX" 2414950 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1034 2405007 2407241 2407356 "RMATCAT" 2410715 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2411697) (-1033 2404382 2404529 2404836 "RMATCAT-" 2404841 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1032 2403949 2404024 2404152 "RINTERP" 2404301 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1031 2403082 2403602 2403632 "RING" 2403688 T RING (NIL) -9 NIL 2403774) (-1030 2402874 2402918 2403015 "RING-" 2403020 NIL RING- (NIL T) -8 NIL NIL) (-1029 2401715 2401952 2402210 "RIDIST" 2402638 T RIDIST (NIL) -7 NIL NIL) (-1028 2393031 2401183 2401389 "RGCHAIN" 2401563 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1027 2392407 2392787 2392828 "RGBCSPC" 2392886 NIL RGBCSPC (NIL T) -9 NIL 2392938) (-1026 2391591 2391946 2391987 "RGBCMDL" 2392219 NIL RGBCMDL (NIL T) -9 NIL 2392333) (-1025 2388585 2389199 2389869 "RF" 2390955 NIL RF (NIL T) -7 NIL NIL) (-1024 2388231 2388294 2388397 "RFFACTOR" 2388516 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1023 2387956 2387991 2388088 "RFFACT" 2388190 NIL RFFACT (NIL T) -7 NIL NIL) (-1022 2386073 2386437 2386819 "RFDIST" 2387596 T RFDIST (NIL) -7 NIL NIL) (-1021 2385526 2385618 2385781 "RETSOL" 2385975 NIL RETSOL (NIL T T) -7 NIL NIL) (-1020 2385162 2385242 2385285 "RETRACT" 2385418 NIL RETRACT (NIL T) -9 NIL 2385505) (-1019 2385011 2385036 2385123 "RETRACT-" 2385128 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1018 2384640 2384833 2384903 "RETAST" 2384963 T RETAST (NIL) -8 NIL NIL) (-1017 2377494 2384293 2384420 "RESULT" 2384535 T RESULT (NIL) -8 NIL NIL) (-1016 2376120 2376763 2376962 "RESRING" 2377397 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1015 2375756 2375805 2375903 "RESLATC" 2376057 NIL RESLATC (NIL T) -7 NIL NIL) (-1014 2375462 2375496 2375603 "REPSQ" 2375715 NIL REPSQ (NIL T) -7 NIL NIL) (-1013 2372884 2373464 2374066 "REP" 2374882 T REP (NIL) -7 NIL NIL) (-1012 2372582 2372616 2372727 "REPDB" 2372843 NIL REPDB (NIL T) -7 NIL NIL) (-1011 2366492 2367871 2369094 "REP2" 2371394 NIL REP2 (NIL T) -7 NIL NIL) (-1010 2362869 2363550 2364358 "REP1" 2365719 NIL REP1 (NIL T) -7 NIL NIL) (-1009 2355595 2361010 2361466 "REGSET" 2362499 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1008 2354408 2354743 2354993 "REF" 2355380 NIL REF (NIL T) -8 NIL NIL) (-1007 2353785 2353888 2354055 "REDORDER" 2354292 NIL REDORDER (NIL T T) -7 NIL NIL) (-1006 2349792 2353000 2353226 "RECLOS" 2353614 NIL RECLOS (NIL T) -8 NIL NIL) (-1005 2348844 2349025 2349240 "REALSOLV" 2349599 T REALSOLV (NIL) -7 NIL NIL) (-1004 2348690 2348731 2348761 "REAL" 2348766 T REAL (NIL) -9 NIL 2348801) (-1003 2345173 2345975 2346859 "REAL0Q" 2347855 NIL REAL0Q (NIL T) -7 NIL NIL) (-1002 2340774 2341762 2342823 "REAL0" 2344154 NIL REAL0 (NIL T) -7 NIL NIL) (-1001 2340272 2340491 2340585 "RDUCEAST" 2340702 T RDUCEAST (NIL) -8 NIL NIL) (-1000 2339677 2339749 2339956 "RDIV" 2340194 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-999 2338750 2338924 2339135 "RDIST" 2339499 NIL RDIST (NIL T) -7 NIL NIL) (-998 2337351 2337638 2338008 "RDETRS" 2338458 NIL RDETRS (NIL T T) -7 NIL NIL) (-997 2335168 2335622 2336158 "RDETR" 2336893 NIL RDETR (NIL T T) -7 NIL NIL) (-996 2333782 2334060 2334462 "RDEEFS" 2334884 NIL RDEEFS (NIL T T) -7 NIL NIL) (-995 2332280 2332586 2333016 "RDEEF" 2333470 NIL RDEEF (NIL T T) -7 NIL NIL) (-994 2326561 2329436 2329464 "RCFIELD" 2330741 T RCFIELD (NIL) -9 NIL 2331471) (-993 2324630 2325134 2325827 "RCFIELD-" 2325900 NIL RCFIELD- (NIL T) -8 NIL NIL) (-992 2320961 2322746 2322787 "RCAGG" 2323858 NIL RCAGG (NIL T) -9 NIL 2324323) (-991 2320592 2320686 2320846 "RCAGG-" 2320851 NIL RCAGG- (NIL T T) -8 NIL NIL) (-990 2319932 2320044 2320207 "RATRET" 2320476 NIL RATRET (NIL T) -7 NIL NIL) (-989 2319489 2319556 2319675 "RATFACT" 2319860 NIL RATFACT (NIL T) -7 NIL NIL) (-988 2318804 2318924 2319074 "RANDSRC" 2319359 T RANDSRC (NIL) -7 NIL NIL) (-987 2318541 2318585 2318656 "RADUTIL" 2318753 T RADUTIL (NIL) -7 NIL NIL) (-986 2311703 2317383 2317691 "RADIX" 2318265 NIL RADIX (NIL NIL) -8 NIL NIL) (-985 2303360 2311547 2311675 "RADFF" 2311680 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-984 2303012 2303087 2303115 "RADCAT" 2303272 T RADCAT (NIL) -9 NIL NIL) (-983 2302797 2302845 2302942 "RADCAT-" 2302947 NIL RADCAT- (NIL T) -8 NIL NIL) (-982 2300948 2302572 2302661 "QUEUE" 2302741 NIL QUEUE (NIL T) -8 NIL NIL) (-981 2297524 2300885 2300930 "QUAT" 2300935 NIL QUAT (NIL T) -8 NIL NIL) (-980 2297162 2297205 2297332 "QUATCT2" 2297475 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-979 2290909 2294211 2294251 "QUATCAT" 2295031 NIL QUATCAT (NIL T) -9 NIL 2295797) (-978 2287053 2288090 2289477 "QUATCAT-" 2289571 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-977 2284573 2286137 2286178 "QUAGG" 2286553 NIL QUAGG (NIL T) -9 NIL 2286728) (-976 2284205 2284398 2284466 "QQUTAST" 2284525 T QQUTAST (NIL) -8 NIL NIL) (-975 2283130 2283603 2283775 "QFORM" 2284077 NIL QFORM (NIL NIL T) -8 NIL NIL) (-974 2274342 2279547 2279587 "QFCAT" 2280245 NIL QFCAT (NIL T) -9 NIL 2281246) (-973 2269914 2271115 2272706 "QFCAT-" 2272800 NIL QFCAT- (NIL T T) -8 NIL NIL) (-972 2269552 2269595 2269722 "QFCAT2" 2269865 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-971 2269012 2269122 2269252 "QEQUAT" 2269442 T QEQUAT (NIL) -8 NIL NIL) (-970 2262160 2263231 2264415 "QCMPACK" 2267945 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-969 2259736 2260157 2260585 "QALGSET" 2261815 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-968 2258981 2259155 2259387 "QALGSET2" 2259556 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-967 2257672 2257895 2258212 "PWFFINTB" 2258754 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-966 2255854 2256022 2256376 "PUSHVAR" 2257486 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-965 2251772 2252826 2252867 "PTRANFN" 2254751 NIL PTRANFN (NIL T) -9 NIL NIL) (-964 2250174 2250465 2250787 "PTPACK" 2251483 NIL PTPACK (NIL T) -7 NIL NIL) (-963 2249806 2249863 2249972 "PTFUNC2" 2250111 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-962 2244333 2248678 2248719 "PTCAT" 2249015 NIL PTCAT (NIL T) -9 NIL 2249168) (-961 2243991 2244026 2244150 "PSQFR" 2244292 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-960 2242586 2242884 2243218 "PSEUDLIN" 2243689 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-959 2229355 2231720 2234044 "PSETPK" 2240346 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-958 2222399 2225113 2225209 "PSETCAT" 2228230 NIL PSETCAT (NIL T T T T) -9 NIL 2229044) (-957 2220235 2220869 2221690 "PSETCAT-" 2221695 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-956 2219584 2219749 2219777 "PSCURVE" 2220045 T PSCURVE (NIL) -9 NIL 2220212) (-955 2215940 2217422 2217487 "PSCAT" 2218331 NIL PSCAT (NIL T T T) -9 NIL 2218571) (-954 2215003 2215219 2215619 "PSCAT-" 2215624 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-953 2213735 2214368 2214573 "PRTITION" 2214818 T PRTITION (NIL) -8 NIL NIL) (-952 2213237 2213456 2213548 "PRTDAST" 2213663 T PRTDAST (NIL) -8 NIL NIL) (-951 2202335 2204541 2206729 "PRS" 2211099 NIL PRS (NIL T T) -7 NIL NIL) (-950 2200193 2201685 2201725 "PRQAGG" 2201908 NIL PRQAGG (NIL T) -9 NIL 2202010) (-949 2199579 2199808 2199836 "PROPLOG" 2200021 T PROPLOG (NIL) -9 NIL 2200143) (-948 2196749 2197393 2197857 "PROPFRML" 2199147 NIL PROPFRML (NIL T) -8 NIL NIL) (-947 2196209 2196319 2196449 "PROPERTY" 2196639 T PROPERTY (NIL) -8 NIL NIL) (-946 2190294 2194375 2195195 "PRODUCT" 2195435 NIL PRODUCT (NIL T T) -8 NIL NIL) (-945 2187607 2189752 2189986 "PR" 2190105 NIL PR (NIL T T) -8 NIL NIL) (-944 2187403 2187435 2187494 "PRINT" 2187568 T PRINT (NIL) -7 NIL NIL) (-943 2186743 2186860 2187012 "PRIMES" 2187283 NIL PRIMES (NIL T) -7 NIL NIL) (-942 2184808 2185209 2185675 "PRIMELT" 2186322 NIL PRIMELT (NIL T) -7 NIL NIL) (-941 2184537 2184586 2184614 "PRIMCAT" 2184738 T PRIMCAT (NIL) -9 NIL NIL) (-940 2180698 2184475 2184520 "PRIMARR" 2184525 NIL PRIMARR (NIL T) -8 NIL NIL) (-939 2179705 2179883 2180111 "PRIMARR2" 2180516 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-938 2179348 2179404 2179515 "PREASSOC" 2179643 NIL PREASSOC (NIL T T) -7 NIL NIL) (-937 2178823 2178956 2178984 "PPCURVE" 2179189 T PPCURVE (NIL) -9 NIL 2179325) (-936 2178445 2178618 2178701 "PORTNUM" 2178760 T PORTNUM (NIL) -8 NIL NIL) (-935 2175804 2176203 2176795 "POLYROOT" 2178026 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-934 2169749 2175408 2175568 "POLY" 2175677 NIL POLY (NIL T) -8 NIL NIL) (-933 2169132 2169190 2169424 "POLYLIFT" 2169685 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-932 2165407 2165856 2166485 "POLYCATQ" 2168677 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-931 2152224 2157582 2157647 "POLYCAT" 2161161 NIL POLYCAT (NIL T T T) -9 NIL 2163089) (-930 2145674 2147535 2149919 "POLYCAT-" 2149924 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-929 2145261 2145329 2145449 "POLY2UP" 2145600 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-928 2144893 2144950 2145059 "POLY2" 2145198 NIL POLY2 (NIL T T) -7 NIL NIL) (-927 2143578 2143817 2144093 "POLUTIL" 2144667 NIL POLUTIL (NIL T T) -7 NIL NIL) (-926 2141933 2142210 2142541 "POLTOPOL" 2143300 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-925 2137451 2141869 2141915 "POINT" 2141920 NIL POINT (NIL T) -8 NIL NIL) (-924 2135638 2135995 2136370 "PNTHEORY" 2137096 T PNTHEORY (NIL) -7 NIL NIL) (-923 2134057 2134354 2134766 "PMTOOLS" 2135336 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-922 2133650 2133728 2133845 "PMSYM" 2133973 NIL PMSYM (NIL T) -7 NIL NIL) (-921 2133160 2133229 2133403 "PMQFCAT" 2133575 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-920 2132515 2132625 2132781 "PMPRED" 2133037 NIL PMPRED (NIL T) -7 NIL NIL) (-919 2131911 2131997 2132158 "PMPREDFS" 2132416 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-918 2130554 2130762 2131147 "PMPLCAT" 2131673 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-917 2130086 2130165 2130317 "PMLSAGG" 2130469 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-916 2129561 2129637 2129818 "PMKERNEL" 2130004 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-915 2129178 2129253 2129366 "PMINS" 2129480 NIL PMINS (NIL T) -7 NIL NIL) (-914 2128606 2128675 2128891 "PMFS" 2129103 NIL PMFS (NIL T T T) -7 NIL NIL) (-913 2127834 2127952 2128157 "PMDOWN" 2128483 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-912 2126997 2127156 2127338 "PMASS" 2127672 T PMASS (NIL) -7 NIL NIL) (-911 2126271 2126382 2126545 "PMASSFS" 2126883 NIL PMASSFS (NIL T T) -7 NIL NIL) (-910 2125926 2125994 2126088 "PLOTTOOL" 2126197 T PLOTTOOL (NIL) -7 NIL NIL) (-909 2120548 2121737 2122885 "PLOT" 2124798 T PLOT (NIL) -8 NIL NIL) (-908 2116362 2117396 2118317 "PLOT3D" 2119647 T PLOT3D (NIL) -8 NIL NIL) (-907 2115274 2115451 2115686 "PLOT1" 2116166 NIL PLOT1 (NIL T) -7 NIL NIL) (-906 2090668 2095340 2100191 "PLEQN" 2110540 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-905 2089986 2090108 2090288 "PINTERP" 2090533 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-904 2089679 2089726 2089829 "PINTERPA" 2089933 NIL PINTERPA (NIL T T) -7 NIL NIL) (-903 2088964 2089485 2089572 "PI" 2089612 T PI (NIL) -8 NIL NIL) (-902 2087361 2088302 2088330 "PID" 2088512 T PID (NIL) -9 NIL 2088646) (-901 2087086 2087123 2087211 "PICOERCE" 2087318 NIL PICOERCE (NIL T) -7 NIL NIL) (-900 2086406 2086545 2086721 "PGROEB" 2086942 NIL PGROEB (NIL T) -7 NIL NIL) (-899 2081993 2082807 2083712 "PGE" 2085521 T PGE (NIL) -7 NIL NIL) (-898 2080117 2080363 2080729 "PGCD" 2081710 NIL PGCD (NIL T T T T) -7 NIL NIL) (-897 2079455 2079558 2079719 "PFRPAC" 2080001 NIL PFRPAC (NIL T) -7 NIL NIL) (-896 2076135 2078003 2078356 "PFR" 2079134 NIL PFR (NIL T) -8 NIL NIL) (-895 2074524 2074768 2075093 "PFOTOOLS" 2075882 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-894 2073057 2073296 2073647 "PFOQ" 2074281 NIL PFOQ (NIL T T T) -7 NIL NIL) (-893 2071530 2071742 2072105 "PFO" 2072841 NIL PFO (NIL T T T T T) -7 NIL NIL) (-892 2068118 2071419 2071488 "PF" 2071493 NIL PF (NIL NIL) -8 NIL NIL) (-891 2065552 2066789 2066817 "PFECAT" 2067402 T PFECAT (NIL) -9 NIL 2067786) (-890 2064997 2065151 2065365 "PFECAT-" 2065370 NIL PFECAT- (NIL T) -8 NIL NIL) (-889 2063601 2063852 2064153 "PFBRU" 2064746 NIL PFBRU (NIL T T) -7 NIL NIL) (-888 2061468 2061819 2062251 "PFBR" 2063252 NIL PFBR (NIL T T T T) -7 NIL NIL) (-887 2057384 2058844 2059520 "PERM" 2060825 NIL PERM (NIL T) -8 NIL NIL) (-886 2052650 2053591 2054461 "PERMGRP" 2056547 NIL PERMGRP (NIL T) -8 NIL NIL) (-885 2050782 2051713 2051754 "PERMCAT" 2052200 NIL PERMCAT (NIL T) -9 NIL 2052505) (-884 2050435 2050476 2050600 "PERMAN" 2050735 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-883 2047971 2050100 2050222 "PENDTREE" 2050346 NIL PENDTREE (NIL T) -8 NIL NIL) (-882 2046064 2046798 2046839 "PDRING" 2047496 NIL PDRING (NIL T) -9 NIL 2047782) (-881 2045167 2045385 2045747 "PDRING-" 2045752 NIL PDRING- (NIL T T) -8 NIL NIL) (-880 2042409 2043160 2043828 "PDEPROB" 2044519 T PDEPROB (NIL) -8 NIL NIL) (-879 2039956 2040458 2041013 "PDEPACK" 2041874 T PDEPACK (NIL) -7 NIL NIL) (-878 2038868 2039058 2039309 "PDECOMP" 2039755 NIL PDECOMP (NIL T T) -7 NIL NIL) (-877 2036473 2037290 2037318 "PDECAT" 2038105 T PDECAT (NIL) -9 NIL 2038818) (-876 2036224 2036257 2036347 "PCOMP" 2036434 NIL PCOMP (NIL T T) -7 NIL NIL) (-875 2034429 2035025 2035322 "PBWLB" 2035953 NIL PBWLB (NIL T) -8 NIL NIL) (-874 2026933 2028502 2029840 "PATTERN" 2033112 NIL PATTERN (NIL T) -8 NIL NIL) (-873 2026565 2026622 2026731 "PATTERN2" 2026870 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-872 2024322 2024710 2025167 "PATTERN1" 2026154 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-871 2021717 2022271 2022752 "PATRES" 2023887 NIL PATRES (NIL T T) -8 NIL NIL) (-870 2021281 2021348 2021480 "PATRES2" 2021644 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-869 2019164 2019569 2019976 "PATMATCH" 2020948 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-868 2018700 2018883 2018924 "PATMAB" 2019031 NIL PATMAB (NIL T) -9 NIL 2019114) (-867 2017245 2017554 2017812 "PATLRES" 2018505 NIL PATLRES (NIL T T T) -8 NIL NIL) (-866 2016791 2016914 2016955 "PATAB" 2016960 NIL PATAB (NIL T) -9 NIL 2017132) (-865 2014272 2014804 2015377 "PARTPERM" 2016238 T PARTPERM (NIL) -7 NIL NIL) (-864 2013893 2013956 2014058 "PARSURF" 2014203 NIL PARSURF (NIL T) -8 NIL NIL) (-863 2013525 2013582 2013691 "PARSU2" 2013830 NIL PARSU2 (NIL T T) -7 NIL NIL) (-862 2013289 2013329 2013396 "PARSER" 2013478 T PARSER (NIL) -7 NIL NIL) (-861 2012910 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1964867 1965428 "OREPCTO" 1966328 NIL OREPCTO (NIL T T) -7 NIL NIL) (-835 1958191 1960358 1960399 "OREPCAT" 1962747 NIL OREPCAT (NIL T) -9 NIL 1963851) (-834 1955338 1956120 1957178 "OREPCAT-" 1957183 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-833 1954515 1954787 1954815 "ORDSET" 1955124 T ORDSET (NIL) -9 NIL 1955288) (-832 1954034 1954156 1954349 "ORDSET-" 1954354 NIL ORDSET- (NIL T) -8 NIL NIL) (-831 1952668 1953425 1953453 "ORDRING" 1953655 T ORDRING (NIL) -9 NIL 1953780) (-830 1952313 1952407 1952551 "ORDRING-" 1952556 NIL ORDRING- (NIL T) -8 NIL NIL) (-829 1951719 1952156 1952184 "ORDMON" 1952189 T ORDMON (NIL) -9 NIL 1952210) (-828 1950881 1951028 1951223 "ORDFUNS" 1951568 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-827 1950392 1950751 1950779 "ORDFIN" 1950784 T ORDFIN (NIL) -9 NIL 1950805) (-826 1946984 1948978 1949387 "ORDCOMP" 1950016 NIL ORDCOMP (NIL T) -8 NIL NIL) (-825 1946250 1946377 1946563 "ORDCOMP2" 1946844 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-824 1942858 1943741 1944555 "OPTPROB" 1945456 T OPTPROB (NIL) -8 NIL NIL) (-823 1939660 1940299 1941003 "OPTPACK" 1942174 T OPTPACK (NIL) -7 NIL NIL) (-822 1937373 1938113 1938141 "OPTCAT" 1938960 T OPTCAT (NIL) -9 NIL 1939610) (-821 1937141 1937180 1937246 "OPQUERY" 1937327 T OPQUERY (NIL) -7 NIL NIL) (-820 1934307 1935452 1935956 "OP" 1936670 NIL OP (NIL T) -8 NIL NIL) (-819 1931152 1933104 1933473 "ONECOMP" 1933971 NIL ONECOMP (NIL T) -8 NIL NIL) (-818 1930457 1930572 1930746 "ONECOMP2" 1931024 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-817 1929876 1929982 1930112 "OMSERVER" 1930347 T OMSERVER (NIL) -7 NIL NIL) (-816 1926764 1929316 1929356 "OMSAGG" 1929417 NIL OMSAGG (NIL T) -9 NIL 1929481) (-815 1925387 1925650 1925932 "OMPKG" 1926502 T OMPKG (NIL) -7 NIL NIL) (-814 1924817 1924920 1924948 "OM" 1925247 T OM (NIL) -9 NIL NIL) (-813 1923399 1924366 1924535 "OMLO" 1924698 NIL OMLO (NIL T T) -8 NIL NIL) (-812 1922324 1922471 1922698 "OMEXPR" 1923225 NIL OMEXPR (NIL T) -7 NIL NIL) (-811 1921642 1921870 1922006 "OMERR" 1922208 T OMERR (NIL) -8 NIL NIL) (-810 1920820 1921063 1921223 "OMERRK" 1921502 T OMERRK (NIL) -8 NIL NIL) (-809 1920298 1920497 1920605 "OMENC" 1920732 T OMENC (NIL) -8 NIL NIL) (-808 1914193 1915378 1916549 "OMDEV" 1919147 T OMDEV (NIL) -8 NIL NIL) (-807 1913262 1913433 1913627 "OMCONN" 1914019 T OMCONN (NIL) -8 NIL NIL) (-806 1911883 1912825 1912853 "OINTDOM" 1912858 T OINTDOM (NIL) -9 NIL 1912879) (-805 1907689 1908873 1909589 "OFMONOID" 1911199 NIL OFMONOID (NIL T) -8 NIL NIL) (-804 1907127 1907626 1907671 "ODVAR" 1907676 NIL ODVAR (NIL T) -8 NIL NIL) (-803 1904585 1906872 1907027 "ODR" 1907032 NIL ODR (NIL T T NIL) -8 NIL NIL) (-802 1896929 1904361 1904487 "ODPOL" 1904492 NIL ODPOL (NIL T) -8 NIL NIL) (-801 1890805 1896801 1896906 "ODP" 1896911 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-800 1889571 1889786 1890061 "ODETOOLS" 1890579 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-799 1886540 1887196 1887912 "ODESYS" 1888904 NIL ODESYS (NIL T T) -7 NIL NIL) (-798 1881422 1882330 1883355 "ODERTRIC" 1885615 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-797 1880848 1880930 1881124 "ODERED" 1881334 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-796 1877736 1878284 1878961 "ODERAT" 1880271 NIL ODERAT (NIL T T) -7 NIL NIL) (-795 1874696 1875160 1875757 "ODEPRRIC" 1877265 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-794 1872666 1873235 1873721 "ODEPROB" 1874230 T ODEPROB (NIL) -8 NIL NIL) (-793 1869188 1869671 1870318 "ODEPRIM" 1872145 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-792 1868437 1868539 1868799 "ODEPAL" 1869080 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-791 1864599 1865390 1866254 "ODEPACK" 1867593 T ODEPACK (NIL) -7 NIL NIL) (-790 1863632 1863739 1863968 "ODEINT" 1864488 NIL ODEINT (NIL T T) -7 NIL NIL) (-789 1857733 1859158 1860605 "ODEIFTBL" 1862205 T ODEIFTBL (NIL) -8 NIL NIL) (-788 1853068 1853854 1854813 "ODEEF" 1856892 NIL ODEEF (NIL T T) -7 NIL NIL) (-787 1852403 1852492 1852722 "ODECONST" 1852973 NIL ODECONST (NIL T T T) -7 NIL NIL) (-786 1850554 1851189 1851217 "ODECAT" 1851822 T ODECAT (NIL) -9 NIL 1852353) (-785 1847461 1850266 1850385 "OCT" 1850467 NIL OCT (NIL T) -8 NIL NIL) (-784 1847099 1847142 1847269 "OCTCT2" 1847412 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-783 1841873 1844273 1844313 "OC" 1845410 NIL OC (NIL T) -9 NIL 1846268) (-782 1839100 1839848 1840838 "OC-" 1840932 NIL OC- (NIL T T) -8 NIL NIL) (-781 1838478 1838920 1838948 "OCAMON" 1838953 T OCAMON (NIL) -9 NIL 1838974) (-780 1838035 1838350 1838378 "OASGP" 1838383 T OASGP (NIL) -9 NIL 1838403) (-779 1837322 1837785 1837813 "OAMONS" 1837853 T OAMONS (NIL) -9 NIL 1837896) (-778 1836762 1837169 1837197 "OAMON" 1837202 T OAMON (NIL) -9 NIL 1837222) (-777 1836066 1836558 1836586 "OAGROUP" 1836591 T OAGROUP (NIL) -9 NIL 1836611) (-776 1835756 1835806 1835894 "NUMTUBE" 1836010 NIL NUMTUBE (NIL T) -7 NIL NIL) (-775 1829329 1830847 1832383 "NUMQUAD" 1834240 T NUMQUAD (NIL) -7 NIL NIL) (-774 1825085 1826073 1827098 "NUMODE" 1828324 T NUMODE (NIL) -7 NIL NIL) (-773 1822466 1823320 1823348 "NUMINT" 1824271 T NUMINT (NIL) -9 NIL 1825035) (-772 1821414 1821611 1821829 "NUMFMT" 1822268 T NUMFMT (NIL) -7 NIL NIL) (-771 1807773 1810718 1813250 "NUMERIC" 1818921 NIL NUMERIC (NIL T) -7 NIL NIL) (-770 1802170 1807222 1807317 "NTSCAT" 1807322 NIL NTSCAT (NIL T T T T) -9 NIL 1807361) (-769 1801364 1801529 1801722 "NTPOLFN" 1802009 NIL NTPOLFN (NIL T) -7 NIL NIL) (-768 1789204 1798189 1799001 "NSUP" 1800585 NIL NSUP (NIL T) -8 NIL NIL) (-767 1788836 1788893 1789002 "NSUP2" 1789141 NIL NSUP2 (NIL T T) -7 NIL NIL) (-766 1778833 1788610 1788743 "NSMP" 1788748 NIL NSMP (NIL T T) -8 NIL NIL) (-765 1777265 1777566 1777923 "NREP" 1778521 NIL NREP (NIL T) -7 NIL NIL) (-764 1775856 1776108 1776466 "NPCOEF" 1777008 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-763 1774922 1775037 1775253 "NORMRETR" 1775737 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-762 1772963 1773253 1773662 "NORMPK" 1774630 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-761 1772648 1772676 1772800 "NORMMA" 1772929 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-760 1772475 1772605 1772634 "NONE" 1772639 T NONE (NIL) -8 NIL NIL) (-759 1772264 1772293 1772362 "NONE1" 1772439 NIL NONE1 (NIL T) -7 NIL NIL) (-758 1771747 1771809 1771995 "NODE1" 1772196 NIL NODE1 (NIL T T) -7 NIL NIL) (-757 1770087 1770910 1771165 "NNI" 1771512 T NNI (NIL) -8 NIL NIL) (-756 1768507 1768820 1769184 "NLINSOL" 1769755 NIL NLINSOL (NIL T) -7 NIL NIL) (-755 1764775 1765743 1766642 "NIPROB" 1767628 T NIPROB (NIL) -8 NIL NIL) (-754 1763532 1763766 1764068 "NFINTBAS" 1764537 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-753 1762976 1763183 1763224 "NETCLT" 1763388 NIL NETCLT (NIL T) -9 NIL 1763477) (-752 1761684 1761915 1762196 "NCODIV" 1762744 NIL NCODIV (NIL T T) -7 NIL NIL) (-751 1761446 1761483 1761558 "NCNTFRAC" 1761641 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-750 1759626 1759990 1760410 "NCEP" 1761071 NIL NCEP (NIL T) -7 NIL NIL) (-749 1758537 1759276 1759304 "NASRING" 1759414 T NASRING (NIL) -9 NIL 1759488) (-748 1758332 1758376 1758470 "NASRING-" 1758475 NIL NASRING- (NIL T) -8 NIL NIL) (-747 1757485 1757984 1758012 "NARNG" 1758129 T NARNG (NIL) -9 NIL 1758220) (-746 1757177 1757244 1757378 "NARNG-" 1757383 NIL NARNG- (NIL T) -8 NIL NIL) (-745 1756056 1756263 1756498 "NAGSP" 1756962 T NAGSP (NIL) -7 NIL NIL) (-744 1747328 1749012 1750685 "NAGS" 1754403 T NAGS (NIL) -7 NIL NIL) (-743 1745876 1746184 1746515 "NAGF07" 1747017 T NAGF07 (NIL) -7 NIL NIL) (-742 1740414 1741705 1743012 "NAGF04" 1744589 T NAGF04 (NIL) -7 NIL NIL) (-741 1733382 1734996 1736629 "NAGF02" 1738801 T NAGF02 (NIL) -7 NIL NIL) (-740 1728606 1729706 1730823 "NAGF01" 1732285 T NAGF01 (NIL) -7 NIL NIL) (-739 1722234 1723800 1725385 "NAGE04" 1727041 T NAGE04 (NIL) -7 NIL NIL) (-738 1713403 1715524 1717654 "NAGE02" 1720124 T NAGE02 (NIL) -7 NIL NIL) (-737 1709356 1710303 1711267 "NAGE01" 1712459 T NAGE01 (NIL) -7 NIL NIL) (-736 1707151 1707685 1708243 "NAGD03" 1708818 T NAGD03 (NIL) -7 NIL NIL) (-735 1698901 1700829 1702783 "NAGD02" 1705217 T NAGD02 (NIL) -7 NIL NIL) (-734 1692712 1694137 1695577 "NAGD01" 1697481 T NAGD01 (NIL) -7 NIL NIL) (-733 1688921 1689743 1690580 "NAGC06" 1691895 T NAGC06 (NIL) -7 NIL NIL) (-732 1687386 1687718 1688074 "NAGC05" 1688585 T NAGC05 (NIL) -7 NIL NIL) (-731 1686762 1686881 1687025 "NAGC02" 1687262 T NAGC02 (NIL) -7 NIL NIL) (-730 1685822 1686379 1686419 "NAALG" 1686498 NIL NAALG (NIL T) -9 NIL 1686559) (-729 1685657 1685686 1685776 "NAALG-" 1685781 NIL NAALG- (NIL T T) -8 NIL NIL) (-728 1679607 1680715 1681902 "MULTSQFR" 1684553 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-727 1678926 1679001 1679185 "MULTFACT" 1679519 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-726 1672019 1675889 1675942 "MTSCAT" 1677012 NIL MTSCAT (NIL T T) -9 NIL 1677526) (-725 1671731 1671785 1671877 "MTHING" 1671959 NIL MTHING (NIL T) -7 NIL NIL) (-724 1671523 1671556 1671616 "MSYSCMD" 1671691 T MSYSCMD (NIL) -7 NIL NIL) (-723 1667635 1670278 1670598 "MSET" 1671236 NIL MSET (NIL T) -8 NIL NIL) (-722 1664730 1667196 1667237 "MSETAGG" 1667242 NIL MSETAGG (NIL T) -9 NIL 1667276) (-721 1660613 1662109 1662854 "MRING" 1664030 NIL MRING (NIL T T) -8 NIL NIL) (-720 1660179 1660246 1660377 "MRF2" 1660540 NIL MRF2 (NIL T T T) -7 NIL NIL) (-719 1659797 1659832 1659976 "MRATFAC" 1660138 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-718 1657409 1657704 1658135 "MPRFF" 1659502 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-717 1651469 1657263 1657360 "MPOLY" 1657365 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-716 1650959 1650994 1651202 "MPCPF" 1651428 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-715 1650473 1650516 1650700 "MPC3" 1650910 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-714 1649668 1649749 1649970 "MPC2" 1650388 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-713 1647969 1648306 1648696 "MONOTOOL" 1649328 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-712 1647220 1647511 1647539 "MONOID" 1647758 T MONOID (NIL) -9 NIL 1647905) (-711 1646766 1646885 1647066 "MONOID-" 1647071 NIL MONOID- (NIL T) -8 NIL NIL) (-710 1637625 1643533 1643592 "MONOGEN" 1644266 NIL MONOGEN (NIL T T) -9 NIL 1644722) (-709 1634843 1635578 1636578 "MONOGEN-" 1636697 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-708 1633702 1634122 1634150 "MONADWU" 1634542 T MONADWU (NIL) -9 NIL 1634780) (-707 1633074 1633233 1633481 "MONADWU-" 1633486 NIL MONADWU- (NIL T) -8 NIL NIL) (-706 1632459 1632677 1632705 "MONAD" 1632912 T MONAD (NIL) -9 NIL 1633024) (-705 1632144 1632222 1632354 "MONAD-" 1632359 NIL MONAD- (NIL T) -8 NIL NIL) (-704 1630460 1631057 1631336 "MOEBIUS" 1631897 NIL MOEBIUS (NIL T) -8 NIL NIL) (-703 1629852 1630230 1630270 "MODULE" 1630275 NIL MODULE (NIL T) -9 NIL 1630301) (-702 1629420 1629516 1629706 "MODULE-" 1629711 NIL MODULE- (NIL T T) -8 NIL NIL) (-701 1627135 1627784 1628111 "MODRING" 1629244 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-700 1624121 1625240 1625761 "MODOP" 1626664 NIL MODOP (NIL T T) -8 NIL NIL) (-699 1622736 1623188 1623465 "MODMONOM" 1623984 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-698 1612543 1621027 1621441 "MODMON" 1622373 NIL MODMON (NIL T T) -8 NIL NIL) (-697 1609734 1611387 1611663 "MODFIELD" 1612418 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-696 1608738 1609015 1609205 "MMLFORM" 1609564 T MMLFORM (NIL) -8 NIL NIL) (-695 1608264 1608307 1608486 "MMAP" 1608689 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-694 1606481 1607214 1607255 "MLO" 1607678 NIL MLO (NIL T) -9 NIL 1607920) (-693 1603848 1604363 1604965 "MLIFT" 1605962 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-692 1603239 1603323 1603477 "MKUCFUNC" 1603759 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-691 1602838 1602908 1603031 "MKRECORD" 1603162 NIL MKRECORD (NIL T T) -7 NIL NIL) (-690 1601886 1602047 1602275 "MKFUNC" 1602649 NIL MKFUNC (NIL T) -7 NIL NIL) (-689 1601274 1601378 1601534 "MKFLCFN" 1601769 NIL MKFLCFN (NIL T) -7 NIL NIL) (-688 1600817 1601184 1601243 "MKCHSET" 1601248 NIL MKCHSET (NIL T) -8 NIL NIL) (-687 1600094 1600196 1600381 "MKBCFUNC" 1600710 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-686 1596836 1599648 1599784 "MINT" 1599978 T MINT (NIL) -8 NIL NIL) (-685 1595648 1595891 1596168 "MHROWRED" 1596591 NIL MHROWRED (NIL T) -7 NIL NIL) (-684 1591074 1594183 1594588 "MFLOAT" 1595263 T MFLOAT (NIL) -8 NIL NIL) (-683 1590431 1590507 1590678 "MFINFACT" 1590986 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-682 1586746 1587594 1588478 "MESH" 1589567 T MESH (NIL) -7 NIL NIL) (-681 1585136 1585448 1585801 "MDDFACT" 1586433 NIL MDDFACT (NIL T) -7 NIL NIL) (-680 1581978 1584295 1584336 "MDAGG" 1584591 NIL MDAGG (NIL T) -9 NIL 1584734) (-679 1571756 1581271 1581478 "MCMPLX" 1581791 T MCMPLX (NIL) -8 NIL NIL) (-678 1570897 1571043 1571243 "MCDEN" 1571605 NIL MCDEN (NIL T T) -7 NIL NIL) (-677 1568787 1569057 1569437 "MCALCFN" 1570627 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-676 1567698 1567871 1568112 "MAYBE" 1568585 NIL MAYBE (NIL T) -8 NIL NIL) (-675 1565310 1565833 1566395 "MATSTOR" 1567169 NIL MATSTOR (NIL T) -7 NIL NIL) (-674 1561316 1564682 1564930 "MATRIX" 1565095 NIL MATRIX (NIL T) -8 NIL NIL) (-673 1557085 1557789 1558525 "MATLIN" 1560673 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-672 1547239 1550377 1550454 "MATCAT" 1555334 NIL MATCAT (NIL T T T) -9 NIL 1556751) (-671 1543603 1544616 1545972 "MATCAT-" 1545977 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-670 1542197 1542350 1542683 "MATCAT2" 1543438 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-669 1540309 1540633 1541017 "MAPPKG3" 1541872 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-668 1539290 1539463 1539685 "MAPPKG2" 1540133 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-667 1537789 1538073 1538400 "MAPPKG1" 1538996 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-666 1536895 1537195 1537372 "MAPPAST" 1537632 T MAPPAST (NIL) -8 NIL NIL) (-665 1536506 1536564 1536687 "MAPHACK3" 1536831 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-664 1536098 1536159 1536273 "MAPHACK2" 1536438 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-663 1535536 1535639 1535781 "MAPHACK1" 1535989 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-662 1533642 1534236 1534540 "MAGMA" 1535264 NIL MAGMA (NIL T) -8 NIL NIL) (-661 1533148 1533366 1533457 "MACROAST" 1533571 T MACROAST (NIL) -8 NIL NIL) (-660 1529615 1531387 1531848 "M3D" 1532720 NIL M3D (NIL T) -8 NIL NIL) (-659 1523770 1527985 1528026 "LZSTAGG" 1528808 NIL LZSTAGG (NIL T) -9 NIL 1529103) (-658 1519743 1520901 1522358 "LZSTAGG-" 1522363 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-657 1516857 1517634 1518121 "LWORD" 1519288 NIL LWORD (NIL T) -8 NIL NIL) (-656 1516460 1516661 1516736 "LSTAST" 1516802 T LSTAST (NIL) -8 NIL NIL) (-655 1509661 1516231 1516365 "LSQM" 1516370 NIL LSQM (NIL NIL T) -8 NIL NIL) (-654 1508885 1509024 1509252 "LSPP" 1509516 NIL LSPP (NIL T T T T) -7 NIL NIL) (-653 1506697 1506998 1507454 "LSMP" 1508574 NIL LSMP (NIL T T T T) -7 NIL NIL) (-652 1503476 1504150 1504880 "LSMP1" 1505999 NIL LSMP1 (NIL T) -7 NIL NIL) (-651 1497402 1502644 1502685 "LSAGG" 1502747 NIL LSAGG (NIL T) -9 NIL 1502825) (-650 1494097 1495021 1496234 "LSAGG-" 1496239 NIL LSAGG- (NIL T T) -8 NIL NIL) (-649 1491723 1493241 1493490 "LPOLY" 1493892 NIL LPOLY (NIL T T) -8 NIL NIL) (-648 1491305 1491390 1491513 "LPEFRAC" 1491632 NIL LPEFRAC (NIL T) -7 NIL NIL) (-647 1489652 1490399 1490652 "LO" 1491137 NIL LO (NIL T T T) -8 NIL NIL) (-646 1489304 1489416 1489444 "LOGIC" 1489555 T LOGIC (NIL) -9 NIL 1489636) (-645 1489166 1489189 1489260 "LOGIC-" 1489265 NIL LOGIC- (NIL T) -8 NIL NIL) (-644 1488359 1488499 1488692 "LODOOPS" 1489022 NIL LODOOPS (NIL T T) -7 NIL NIL) (-643 1485817 1488275 1488341 "LODO" 1488346 NIL LODO (NIL T NIL) -8 NIL NIL) (-642 1484355 1484590 1484943 "LODOF" 1485564 NIL LODOF (NIL T T) -7 NIL NIL) (-641 1480711 1483108 1483149 "LODOCAT" 1483587 NIL LODOCAT (NIL T) -9 NIL 1483798) (-640 1480444 1480502 1480629 "LODOCAT-" 1480634 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-639 1477799 1480285 1480403 "LODO2" 1480408 NIL LODO2 (NIL T T) -8 NIL NIL) (-638 1475269 1477736 1477781 "LODO1" 1477786 NIL LODO1 (NIL T) -8 NIL NIL) (-637 1474129 1474294 1474606 "LODEEF" 1475092 NIL LODEEF (NIL T T T) -7 NIL NIL) (-636 1469415 1472259 1472300 "LNAGG" 1473247 NIL LNAGG (NIL T) -9 NIL 1473691) (-635 1468562 1468776 1469118 "LNAGG-" 1469123 NIL LNAGG- (NIL T T) -8 NIL NIL) (-634 1464725 1465487 1466126 "LMOPS" 1467977 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-633 1464120 1464482 1464523 "LMODULE" 1464584 NIL LMODULE (NIL T) -9 NIL 1464626) (-632 1461366 1463765 1463888 "LMDICT" 1464030 NIL LMDICT (NIL T) -8 NIL NIL) (-631 1461092 1461274 1461334 "LITERAL" 1461339 NIL LITERAL (NIL T) -8 NIL NIL) (-630 1454319 1460038 1460336 "LIST" 1460827 NIL LIST (NIL T) -8 NIL NIL) (-629 1453844 1453918 1454057 "LIST3" 1454239 NIL LIST3 (NIL T T T) -7 NIL NIL) (-628 1452851 1453029 1453257 "LIST2" 1453662 NIL LIST2 (NIL T T) -7 NIL NIL) (-627 1450985 1451297 1451696 "LIST2MAP" 1452498 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-626 1449715 1450351 1450392 "LINEXP" 1450647 NIL LINEXP (NIL T) -9 NIL 1450796) (-625 1448362 1448622 1448919 "LINDEP" 1449467 NIL LINDEP (NIL T T) -7 NIL NIL) (-624 1445129 1445848 1446625 "LIMITRF" 1447617 NIL LIMITRF (NIL T) -7 NIL NIL) (-623 1443405 1443700 1444116 "LIMITPS" 1444824 NIL LIMITPS (NIL T T) -7 NIL NIL) (-622 1437860 1442916 1443144 "LIE" 1443226 NIL LIE (NIL T T) -8 NIL NIL) (-621 1436909 1437352 1437392 "LIECAT" 1437532 NIL LIECAT (NIL T) -9 NIL 1437683) (-620 1436750 1436777 1436865 "LIECAT-" 1436870 NIL LIECAT- (NIL T T) -8 NIL NIL) (-619 1429362 1436199 1436364 "LIB" 1436605 T LIB (NIL) -8 NIL NIL) (-618 1424999 1425880 1426815 "LGROBP" 1428479 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-617 1422865 1423139 1423501 "LF" 1424720 NIL LF (NIL T T) -7 NIL NIL) (-616 1421705 1422397 1422425 "LFCAT" 1422632 T LFCAT (NIL) -9 NIL 1422771) (-615 1418609 1419237 1419925 "LEXTRIPK" 1421069 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-614 1415380 1416179 1416682 "LEXP" 1418189 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-613 1414883 1415101 1415193 "LETAST" 1415308 T LETAST (NIL) -8 NIL NIL) (-612 1413281 1413594 1413995 "LEADCDET" 1414565 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-611 1412471 1412545 1412774 "LAZM3PK" 1413202 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-610 1407427 1410548 1411086 "LAUPOL" 1411983 NIL LAUPOL (NIL T T) -8 NIL NIL) (-609 1406992 1407036 1407204 "LAPLACE" 1407377 NIL LAPLACE (NIL T T) -7 NIL NIL) (-608 1404966 1406093 1406344 "LA" 1406825 NIL LA (NIL T T T) -8 NIL NIL) (-607 1404047 1404597 1404638 "LALG" 1404700 NIL LALG (NIL T) -9 NIL 1404759) (-606 1403761 1403820 1403956 "LALG-" 1403961 NIL LALG- (NIL T T) -8 NIL NIL) (-605 1403596 1403620 1403661 "KVTFROM" 1403723 NIL KVTFROM (NIL T) -9 NIL NIL) (-604 1402396 1402813 1403042 "KTVLOGIC" 1403387 T KTVLOGIC (NIL) -8 NIL NIL) (-603 1402231 1402255 1402296 "KRCFROM" 1402358 NIL KRCFROM (NIL T) -9 NIL NIL) (-602 1401135 1401322 1401621 "KOVACIC" 1402031 NIL KOVACIC (NIL T T) -7 NIL NIL) (-601 1400970 1400994 1401035 "KONVERT" 1401097 NIL KONVERT (NIL T) -9 NIL NIL) (-600 1400805 1400829 1400870 "KOERCE" 1400932 NIL KOERCE (NIL T) -9 NIL NIL) (-599 1398539 1399299 1399692 "KERNEL" 1400444 NIL KERNEL (NIL T) -8 NIL NIL) (-598 1398041 1398122 1398252 "KERNEL2" 1398453 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-597 1391892 1396580 1396634 "KDAGG" 1397011 NIL KDAGG (NIL T T) -9 NIL 1397217) (-596 1391421 1391545 1391750 "KDAGG-" 1391755 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-595 1384596 1391082 1391237 "KAFILE" 1391299 NIL KAFILE (NIL T) -8 NIL NIL) (-594 1379051 1384107 1384335 "JORDAN" 1384417 NIL JORDAN (NIL T T) -8 NIL NIL) (-593 1378457 1378700 1378821 "JOINAST" 1378950 T JOINAST (NIL) -8 NIL NIL) (-592 1378303 1378362 1378417 "JAVACODE" 1378422 T JAVACODE (NIL) -8 NIL NIL) (-591 1374602 1376508 1376562 "IXAGG" 1377491 NIL IXAGG (NIL T T) -9 NIL 1377950) (-590 1373521 1373827 1374246 "IXAGG-" 1374251 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-589 1369101 1373443 1373502 "IVECTOR" 1373507 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-588 1367867 1368104 1368370 "ITUPLE" 1368868 NIL ITUPLE (NIL T) -8 NIL NIL) (-587 1366303 1366480 1366786 "ITRIGMNP" 1367689 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-586 1365048 1365252 1365535 "ITFUN3" 1366079 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-585 1364680 1364737 1364846 "ITFUN2" 1364985 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-584 1362517 1363542 1363841 "ITAYLOR" 1364414 NIL ITAYLOR (NIL T) -8 NIL NIL) (-583 1351499 1356654 1357817 "ISUPS" 1361387 NIL ISUPS (NIL T) -8 NIL NIL) (-582 1350603 1350743 1350979 "ISUMP" 1351346 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-581 1345867 1350404 1350483 "ISTRING" 1350556 NIL ISTRING (NIL NIL) -8 NIL NIL) (-580 1345370 1345588 1345680 "ISAST" 1345795 T ISAST (NIL) -8 NIL NIL) (-579 1344580 1344661 1344877 "IRURPK" 1345284 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-578 1343516 1343717 1343957 "IRSN" 1344360 T IRSN (NIL) -7 NIL NIL) (-577 1341545 1341900 1342336 "IRRF2F" 1343154 NIL IRRF2F (NIL T) -7 NIL NIL) (-576 1341292 1341330 1341406 "IRREDFFX" 1341501 NIL IRREDFFX (NIL T) -7 NIL NIL) (-575 1339907 1340166 1340465 "IROOT" 1341025 NIL IROOT (NIL T) -7 NIL NIL) (-574 1336539 1337591 1338283 "IR" 1339247 NIL IR (NIL T) -8 NIL NIL) (-573 1334152 1334647 1335213 "IR2" 1336017 NIL IR2 (NIL T T) -7 NIL NIL) (-572 1333224 1333337 1333558 "IR2F" 1334035 NIL IR2F (NIL T T) -7 NIL NIL) (-571 1333015 1333049 1333109 "IPRNTPK" 1333184 T IPRNTPK (NIL) -7 NIL NIL) (-570 1329634 1332904 1332973 "IPF" 1332978 NIL IPF (NIL NIL) -8 NIL NIL) (-569 1327997 1329559 1329616 "IPADIC" 1329621 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-568 1327328 1327555 1327692 "IP4ADDR" 1327880 T IP4ADDR (NIL) -8 NIL NIL) (-567 1326828 1327032 1327142 "IOMODE" 1327238 T IOMODE (NIL) -8 NIL NIL) (-566 1326186 1326425 1326552 "IOBFILE" 1326721 T IOBFILE (NIL) -8 NIL NIL) (-565 1325950 1326090 1326118 "IOBCON" 1326123 T IOBCON (NIL) -9 NIL 1326144) (-564 1325447 1325505 1325695 "INVLAPLA" 1325886 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-563 1315096 1317449 1319835 "INTTR" 1323111 NIL INTTR (NIL T T) -7 NIL NIL) (-562 1311440 1312182 1313046 "INTTOOLS" 1314281 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-561 1311026 1311117 1311234 "INTSLPE" 1311343 T INTSLPE (NIL) -7 NIL NIL) (-560 1309021 1310949 1311008 "INTRVL" 1311013 NIL INTRVL (NIL T) -8 NIL NIL) (-559 1306623 1307135 1307710 "INTRF" 1308506 NIL INTRF (NIL T) -7 NIL NIL) (-558 1306034 1306131 1306273 "INTRET" 1306521 NIL INTRET (NIL T) -7 NIL NIL) (-557 1304031 1304420 1304890 "INTRAT" 1305642 NIL INTRAT (NIL T T) -7 NIL NIL) (-556 1301259 1301842 1302468 "INTPM" 1303516 NIL INTPM (NIL T T) -7 NIL NIL) (-555 1297962 1298561 1299306 "INTPAF" 1300645 NIL INTPAF (NIL T T T) -7 NIL NIL) (-554 1293141 1294103 1295154 "INTPACK" 1296931 T INTPACK (NIL) -7 NIL NIL) (-553 1290053 1292870 1292997 "INT" 1293034 T INT (NIL) -8 NIL NIL) (-552 1289305 1289457 1289665 "INTHERTR" 1289895 NIL INTHERTR (NIL T T) -7 NIL NIL) (-551 1288744 1288824 1289012 "INTHERAL" 1289219 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-550 1286590 1287033 1287490 "INTHEORY" 1288307 T INTHEORY (NIL) -7 NIL NIL) (-549 1277898 1279519 1281298 "INTG0" 1284942 NIL INTG0 (NIL T T T) -7 NIL NIL) (-548 1258471 1263261 1268071 "INTFTBL" 1273108 T INTFTBL (NIL) -8 NIL NIL) (-547 1257720 1257858 1258031 "INTFACT" 1258330 NIL INTFACT (NIL T) -7 NIL NIL) (-546 1255105 1255551 1256115 "INTEF" 1257274 NIL INTEF (NIL T T) -7 NIL NIL) (-545 1253572 1254277 1254305 "INTDOM" 1254606 T INTDOM (NIL) -9 NIL 1254813) (-544 1252941 1253115 1253357 "INTDOM-" 1253362 NIL INTDOM- (NIL T) -8 NIL NIL) (-543 1249436 1251325 1251379 "INTCAT" 1252178 NIL INTCAT (NIL T) -9 NIL 1252498) (-542 1248909 1249011 1249139 "INTBIT" 1249328 T INTBIT (NIL) -7 NIL NIL) (-541 1247580 1247734 1248048 "INTALG" 1248754 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-540 1247037 1247127 1247297 "INTAF" 1247484 NIL INTAF (NIL T T) -7 NIL NIL) (-539 1240491 1246847 1246987 "INTABL" 1246992 NIL INTABL (NIL T T T) -8 NIL NIL) (-538 1235506 1238180 1238208 "INS" 1239142 T INS (NIL) -9 NIL 1239807) (-537 1232746 1233517 1234491 "INS-" 1234564 NIL INS- (NIL T) -8 NIL NIL) (-536 1231521 1231748 1232046 "INPSIGN" 1232499 NIL INPSIGN (NIL T T) -7 NIL NIL) (-535 1230639 1230756 1230953 "INPRODPF" 1231401 NIL INPRODPF (NIL T T) -7 NIL NIL) (-534 1229533 1229650 1229887 "INPRODFF" 1230519 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-533 1228533 1228685 1228945 "INNMFACT" 1229369 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-532 1227730 1227827 1228015 "INMODGCD" 1228432 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-531 1226239 1226483 1226807 "INFSP" 1227475 NIL INFSP (NIL T T T) -7 NIL NIL) (-530 1225423 1225540 1225723 "INFPROD0" 1226119 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-529 1222305 1223488 1224003 "INFORM" 1224916 T INFORM (NIL) -8 NIL NIL) (-528 1221915 1221975 1222073 "INFORM1" 1222240 NIL INFORM1 (NIL T) -7 NIL NIL) (-527 1221438 1221527 1221641 "INFINITY" 1221821 T INFINITY (NIL) -7 NIL NIL) (-526 1220883 1221156 1221264 "INETCLTS" 1221350 T INETCLTS (NIL) -8 NIL NIL) (-525 1219500 1219749 1220070 "INEP" 1220631 NIL INEP (NIL T T T) -7 NIL NIL) (-524 1218776 1219397 1219462 "INDE" 1219467 NIL INDE (NIL T) -8 NIL NIL) (-523 1218340 1218408 1218525 "INCRMAPS" 1218703 NIL INCRMAPS (NIL T) -7 NIL NIL) (-522 1217358 1217609 1217815 "INBFILE" 1218154 T INBFILE (NIL) -8 NIL NIL) (-521 1212669 1213594 1214538 "INBFF" 1216446 NIL INBFF (NIL T) -7 NIL NIL) (-520 1212338 1212414 1212442 "INBCON" 1212575 T INBCON (NIL) -9 NIL 1212653) (-519 1212178 1212213 1212289 "INBCON-" 1212294 NIL INBCON- (NIL T) -8 NIL NIL) (-518 1211680 1211899 1211991 "INAST" 1212106 T INAST (NIL) -8 NIL NIL) (-517 1211134 1211359 1211465 "IMPTAST" 1211594 T IMPTAST (NIL) -8 NIL NIL) (-516 1207628 1210978 1211082 "IMATRIX" 1211087 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-515 1206340 1206463 1206778 "IMATQF" 1207484 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-514 1204560 1204787 1205124 "IMATLIN" 1206096 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-513 1199186 1204484 1204542 "ILIST" 1204547 NIL ILIST (NIL T NIL) -8 NIL NIL) (-512 1197139 1199046 1199159 "IIARRAY2" 1199164 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-511 1192572 1197050 1197114 "IFF" 1197119 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-510 1191946 1192189 1192305 "IFAST" 1192476 T IFAST (NIL) -8 NIL NIL) (-509 1186989 1191238 1191426 "IFARRAY" 1191803 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-508 1186196 1186893 1186966 "IFAMON" 1186971 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-507 1185780 1185845 1185899 "IEVALAB" 1186106 NIL IEVALAB (NIL T T) -9 NIL NIL) (-506 1185455 1185523 1185683 "IEVALAB-" 1185688 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-505 1185113 1185369 1185432 "IDPO" 1185437 NIL IDPO (NIL T T) -8 NIL NIL) (-504 1184390 1185002 1185077 "IDPOAMS" 1185082 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-503 1183724 1184279 1184354 "IDPOAM" 1184359 NIL IDPOAM (NIL T T) -8 NIL NIL) (-502 1182809 1183059 1183112 "IDPC" 1183525 NIL IDPC (NIL T T) -9 NIL 1183674) (-501 1182305 1182701 1182774 "IDPAM" 1182779 NIL IDPAM (NIL T T) -8 NIL NIL) (-500 1181708 1182197 1182270 "IDPAG" 1182275 NIL IDPAG (NIL T T) -8 NIL NIL) (-499 1181438 1181623 1181673 "IDENT" 1181678 T IDENT (NIL) -8 NIL NIL) (-498 1177693 1178541 1179436 "IDECOMP" 1180595 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-497 1170566 1171616 1172663 "IDEAL" 1176729 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-496 1169730 1169842 1170041 "ICDEN" 1170450 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-495 1168829 1169210 1169357 "ICARD" 1169603 T ICARD (NIL) -8 NIL NIL) (-494 1166889 1167202 1167607 "IBPTOOLS" 1168506 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-493 1162523 1166509 1166622 "IBITS" 1166808 NIL IBITS (NIL NIL) -8 NIL NIL) (-492 1159246 1159822 1160517 "IBATOOL" 1161940 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-491 1157026 1157487 1158020 "IBACHIN" 1158781 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-490 1154903 1156872 1156975 "IARRAY2" 1156980 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-489 1151056 1154829 1154886 "IARRAY1" 1154891 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-488 1145049 1149468 1149949 "IAN" 1150595 T IAN (NIL) -8 NIL NIL) (-487 1144560 1144617 1144790 "IALGFACT" 1144986 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-486 1144088 1144201 1144229 "HYPCAT" 1144436 T HYPCAT (NIL) -9 NIL NIL) (-485 1143626 1143743 1143929 "HYPCAT-" 1143934 NIL HYPCAT- (NIL T) -8 NIL NIL) (-484 1143248 1143421 1143504 "HOSTNAME" 1143563 T HOSTNAME (NIL) -8 NIL NIL) (-483 1143093 1143130 1143171 "HOMOTOP" 1143176 NIL HOMOTOP (NIL T) -9 NIL 1143209) (-482 1139772 1141103 1141144 "HOAGG" 1142125 NIL HOAGG (NIL T) -9 NIL 1142804) (-481 1138366 1138765 1139291 "HOAGG-" 1139296 NIL HOAGG- (NIL T T) -8 NIL NIL) (-480 1132408 1137963 1138111 "HEXADEC" 1138238 T HEXADEC (NIL) -8 NIL NIL) (-479 1131156 1131378 1131641 "HEUGCD" 1132185 NIL HEUGCD (NIL T) -7 NIL NIL) (-478 1130259 1130993 1131123 "HELLFDIV" 1131128 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-477 1128487 1130036 1130124 "HEAP" 1130203 NIL HEAP (NIL T) -8 NIL NIL) (-476 1127778 1128039 1128173 "HEADAST" 1128373 T HEADAST (NIL) -8 NIL NIL) (-475 1121698 1127693 1127755 "HDP" 1127760 NIL HDP (NIL NIL T) -8 NIL NIL) (-474 1115449 1121333 1121485 "HDMP" 1121599 NIL HDMP (NIL NIL T) -8 NIL NIL) (-473 1114774 1114913 1115077 "HB" 1115305 T HB (NIL) -7 NIL NIL) (-472 1108271 1114620 1114724 "HASHTBL" 1114729 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-471 1107774 1107992 1108084 "HASAST" 1108199 T HASAST (NIL) -8 NIL NIL) (-470 1105586 1107396 1107578 "HACKPI" 1107612 T HACKPI (NIL) -8 NIL NIL) (-469 1101281 1105439 1105552 "GTSET" 1105557 NIL GTSET (NIL T T T T) -8 NIL NIL) (-468 1094807 1101159 1101257 "GSTBL" 1101262 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-467 1087120 1093838 1094103 "GSERIES" 1094598 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-466 1086287 1086678 1086706 "GROUP" 1086909 T GROUP (NIL) -9 NIL 1087043) (-465 1085653 1085812 1086063 "GROUP-" 1086068 NIL GROUP- (NIL T) -8 NIL NIL) (-464 1084022 1084341 1084728 "GROEBSOL" 1085330 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-463 1082962 1083224 1083275 "GRMOD" 1083804 NIL GRMOD (NIL T T) -9 NIL 1083972) (-462 1082730 1082766 1082894 "GRMOD-" 1082899 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-461 1078056 1079084 1080084 "GRIMAGE" 1081750 T GRIMAGE (NIL) -8 NIL NIL) (-460 1076523 1076783 1077107 "GRDEF" 1077752 T GRDEF (NIL) -7 NIL NIL) (-459 1075967 1076083 1076224 "GRAY" 1076402 T GRAY (NIL) -7 NIL NIL) (-458 1075180 1075560 1075611 "GRALG" 1075764 NIL GRALG (NIL T T) -9 NIL 1075857) (-457 1074841 1074914 1075077 "GRALG-" 1075082 NIL GRALG- (NIL T T T) -8 NIL NIL) (-456 1071645 1074426 1074604 "GPOLSET" 1074748 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-455 1070999 1071056 1071314 "GOSPER" 1071582 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-454 1066758 1067437 1067963 "GMODPOL" 1070698 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-453 1065763 1065947 1066185 "GHENSEL" 1066570 NIL GHENSEL (NIL T T) -7 NIL NIL) (-452 1059814 1060657 1061684 "GENUPS" 1064847 NIL GENUPS (NIL T T) -7 NIL NIL) (-451 1059511 1059562 1059651 "GENUFACT" 1059757 NIL GENUFACT (NIL T) -7 NIL NIL) (-450 1058923 1059000 1059165 "GENPGCD" 1059429 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-449 1058397 1058432 1058645 "GENMFACT" 1058882 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-448 1056965 1057220 1057527 "GENEEZ" 1058140 NIL GENEEZ (NIL T T) -7 NIL NIL) (-447 1050878 1056576 1056738 "GDMP" 1056888 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-446 1040255 1044649 1045755 "GCNAALG" 1049861 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-445 1038682 1039510 1039538 "GCDDOM" 1039793 T GCDDOM (NIL) -9 NIL 1039950) (-444 1038152 1038279 1038494 "GCDDOM-" 1038499 NIL GCDDOM- (NIL T) -8 NIL NIL) (-443 1036824 1037009 1037313 "GB" 1037931 NIL GB (NIL T T T T) -7 NIL NIL) (-442 1025444 1027770 1030162 "GBINTERN" 1034515 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-441 1023281 1023573 1023994 "GBF" 1025119 NIL GBF (NIL T T T T) -7 NIL NIL) (-440 1022062 1022227 1022494 "GBEUCLID" 1023097 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-439 1021411 1021536 1021685 "GAUSSFAC" 1021933 T GAUSSFAC (NIL) -7 NIL NIL) (-438 1019778 1020080 1020394 "GALUTIL" 1021130 NIL GALUTIL (NIL T) -7 NIL NIL) (-437 1018086 1018360 1018684 "GALPOLYU" 1019505 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-436 1015451 1015741 1016148 "GALFACTU" 1017783 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-435 1007257 1008756 1010364 "GALFACT" 1013883 NIL GALFACT (NIL T) -7 NIL NIL) (-434 1004645 1005303 1005331 "FVFUN" 1006487 T FVFUN (NIL) -9 NIL 1007207) (-433 1003911 1004093 1004121 "FVC" 1004412 T FVC (NIL) -9 NIL 1004595) (-432 1003553 1003708 1003789 "FUNCTION" 1003863 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-431 1001324 1001875 1002341 "FT" 1003107 T FT (NIL) -8 NIL NIL) (-430 1000142 1000625 1000828 "FTEM" 1001141 T FTEM (NIL) -8 NIL NIL) (-429 998398 998687 999091 "FSUPFACT" 999833 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-428 996795 997084 997416 "FST" 998086 T FST (NIL) -8 NIL NIL) (-427 995966 996072 996267 "FSRED" 996677 NIL FSRED (NIL T T) -7 NIL NIL) (-426 994645 994900 995254 "FSPRMELT" 995681 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-425 991730 992168 992667 "FSPECF" 994208 NIL FSPECF (NIL T T) -7 NIL NIL) (-424 973790 982233 982273 "FS" 986121 NIL FS (NIL T) -9 NIL 988410) (-423 962440 965430 969486 "FS-" 969783 NIL FS- (NIL T T) -8 NIL NIL) (-422 961954 962008 962185 "FSINT" 962381 NIL FSINT (NIL T T) -7 NIL NIL) (-421 960281 960947 961250 "FSERIES" 961733 NIL FSERIES (NIL T T) -8 NIL NIL) (-420 959295 959411 959642 "FSCINT" 960161 NIL FSCINT (NIL T T) -7 NIL NIL) (-419 955529 958239 958280 "FSAGG" 958650 NIL FSAGG (NIL T) -9 NIL 958909) (-418 953291 953892 954688 "FSAGG-" 954783 NIL FSAGG- (NIL T T) -8 NIL NIL) (-417 952333 952476 952703 "FSAGG2" 953144 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-416 949988 950267 950821 "FS2UPS" 952051 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-415 949570 949613 949768 "FS2" 949939 NIL FS2 (NIL T T T T) -7 NIL NIL) (-414 948427 948598 948907 "FS2EXPXP" 949395 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-413 947853 947968 948120 "FRUTIL" 948307 NIL FRUTIL (NIL T) -7 NIL NIL) (-412 939308 943348 944706 "FR" 946527 NIL FR (NIL T) -8 NIL NIL) (-411 934383 937026 937066 "FRNAALG" 938462 NIL FRNAALG (NIL T) -9 NIL 939069) (-410 930061 931132 932407 "FRNAALG-" 933157 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-409 929699 929742 929869 "FRNAAF2" 930012 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-408 928106 928553 928848 "FRMOD" 929511 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-407 925885 926489 926806 "FRIDEAL" 927897 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-406 925080 925167 925456 "FRIDEAL2" 925792 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-405 924213 924627 924668 "FRETRCT" 924673 NIL FRETRCT (NIL T) -9 NIL 924849) (-404 923325 923556 923907 "FRETRCT-" 923912 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-403 920537 921713 921772 "FRAMALG" 922654 NIL FRAMALG (NIL T T) -9 NIL 922946) (-402 918671 919126 919756 "FRAMALG-" 919979 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-401 912629 918146 918422 "FRAC" 918427 NIL FRAC (NIL T) -8 NIL NIL) (-400 912265 912322 912429 "FRAC2" 912566 NIL FRAC2 (NIL T T) -7 NIL NIL) (-399 911901 911958 912065 "FR2" 912202 NIL FR2 (NIL T T) -7 NIL NIL) (-398 906574 909426 909454 "FPS" 910573 T FPS (NIL) -9 NIL 911130) (-397 906023 906132 906296 "FPS-" 906442 NIL FPS- (NIL T) -8 NIL NIL) (-396 903477 905112 905140 "FPC" 905365 T FPC (NIL) -9 NIL 905507) (-395 903270 903310 903407 "FPC-" 903412 NIL FPC- (NIL T) -8 NIL NIL) (-394 902148 902758 902799 "FPATMAB" 902804 NIL FPATMAB (NIL T) -9 NIL 902956) (-393 899848 900324 900750 "FPARFRAC" 901785 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-392 895241 895740 896422 "FORTRAN" 899280 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-391 892957 893457 893996 "FORT" 894722 T FORT (NIL) -7 NIL NIL) (-390 890633 891195 891223 "FORTFN" 892283 T FORTFN (NIL) -9 NIL 892907) (-389 890397 890447 890475 "FORTCAT" 890534 T FORTCAT (NIL) -9 NIL 890596) (-388 888530 889013 889403 "FORMULA" 890027 T FORMULA (NIL) -8 NIL NIL) (-387 888318 888348 888417 "FORMULA1" 888494 NIL FORMULA1 (NIL T) -7 NIL NIL) (-386 887841 887893 888066 "FORDER" 888260 NIL FORDER (NIL T T T T) -7 NIL NIL) (-385 886937 887101 887294 "FOP" 887668 T FOP (NIL) -7 NIL NIL) (-384 885545 886217 886391 "FNLA" 886819 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-383 884300 884689 884717 "FNCAT" 885177 T FNCAT (NIL) -9 NIL 885437) (-382 883866 884259 884287 "FNAME" 884292 T FNAME (NIL) -8 NIL NIL) (-381 882529 883458 883486 "FMTC" 883491 T FMTC (NIL) -9 NIL 883527) (-380 878891 880052 880681 "FMONOID" 881933 NIL FMONOID (NIL T) -8 NIL NIL) (-379 878110 878633 878782 "FM" 878787 NIL FM (NIL T T) -8 NIL NIL) (-378 875534 876180 876208 "FMFUN" 877352 T FMFUN (NIL) -9 NIL 878060) (-377 874803 874984 875012 "FMC" 875302 T FMC (NIL) -9 NIL 875484) (-376 871997 872831 872885 "FMCAT" 874080 NIL FMCAT (NIL T T) -9 NIL 874575) (-375 870890 871763 871863 "FM1" 871942 NIL FM1 (NIL T T) -8 NIL NIL) (-374 868664 869080 869574 "FLOATRP" 870441 NIL FLOATRP (NIL T) -7 NIL NIL) (-373 862288 866393 867014 "FLOAT" 868063 T FLOAT (NIL) -8 NIL NIL) (-372 859726 860226 860804 "FLOATCP" 861755 NIL FLOATCP (NIL T) -7 NIL NIL) (-371 858535 859339 859380 "FLINEXP" 859385 NIL FLINEXP (NIL T) -9 NIL 859478) (-370 857689 857924 858252 "FLINEXP-" 858257 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-369 856765 856909 857133 "FLASORT" 857541 NIL FLASORT (NIL T T) -7 NIL NIL) (-368 853982 854824 854876 "FLALG" 856103 NIL FLALG (NIL T T) -9 NIL 856570) (-367 847766 851468 851509 "FLAGG" 852771 NIL FLAGG (NIL T) -9 NIL 853423) (-366 846492 846831 847321 "FLAGG-" 847326 NIL FLAGG- (NIL T T) -8 NIL NIL) (-365 845534 845677 845904 "FLAGG2" 846345 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-364 842509 843483 843542 "FINRALG" 844670 NIL FINRALG (NIL T T) -9 NIL 845178) (-363 841669 841898 842237 "FINRALG-" 842242 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-362 841075 841288 841316 "FINITE" 841512 T FINITE (NIL) -9 NIL 841619) (-361 833533 835694 835734 "FINAALG" 839401 NIL FINAALG (NIL T) -9 NIL 840854) (-360 828874 829915 831059 "FINAALG-" 832438 NIL FINAALG- (NIL T T) -8 NIL NIL) (-359 828269 828629 828732 "FILE" 828804 NIL FILE (NIL T) -8 NIL NIL) (-358 826953 827265 827319 "FILECAT" 828003 NIL FILECAT (NIL T T) -9 NIL 828219) (-357 824821 826315 826343 "FIELD" 826383 T FIELD (NIL) -9 NIL 826463) (-356 823441 823826 824337 "FIELD-" 824342 NIL FIELD- (NIL T) -8 NIL NIL) (-355 821319 822076 822423 "FGROUP" 823127 NIL FGROUP (NIL T) -8 NIL NIL) (-354 820409 820573 820793 "FGLMICPK" 821151 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-353 816276 820334 820391 "FFX" 820396 NIL FFX (NIL T NIL) -8 NIL NIL) (-352 815877 815938 816073 "FFSLPE" 816209 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-351 811870 812649 813445 "FFPOLY" 815113 NIL FFPOLY (NIL T) -7 NIL NIL) (-350 811374 811410 811619 "FFPOLY2" 811828 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-349 807260 811293 811356 "FFP" 811361 NIL FFP (NIL T NIL) -8 NIL NIL) (-348 802693 807171 807235 "FF" 807240 NIL FF (NIL NIL NIL) -8 NIL NIL) (-347 797854 802036 802226 "FFNBX" 802547 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-346 792828 796989 797247 "FFNBP" 797708 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-345 787496 792112 792323 "FFNB" 792661 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-344 786328 786526 786841 "FFINTBAS" 787293 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-343 782556 784735 784763 "FFIELDC" 785383 T FFIELDC (NIL) -9 NIL 785759) (-342 781219 781589 782086 "FFIELDC-" 782091 NIL FFIELDC- (NIL T) -8 NIL NIL) (-341 780789 780834 780958 "FFHOM" 781161 NIL FFHOM (NIL T T T) -7 NIL NIL) (-340 778487 778971 779488 "FFF" 780304 NIL FFF (NIL T) -7 NIL NIL) (-339 774140 778229 778330 "FFCGX" 778430 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-338 769807 773872 773979 "FFCGP" 774083 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-337 765025 769534 769642 "FFCG" 769743 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-336 746858 755896 755982 "FFCAT" 761147 NIL FFCAT (NIL T T T) -9 NIL 762598) (-335 742056 743103 744417 "FFCAT-" 745647 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-334 741467 741510 741745 "FFCAT2" 742007 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-333 730679 734439 735659 "FEXPR" 740319 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-332 729679 730114 730155 "FEVALAB" 730239 NIL FEVALAB (NIL T) -9 NIL 730500) (-331 728838 729048 729386 "FEVALAB-" 729391 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-330 727431 728221 728424 "FDIV" 728737 NIL FDIV (NIL T T T T) -8 NIL NIL) (-329 724497 725212 725327 "FDIVCAT" 726895 NIL FDIVCAT (NIL T T T T) -9 NIL 727332) (-328 724259 724286 724456 "FDIVCAT-" 724461 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-327 723479 723566 723843 "FDIV2" 724166 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-326 722165 722424 722713 "FCPAK1" 723210 T FCPAK1 (NIL) -7 NIL NIL) (-325 721293 721665 721806 "FCOMP" 722056 NIL FCOMP (NIL T) -8 NIL NIL) (-324 705029 708443 711981 "FC" 717775 T FC (NIL) -8 NIL NIL) (-323 697608 701593 701633 "FAXF" 703435 NIL FAXF (NIL T) -9 NIL 704127) (-322 694887 695542 696367 "FAXF-" 696832 NIL FAXF- (NIL T T) -8 NIL NIL) (-321 689987 694263 694439 "FARRAY" 694744 NIL FARRAY (NIL T) -8 NIL NIL) (-320 685240 687272 687325 "FAMR" 688348 NIL FAMR (NIL T T) -9 NIL 688808) (-319 684130 684432 684867 "FAMR-" 684872 NIL FAMR- (NIL T T T) -8 NIL NIL) (-318 683326 684052 684105 "FAMONOID" 684110 NIL FAMONOID (NIL T) -8 NIL NIL) (-317 681138 681822 681875 "FAMONC" 682816 NIL FAMONC (NIL T T) -9 NIL 683202) (-316 679830 680892 681029 "FAGROUP" 681034 NIL FAGROUP (NIL T) -8 NIL NIL) (-315 677625 677944 678347 "FACUTIL" 679511 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-314 676724 676909 677131 "FACTFUNC" 677435 NIL FACTFUNC (NIL T) -7 NIL NIL) (-313 669129 675975 676187 "EXPUPXS" 676580 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-312 666612 667152 667738 "EXPRTUBE" 668563 T EXPRTUBE (NIL) -7 NIL NIL) (-311 662806 663398 664135 "EXPRODE" 665951 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 648180 661461 661889 "EXPR" 662410 NIL EXPR (NIL T) -8 NIL NIL) (-309 642587 643174 643987 "EXPR2UPS" 647478 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 642223 642280 642387 "EXPR2" 642524 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 633628 641355 641652 "EXPEXPAN" 642060 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 633455 633585 633614 "EXIT" 633619 T EXIT (NIL) -8 NIL NIL) (-305 632962 633179 633270 "EXITAST" 633384 T EXITAST (NIL) -8 NIL NIL) (-304 632589 632651 632764 "EVALCYC" 632894 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 632130 632248 632289 "EVALAB" 632459 NIL EVALAB (NIL T) -9 NIL 632563) (-302 631611 631733 631954 "EVALAB-" 631959 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 629079 630347 630375 "EUCDOM" 630930 T EUCDOM (NIL) -9 NIL 631280) (-300 627484 627926 628516 "EUCDOM-" 628521 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 615024 617782 620532 "ESTOOLS" 624754 T ESTOOLS (NIL) -7 NIL NIL) (-298 614656 614713 614822 "ESTOOLS2" 614961 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 614407 614449 614529 "ESTOOLS1" 614608 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 608312 610040 610068 "ES" 612836 T ES (NIL) -9 NIL 614245) (-295 603259 604546 606363 "ES-" 606527 NIL ES- (NIL T) -8 NIL NIL) (-294 599634 600394 601174 "ESCONT" 602499 T ESCONT (NIL) -7 NIL NIL) (-293 599379 599411 599493 "ESCONT1" 599596 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 599054 599104 599204 "ES2" 599323 NIL ES2 (NIL T T) -7 NIL NIL) (-291 598684 598742 598851 "ES1" 598990 NIL ES1 (NIL T T) -7 NIL NIL) (-290 597900 598029 598205 "ERROR" 598528 T ERROR (NIL) -7 NIL NIL) (-289 591403 597759 597850 "EQTBL" 597855 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 583960 586717 588166 "EQ" 589987 NIL -3244 (NIL T) -8 NIL NIL) (-287 583592 583649 583758 "EQ2" 583897 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 578884 579930 581023 "EP" 582531 NIL EP (NIL T) -7 NIL NIL) (-285 577466 577767 578084 "ENV" 578587 T ENV (NIL) -8 NIL NIL) (-284 576645 577165 577193 "ENTIRER" 577198 T ENTIRER (NIL) -9 NIL 577244) (-283 573147 574600 574970 "EMR" 576444 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-282 572291 572476 572530 "ELTAGG" 572910 NIL ELTAGG (NIL T T) -9 NIL 573121) (-281 572010 572072 572213 "ELTAGG-" 572218 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-280 571799 571828 571882 "ELTAB" 571966 NIL ELTAB (NIL T T) -9 NIL NIL) (-279 570925 571071 571270 "ELFUTS" 571650 NIL ELFUTS (NIL T T) -7 NIL NIL) (-278 570667 570723 570751 "ELEMFUN" 570856 T ELEMFUN (NIL) -9 NIL NIL) (-277 570537 570558 570626 "ELEMFUN-" 570631 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-276 565428 568637 568678 "ELAGG" 569618 NIL ELAGG (NIL T) -9 NIL 570081) (-275 563713 564147 564810 "ELAGG-" 564815 NIL ELAGG- (NIL T T) -8 NIL NIL) (-274 562370 562650 562945 "ELABEXPR" 563438 T ELABEXPR (NIL) -8 NIL NIL) (-273 555236 557037 557864 "EFUPXS" 561646 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-272 548686 550487 551297 "EFULS" 554512 NIL EFULS (NIL T T T) -8 NIL NIL) (-271 546108 546466 546945 "EFSTRUC" 548318 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-270 535180 536745 538305 "EF" 544623 NIL EF (NIL T T) -7 NIL NIL) (-269 534281 534665 534814 "EAB" 535051 T EAB (NIL) -8 NIL NIL) (-268 533490 534240 534268 "E04UCFA" 534273 T E04UCFA (NIL) -8 NIL NIL) (-267 532699 533449 533477 "E04NAFA" 533482 T E04NAFA (NIL) -8 NIL NIL) (-266 531908 532658 532686 "E04MBFA" 532691 T E04MBFA (NIL) -8 NIL NIL) (-265 531117 531867 531895 "E04JAFA" 531900 T E04JAFA (NIL) -8 NIL NIL) (-264 530328 531076 531104 "E04GCFA" 531109 T E04GCFA (NIL) -8 NIL NIL) (-263 529539 530287 530315 "E04FDFA" 530320 T E04FDFA (NIL) -8 NIL NIL) (-262 528748 529498 529526 "E04DGFA" 529531 T E04DGFA (NIL) -8 NIL NIL) (-261 522926 524273 525637 "E04AGNT" 527404 T E04AGNT (NIL) -7 NIL NIL) (-260 521632 522112 522152 "DVARCAT" 522627 NIL DVARCAT (NIL T) -9 NIL 522826) (-259 520836 521048 521362 "DVARCAT-" 521367 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-258 513736 520635 520764 "DSMP" 520769 NIL DSMP (NIL T T T) -8 NIL NIL) (-257 508546 509681 510749 "DROPT" 512688 T DROPT (NIL) -8 NIL NIL) (-256 508211 508270 508368 "DROPT1" 508481 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 503326 504452 505589 "DROPT0" 507094 T DROPT0 (NIL) -7 NIL NIL) (-254 501671 501996 502382 "DRAWPT" 502960 T DRAWPT (NIL) -7 NIL NIL) (-253 496258 497181 498260 "DRAW" 500645 NIL DRAW (NIL T) -7 NIL NIL) (-252 495891 495944 496062 "DRAWHACK" 496199 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 494622 494891 495182 "DRAWCX" 495620 T DRAWCX (NIL) -7 NIL NIL) (-250 494138 494206 494357 "DRAWCURV" 494548 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 484609 486568 488683 "DRAWCFUN" 492043 T DRAWCFUN (NIL) -7 NIL NIL) (-248 481422 483304 483345 "DQAGG" 483974 NIL DQAGG (NIL T) -9 NIL 484247) (-247 469701 476400 476483 "DPOLCAT" 478335 NIL DPOLCAT (NIL T T T T) -9 NIL 478880) (-246 464540 465886 467844 "DPOLCAT-" 467849 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-245 457695 464401 464499 "DPMO" 464504 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-244 450753 457475 457642 "DPMM" 457647 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-243 450173 450376 450490 "DOMAIN" 450659 T DOMAIN (NIL) -8 NIL NIL) (-242 443924 449808 449960 "DMP" 450074 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 443524 443580 443724 "DLP" 443862 NIL DLP (NIL T) -7 NIL NIL) (-240 437394 442851 443041 "DLIST" 443366 NIL DLIST (NIL T) -8 NIL NIL) (-239 434240 436249 436290 "DLAGG" 436840 NIL DLAGG (NIL T) -9 NIL 437069) (-238 433053 433683 433711 "DIVRING" 433803 T DIVRING (NIL) -9 NIL 433886) (-237 432290 432480 432780 "DIVRING-" 432785 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 430392 430749 431155 "DISPLAY" 431904 T DISPLAY (NIL) -7 NIL NIL) (-235 424334 430306 430369 "DIRPROD" 430374 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-234 423182 423385 423650 "DIRPROD2" 424127 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-233 412445 418397 418450 "DIRPCAT" 418860 NIL DIRPCAT (NIL NIL T) -9 NIL 419700) (-232 409771 410413 411294 "DIRPCAT-" 411631 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-231 409058 409218 409404 "DIOSP" 409605 T DIOSP (NIL) -7 NIL NIL) (-230 405760 407970 408011 "DIOPS" 408445 NIL DIOPS (NIL T) -9 NIL 408674) (-229 405309 405423 405614 "DIOPS-" 405619 NIL DIOPS- (NIL T T) -8 NIL NIL) (-228 404201 404795 404823 "DIFRING" 405010 T DIFRING (NIL) -9 NIL 405120) (-227 403847 403924 404076 "DIFRING-" 404081 NIL DIFRING- (NIL T) -8 NIL NIL) (-226 401652 402890 402931 "DIFEXT" 403294 NIL DIFEXT (NIL T) -9 NIL 403588) (-225 399937 400365 401031 "DIFEXT-" 401036 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-224 397259 399469 399510 "DIAGG" 399515 NIL DIAGG (NIL T) -9 NIL 399535) (-223 396643 396800 397052 "DIAGG-" 397057 NIL DIAGG- (NIL T T) -8 NIL NIL) (-222 392108 395602 395879 "DHMATRIX" 396412 NIL DHMATRIX (NIL T) -8 NIL NIL) (-221 387720 388629 389639 "DFSFUN" 391118 T DFSFUN (NIL) -7 NIL NIL) (-220 382836 386651 386963 "DFLOAT" 387428 T DFLOAT (NIL) -8 NIL NIL) (-219 381064 381345 381741 "DFINTTLS" 382544 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-218 378129 379085 379485 "DERHAM" 380730 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-217 375978 377904 377993 "DEQUEUE" 378073 NIL DEQUEUE (NIL T) -8 NIL NIL) (-216 375193 375326 375522 "DEGRED" 375840 NIL DEGRED (NIL T T) -7 NIL NIL) (-215 371588 372333 373186 "DEFINTRF" 374421 NIL DEFINTRF (NIL T) -7 NIL NIL) (-214 369115 369584 370183 "DEFINTEF" 371107 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-213 368492 368735 368850 "DEFAST" 369020 T DEFAST (NIL) -8 NIL NIL) (-212 362534 368089 368237 "DECIMAL" 368364 T DECIMAL (NIL) -8 NIL NIL) (-211 360046 360504 361010 "DDFACT" 362078 NIL DDFACT (NIL T T) -7 NIL NIL) (-210 359642 359685 359836 "DBLRESP" 359997 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-209 357541 357875 358235 "DBASE" 359409 NIL DBASE (NIL T) -8 NIL NIL) (-208 356810 357021 357167 "DATAARY" 357440 NIL DATAARY (NIL NIL T) -8 NIL NIL) (-207 355943 356769 356797 "D03FAFA" 356802 T D03FAFA (NIL) -8 NIL NIL) (-206 355077 355902 355930 "D03EEFA" 355935 T D03EEFA (NIL) -8 NIL NIL) (-205 353027 353493 353982 "D03AGNT" 354608 T D03AGNT (NIL) -7 NIL NIL) (-204 352343 352986 353014 "D02EJFA" 353019 T D02EJFA (NIL) -8 NIL NIL) (-203 351659 352302 352330 "D02CJFA" 352335 T D02CJFA (NIL) -8 NIL NIL) (-202 350975 351618 351646 "D02BHFA" 351651 T D02BHFA (NIL) -8 NIL NIL) (-201 350291 350934 350962 "D02BBFA" 350967 T D02BBFA (NIL) -8 NIL NIL) (-200 343489 345077 346683 "D02AGNT" 348705 T D02AGNT (NIL) -7 NIL NIL) (-199 341258 341780 342326 "D01WGTS" 342963 T D01WGTS (NIL) -7 NIL NIL) (-198 340353 341217 341245 "D01TRNS" 341250 T D01TRNS (NIL) -8 NIL NIL) (-197 339448 340312 340340 "D01GBFA" 340345 T D01GBFA (NIL) -8 NIL NIL) (-196 338543 339407 339435 "D01FCFA" 339440 T D01FCFA (NIL) -8 NIL NIL) (-195 337638 338502 338530 "D01ASFA" 338535 T D01ASFA (NIL) -8 NIL NIL) (-194 336733 337597 337625 "D01AQFA" 337630 T D01AQFA (NIL) -8 NIL NIL) (-193 335828 336692 336720 "D01APFA" 336725 T D01APFA (NIL) -8 NIL NIL) (-192 334923 335787 335815 "D01ANFA" 335820 T D01ANFA (NIL) -8 NIL NIL) (-191 334018 334882 334910 "D01AMFA" 334915 T D01AMFA (NIL) -8 NIL NIL) (-190 333113 333977 334005 "D01ALFA" 334010 T D01ALFA (NIL) -8 NIL NIL) (-189 332208 333072 333100 "D01AKFA" 333105 T D01AKFA (NIL) -8 NIL NIL) (-188 331303 332167 332195 "D01AJFA" 332200 T D01AJFA (NIL) -8 NIL NIL) (-187 324600 326151 327712 "D01AGNT" 329762 T D01AGNT (NIL) -7 NIL NIL) (-186 323937 324065 324217 "CYCLOTOM" 324468 T CYCLOTOM (NIL) -7 NIL NIL) (-185 320672 321385 322112 "CYCLES" 323230 T CYCLES (NIL) -7 NIL NIL) (-184 319984 320118 320289 "CVMP" 320533 NIL CVMP (NIL T) -7 NIL NIL) (-183 317755 318013 318389 "CTRIGMNP" 319712 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-182 317172 317378 317492 "CTOR" 317661 T CTOR (NIL) -8 NIL NIL) (-181 316708 316903 317004 "CTORKIND" 317091 T CTORKIND (NIL) -8 NIL NIL) (-180 316219 316408 316507 "CTORCALL" 316629 T CTORCALL (NIL) -8 NIL NIL) (-179 315593 315692 315845 "CSTTOOLS" 316116 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 311392 312049 312807 "CRFP" 314905 NIL CRFP (NIL T T) -7 NIL NIL) (-177 310894 311113 311205 "CRCEAST" 311320 T CRCEAST (NIL) -8 NIL NIL) (-176 309941 310126 310354 "CRAPACK" 310698 NIL CRAPACK (NIL T) -7 NIL NIL) (-175 309325 309426 309630 "CPMATCH" 309817 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-174 309050 309078 309184 "CPIMA" 309291 NIL CPIMA (NIL T T T) -7 NIL NIL) (-173 305414 306086 306804 "COORDSYS" 308385 NIL COORDSYS (NIL T) -7 NIL NIL) (-172 304798 304927 305077 "CONTOUR" 305284 T CONTOUR (NIL) -8 NIL NIL) (-171 300724 302801 303293 "CONTFRAC" 304338 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 300604 300625 300653 "CONDUIT" 300690 T CONDUIT (NIL) -9 NIL NIL) (-169 299777 300297 300325 "COMRING" 300330 T COMRING (NIL) -9 NIL 300382) (-168 298858 299135 299319 "COMPPROP" 299613 T COMPPROP (NIL) -8 NIL NIL) (-167 298519 298554 298682 "COMPLPAT" 298817 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-166 288576 298328 298437 "COMPLEX" 298442 NIL COMPLEX (NIL T) -8 NIL NIL) (-165 288212 288269 288376 "COMPLEX2" 288513 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-164 287930 287965 288063 "COMPFACT" 288171 NIL COMPFACT (NIL T T) -7 NIL NIL) (-163 272103 282323 282363 "COMPCAT" 283367 NIL COMPCAT (NIL T) -9 NIL 284752) (-162 261618 264542 268169 "COMPCAT-" 268525 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-161 261347 261375 261478 "COMMUPC" 261584 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-160 261142 261175 261234 "COMMONOP" 261308 T COMMONOP (NIL) -7 NIL NIL) (-159 260725 260893 260980 "COMM" 261075 T COMM (NIL) -8 NIL NIL) (-158 260329 260529 260604 "COMMAAST" 260670 T COMMAAST (NIL) -8 NIL NIL) (-157 259578 259772 259800 "COMBOPC" 260138 T COMBOPC (NIL) -9 NIL 260313) (-156 258474 258684 258926 "COMBINAT" 259368 NIL COMBINAT (NIL T) -7 NIL NIL) (-155 254672 255245 255885 "COMBF" 257896 NIL COMBF (NIL T T) -7 NIL NIL) (-154 253458 253788 254023 "COLOR" 254457 T COLOR (NIL) -8 NIL NIL) (-153 252961 253179 253271 "COLONAST" 253386 T COLONAST (NIL) -8 NIL NIL) (-152 252601 252648 252773 "CMPLXRT" 252908 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-151 252076 252301 252400 "CLLCTAST" 252522 T CLLCTAST (NIL) -8 NIL NIL) (-150 247578 248606 249686 "CLIP" 251016 T CLIP (NIL) -7 NIL NIL) (-149 245960 246684 246923 "CLIF" 247405 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-148 242182 244106 244147 "CLAGG" 245076 NIL CLAGG (NIL T) -9 NIL 245612) (-147 240604 241061 241644 "CLAGG-" 241649 NIL CLAGG- (NIL T T) -8 NIL NIL) (-146 240148 240233 240373 "CINTSLPE" 240513 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-145 237649 238120 238668 "CHVAR" 239676 NIL CHVAR (NIL T T T) -7 NIL NIL) (-144 236892 237412 237440 "CHARZ" 237445 T CHARZ (NIL) -9 NIL 237460) (-143 236646 236686 236764 "CHARPOL" 236846 NIL CHARPOL (NIL T) -7 NIL NIL) (-142 235773 236326 236354 "CHARNZ" 236401 T CHARNZ (NIL) -9 NIL 236457) (-141 233798 234463 234798 "CHAR" 235458 T CHAR (NIL) -8 NIL NIL) (-140 233524 233585 233613 "CFCAT" 233724 T CFCAT (NIL) -9 NIL NIL) (-139 232769 232880 233062 "CDEN" 233408 NIL CDEN (NIL T T T) -7 NIL NIL) (-138 228761 231922 232202 "CCLASS" 232509 T CCLASS (NIL) -8 NIL NIL) (-137 228680 228706 228741 "CATEGORY" 228746 T -10 (NIL) -8 NIL NIL) (-136 228154 228380 228479 "CATAST" 228601 T CATAST (NIL) -8 NIL NIL) (-135 227657 227875 227967 "CASEAST" 228082 T CASEAST (NIL) -8 NIL NIL) (-134 222709 223686 224439 "CARTEN" 226960 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-133 221817 221965 222186 "CARTEN2" 222556 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-132 220159 220967 221224 "CARD" 221580 T CARD (NIL) -8 NIL NIL) (-131 219762 219963 220038 "CAPSLAST" 220104 T CAPSLAST (NIL) -8 NIL NIL) (-130 219134 219462 219490 "CACHSET" 219622 T CACHSET (NIL) -9 NIL 219699) (-129 218630 218926 218954 "CABMON" 219004 T CABMON (NIL) -9 NIL 219060) (-128 217658 218086 218259 "BYTE" 218477 T BYTE (NIL) -8 NIL NIL) (-127 213067 217126 217289 "BYTEBUF" 217515 T BYTEBUF (NIL) -8 NIL NIL) (-126 210624 212759 212866 "BTREE" 212993 NIL BTREE (NIL T) -8 NIL NIL) (-125 208122 210272 210394 "BTOURN" 210534 NIL BTOURN (NIL T) -8 NIL NIL) (-124 205540 207593 207634 "BTCAT" 207702 NIL BTCAT (NIL T) -9 NIL 207779) (-123 205207 205287 205436 "BTCAT-" 205441 NIL BTCAT- (NIL T T) -8 NIL NIL) (-122 200499 204350 204378 "BTAGG" 204600 T BTAGG (NIL) -9 NIL 204761) (-121 199989 200114 200320 "BTAGG-" 200325 NIL BTAGG- (NIL T) -8 NIL NIL) (-120 197033 199267 199482 "BSTREE" 199806 NIL BSTREE (NIL T) -8 NIL NIL) (-119 196171 196297 196481 "BRILL" 196889 NIL BRILL (NIL T) -7 NIL NIL) (-118 192872 194899 194940 "BRAGG" 195589 NIL BRAGG (NIL T) -9 NIL 195846) (-117 191401 191807 192362 "BRAGG-" 192367 NIL BRAGG- (NIL T T) -8 NIL NIL) (-116 184665 190747 190931 "BPADICRT" 191249 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-115 183015 184602 184647 "BPADIC" 184652 NIL BPADIC (NIL NIL) -8 NIL NIL) (-114 182713 182743 182857 "BOUNDZRO" 182979 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-113 178228 179319 180186 "BOP" 181866 T BOP (NIL) -8 NIL NIL) (-112 175849 176293 176813 "BOP1" 177741 NIL BOP1 (NIL T) -7 NIL NIL) (-111 174587 175273 175466 "BOOLEAN" 175676 T BOOLEAN (NIL) -8 NIL NIL) (-110 173949 174327 174381 "BMODULE" 174386 NIL BMODULE (NIL T T) -9 NIL 174451) (-109 169779 173747 173820 "BITS" 173896 T BITS (NIL) -8 NIL NIL) (-108 169191 169313 169455 "BINDING" 169657 T BINDING (NIL) -8 NIL NIL) (-107 163236 168790 168937 "BINARY" 169064 T BINARY (NIL) -8 NIL NIL) (-106 161063 162491 162532 "BGAGG" 162792 NIL BGAGG (NIL T) -9 NIL 162929) (-105 160894 160926 161017 "BGAGG-" 161022 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159992 160278 160483 "BFUNCT" 160709 T BFUNCT (NIL) -8 NIL NIL) (-103 158682 158860 159148 "BEZOUT" 159816 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155199 157534 157864 "BBTREE" 158385 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154933 154986 155014 "BASTYPE" 155133 T BASTYPE (NIL) -9 NIL NIL) (-100 154785 154814 154887 "BASTYPE-" 154892 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154223 154299 154449 "BALFACT" 154696 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 153106 153638 153824 "AUTOMOR" 154068 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152832 152837 152863 "ATTREG" 152868 T ATTREG (NIL) -9 NIL NIL) (-96 151111 151529 151881 "ATTRBUT" 152498 T ATTRBUT (NIL) -8 NIL NIL) (-95 150746 150939 151005 "ATTRAST" 151063 T ATTRAST (NIL) -8 NIL NIL) (-94 150282 150395 150421 "ATRIG" 150622 T ATRIG (NIL) -9 NIL NIL) (-93 150091 150132 150219 "ATRIG-" 150224 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149762 149922 149948 "ASTCAT" 149953 T ASTCAT (NIL) -9 NIL 149983) (-91 149489 149548 149667 "ASTCAT-" 149672 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147686 149265 149353 "ASTACK" 149432 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146191 146488 146853 "ASSOCEQ" 147368 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145223 145850 145974 "ASP9" 146098 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 144987 145171 145210 "ASP8" 145215 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 143856 144592 144734 "ASP80" 144876 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 142755 143491 143623 "ASP7" 143755 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141709 142432 142550 "ASP78" 142668 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140678 141389 141506 "ASP77" 141623 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 139590 140316 140447 "ASP74" 140578 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 138490 139225 139357 "ASP73" 139489 NIL ASP73 (NIL NIL) -8 NIL NIL) (-80 137594 138316 138416 "ASP6" 138421 NIL ASP6 (NIL NIL) -8 NIL NIL) (-79 136542 137271 137389 "ASP55" 137507 NIL ASP55 (NIL NIL) -8 NIL NIL) (-78 135492 136216 136335 "ASP50" 136454 NIL ASP50 (NIL NIL) -8 NIL NIL) (-77 134580 135193 135303 "ASP4" 135413 NIL ASP4 (NIL NIL) -8 NIL NIL) (-76 133668 134281 134391 "ASP49" 134501 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 132453 133207 133375 "ASP42" 133557 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131230 131986 132156 "ASP41" 132340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130180 130907 131025 "ASP35" 131143 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129945 130128 130167 "ASP34" 130172 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129682 129749 129825 "ASP33" 129900 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128577 129317 129449 "ASP31" 129581 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128342 128525 128564 "ASP30" 128569 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 128077 128146 128222 "ASP29" 128297 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127842 128025 128064 "ASP28" 128069 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127607 127790 127829 "ASP27" 127834 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126691 127305 127416 "ASP24" 127527 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125768 126493 126605 "ASP20" 126610 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 124856 125469 125579 "ASP1" 125689 NIL ASP1 (NIL NIL) -8 NIL NIL) (-62 123800 124530 124649 "ASP19" 124768 NIL ASP19 (NIL NIL) -8 NIL NIL) (-61 123537 123604 123680 "ASP12" 123755 NIL ASP12 (NIL NIL) -8 NIL NIL) (-60 122389 123136 123280 "ASP10" 123424 NIL ASP10 (NIL NIL) -8 NIL NIL) (-59 120288 122233 122324 "ARRAY2" 122329 NIL ARRAY2 (NIL T) -8 NIL NIL) (-58 116104 119936 120050 "ARRAY1" 120205 NIL ARRAY1 (NIL T) -8 NIL NIL) (-57 115136 115309 115530 "ARRAY12" 115927 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-56 109495 111366 111441 "ARR2CAT" 114071 NIL ARR2CAT (NIL T T T) -9 NIL 114829) (-55 106929 107673 108627 "ARR2CAT-" 108632 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-54 105677 105829 106135 "APPRULE" 106765 NIL APPRULE (NIL T T T) -7 NIL NIL) (-53 105328 105376 105495 "APPLYORE" 105623 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-52 104302 104593 104788 "ANY" 105151 T ANY (NIL) -8 NIL NIL) (-51 103580 103703 103860 "ANY1" 104176 NIL ANY1 (NIL T) -7 NIL NIL) (-50 101145 102017 102344 "ANTISYM" 103304 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-49 100660 100849 100946 "ANON" 101066 T ANON (NIL) -8 NIL NIL) (-48 94792 99199 99653 "AN" 100224 T AN (NIL) -8 NIL NIL) (-47 91048 92402 92453 "AMR" 93201 NIL AMR (NIL T T) -9 NIL 93801) (-46 90160 90381 90744 "AMR-" 90749 NIL AMR- (NIL T T T) -8 NIL NIL) (-45 74710 90077 90138 "ALIST" 90143 NIL ALIST (NIL T T) -8 NIL NIL) (-44 71547 74304 74473 "ALGSC" 74628 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-43 68103 68657 69264 "ALGPKG" 70987 NIL ALGPKG (NIL T T) -7 NIL NIL) (-42 67380 67481 67665 "ALGMFACT" 67989 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 63119 63804 64459 "ALGMANIP" 66903 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54525 62745 62895 "ALGFF" 63052 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53721 53852 54031 "ALGFACT" 54383 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52786 53352 53390 "ALGEBRA" 53395 NIL ALGEBRA (NIL T) -9 NIL 53436) (-37 52504 52563 52695 "ALGEBRA-" 52700 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 845860c4..7ea1f5d1 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,61 +1,36 @@ -(739356 . 3436193630) -(((*1 *2 *3 *1) - (-12 (|has| *1 (-6 -4369)) (-4 *1 (-482 *3)) (-4 *3 (-1192)) - (-4 *3 (-1079)) (-5 *2 (-111)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-887 *4)) (-4 *4 (-1079)) (-5 *2 (-111)) - (-5 *1 (-886 *4)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-903)) (-5 *2 (-111)) (-5 *1 (-1080 *4 *5)) (-14 *4 *3) - (-14 *5 *3)))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-757)) (-5 *1 (-839 *2)) (-4 *2 (-169)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1151 (-553))) (-5 *1 (-924)) (-5 *3 (-553))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1137) (-760))) (-5 *1 (-113))))) -(((*1 *2 *2) - (-12 (-4 *3 (-545)) (-5 *1 (-41 *3 *2)) - (-4 *2 - (-13 (-357) (-296) - (-10 -8 (-15 -4013 ((-1104 *3 (-599 $)) $)) - (-15 -4024 ((-1104 *3 (-599 $)) $)) - (-15 -3212 ($ (-1104 *3 (-599 $))))))))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-545)) (-5 *1 (-41 *3 *2)) - (-4 *2 - (-13 (-357) (-296) - (-10 -8 (-15 -4013 ((-1104 *3 (-599 $)) $)) - (-15 -4024 ((-1104 *3 (-599 $)) $)) - (-15 -3212 ($ (-1104 *3 (-599 $))))))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-630 *2)) - (-4 *2 - (-13 (-357) (-296) - (-10 -8 (-15 -4013 ((-1104 *4 (-599 $)) $)) - (-15 -4024 ((-1104 *4 (-599 $)) $)) - (-15 -3212 ($ (-1104 *4 (-599 $))))))) - (-4 *4 (-545)) (-5 *1 (-41 *4 *2)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-630 (-599 *2))) - (-4 *2 - (-13 (-357) (-296) - (-10 -8 (-15 -4013 ((-1104 *4 (-599 $)) $)) - (-15 -4024 ((-1104 *4 (-599 $)) $)) - (-15 -3212 ($ (-1104 *4 (-599 $))))))) - (-4 *4 (-545)) (-5 *1 (-41 *4 *2))))) -(((*1 *2 *3) (-12 (-5 *3 (-1137)) (-5 *2 (-52)) (-5 *1 (-815))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-545)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-951 *4 *3)) (-4 *3 (-1214 *4))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-357)) (-4 *7 (-1214 *5)) (-4 *4 (-710 *5 *7)) - (-5 *2 (-2 (|:| -1317 (-674 *6)) (|:| |vec| (-1238 *5)))) - (-5 *1 (-797 *5 *6 *7 *4 *3)) (-4 *6 (-641 *5)) (-4 *3 (-641 *4))))) +(733959 . 3437447583) +(((*1 *2 *1 *1) (-12 (-4 *1 (-301)) (-5 *2 (-111))))) +(((*1 *2 *2 *2) + (-12 (-4 *3 (-1192)) (-5 *1 (-179 *3 *2)) (-4 *2 (-659 *3))))) (((*1 *2 *3 *2) - (-12 (-5 *2 (-903)) (-5 *3 (-630 (-257))) (-5 *1 (-255)))) - ((*1 *1 *2) (-12 (-5 *2 (-903)) (-5 *1 (-257))))) + (-12 (-5 *2 (-1135 (-630 (-553)))) (-5 *3 (-630 (-553))) + (-5 *1 (-865))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-545) (-833) (-1020 (-553)))) (-4 *5 (-424 *4)) + (-5 *2 + (-3 (|:| |overq| (-1151 (-401 (-553)))) + (|:| |overan| (-1151 (-48))) (|:| -4140 (-111)))) + (-5 *1 (-429 *4 *5 *3)) (-4 *3 (-1214 *5))))) +(((*1 *2 *2 *1 *3 *4) + (-12 (-5 *2 (-630 *8)) (-5 *3 (-1 *8 *8 *8)) + (-5 *4 (-1 (-111) *8 *8)) (-4 *1 (-1185 *5 *6 *7 *8)) (-4 *5 (-545)) + (-4 *6 (-779)) (-4 *7 (-833)) (-4 *8 (-1045 *5 *6 *7))))) +(((*1 *2 *1) (-12 (-5 *2 (-1243)) (-5 *1 (-808))))) +(((*1 *2) (-12 (-5 *2 (-373)) (-5 *1 (-1022))))) +(((*1 *1 *1 *2 *2 *2) (-12 (-5 *2 (-1073 (-220))) (-5 *1 (-908)))) + ((*1 *1 *1 *2 *2) (-12 (-5 *2 (-1073 (-220))) (-5 *1 (-909)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1073 (-220))) (-5 *1 (-909)))) + ((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-553)) (-5 *1 (-473))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-630 *7)) (-5 *3 (-553)) (-4 *7 (-931 *4 *5 *6)) + (-4 *4 (-445)) (-4 *5 (-779)) (-4 *6 (-833)) + (-5 *1 (-442 *4 *5 *6 *7))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-163 *2)) (-4 *2 (-169))))) +(((*1 *2 *3) (-12 (-5 *3 (-807)) (-5 *2 (-52)) (-5 *1 (-817))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-757)) (-5 *2 (-1238 (-630 (-553)))) (-5 *1 (-473)))) ((*1 *1 *2 *3) @@ -63,101 +38,23 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1192)) (-5 *1 (-1135 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1192)) (-5 *1 (-1135 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1155)) (-5 *2 (-1243)) (-5 *1 (-808))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-220)) (-5 *4 (-553)) - (-5 *5 (-3 (|:| |fn| (-382)) (|:| |fp| (-63 -3219)))) - (-5 *2 (-1017)) (-5 *1 (-734))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1151 *1)) (-4 *1 (-445)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1151 *6)) (-4 *6 (-931 *5 *3 *4)) (-4 *3 (-779)) - (-4 *4 (-833)) (-4 *5 (-891)) (-5 *1 (-450 *3 *4 *5 *6)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-1151 *1)) (-4 *1 (-891))))) -(((*1 *2 *2) - (-12 (-5 *2 (-1238 *1)) (-4 *1 (-336 *3 *4 *5)) (-4 *3 (-1196)) - (-4 *4 (-1214 *3)) (-4 *5 (-1214 (-401 *4)))))) -(((*1 *2 *3) (-12 (-5 *3 (-925 *2)) (-5 *1 (-964 *2)) (-4 *2 (-1031))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 (-1135 *4) (-1135 *4))) (-5 *2 (-1135 *4)) - (-5 *1 (-1263 *4)) (-4 *4 (-1192)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 (-630 (-1135 *5)) (-630 (-1135 *5)))) (-5 *4 (-553)) - (-5 *2 (-630 (-1135 *5))) (-5 *1 (-1263 *5)) (-4 *5 (-1192))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-220)) (-5 *4 (-553)) (-5 *2 (-1017)) (-5 *1 (-744))))) -(((*1 *2) - (-12 (-5 *2 (-111)) (-5 *1 (-435 *3)) (-4 *3 (-1214 (-553)))))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-574 *3)) (-4 *3 (-357))))) +(((*1 *2 *1) (-12 (-5 *2 (-630 (-172))) (-5 *1 (-1064))))) +(((*1 *2 *3) (-12 (-5 *3 (-757)) (-5 *2 (-1 (-373))) (-5 *1 (-1022))))) (((*1 *2 *1) - (-12 (-4 *1 (-367 *3)) (-4 *3 (-1192)) (-4 *3 (-833)) (-5 *2 (-111)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-111) *4 *4)) (-4 *1 (-367 *4)) (-4 *4 (-1192)) - (-5 *2 (-111))))) -(((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1123)) (-5 *3 (-553)) (-5 *2 (-111))))) + (|partial| -12 (-5 *2 (-1041 (-1006 *3) (-1151 (-1006 *3)))) + (-5 *1 (-1006 *3)) (-4 *3 (-13 (-831) (-357) (-1004)))))) (((*1 *1 *1) - (-12 (-4 *1 (-1045 *2 *3 *4)) (-4 *2 (-1031)) (-4 *3 (-779)) - (-4 *4 (-833)) (-4 *2 (-445))))) -(((*1 *2 *3) (-12 (-5 *3 (-757)) (-5 *2 (-1 (-373))) (-5 *1 (-1022))))) -(((*1 *2 *1) (-12 (-5 *2 (-1243)) (-5 *1 (-808))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-1155)) (-4 *5 (-601 (-874 (-553)))) - (-4 *5 (-868 (-553))) - (-4 *5 (-13 (-833) (-1020 (-553)) (-445) (-626 (-553)))) - (-5 *2 (-2 (|:| |special| *3) (|:| |integrand| *3))) - (-5 *1 (-556 *5 *3)) (-4 *3 (-616)) - (-4 *3 (-13 (-27) (-1177) (-424 *5))))) - ((*1 *2 *2 *3 *4 *4) - (|partial| -12 (-5 *3 (-1155)) (-5 *4 (-826 *2)) (-4 *2 (-1118)) - (-4 *2 (-13 (-27) (-1177) (-424 *5))) - (-4 *5 (-601 (-874 (-553)))) (-4 *5 (-868 (-553))) - (-4 *5 (-13 (-833) (-1020 (-553)) (-445) (-626 (-553)))) - (-5 *1 (-556 *5 *2))))) + (-12 (-4 *2 (-343)) (-4 *2 (-1031)) (-5 *1 (-698 *2 *3)) + (-4 *3 (-1214 *2))))) +(((*1 *1 *1 *1) (-5 *1 (-845)))) (((*1 *2 *3) - (-12 (-5 *3 (-630 *7)) (-4 *7 (-931 *4 *5 *6)) (-4 *4 (-445)) - (-4 *5 (-779)) (-4 *6 (-833)) (-5 *2 (-1243)) - (-5 *1 (-442 *4 *5 *6 *7))))) + (-12 (-5 *3 (-1155)) (-5 *2 (-1 *6 *5)) (-5 *1 (-692 *4 *5 *6)) + (-4 *4 (-601 (-529))) (-4 *5 (-1192)) (-4 *6 (-1192))))) +(((*1 *1) (-5 *1 (-789)))) (((*1 *2 *2) - (-12 (-5 *2 (-925 *3)) (-4 *3 (-13 (-357) (-1177) (-984))) - (-5 *1 (-173 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-757)) (-4 *4 (-357)) (-5 *1 (-878 *2 *4)) - (-4 *2 (-1214 *4))))) -(((*1 *1 *1) - (-12 (-5 *1 (-583 *2)) (-4 *2 (-38 (-401 (-553)))) (-4 *2 (-1031))))) -(((*1 *2 *3) - (-12 (-5 *3 (-310 (-220))) (-5 *2 (-310 (-373))) (-5 *1 (-299))))) -(((*1 *1 *2 *2) (-12 (-4 *1 (-163 *2)) (-4 *2 (-169))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-1017)) (-5 *1 (-299)))) - ((*1 *2 *3) - (-12 (-5 *3 (-630 (-1017))) (-5 *2 (-1017)) (-5 *1 (-299)))) - ((*1 *1 *2) (-12 (-5 *2 (-630 *1)) (-4 *1 (-636 *3)) (-4 *3 (-1192)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-636 *2)) (-4 *2 (-1192)))) - ((*1 *1 *2 *1) (-12 (-4 *1 (-636 *2)) (-4 *2 (-1192)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-636 *2)) (-4 *2 (-1192)))) - ((*1 *1 *1 *1) (-5 *1 (-1043))) - ((*1 *2 *3) - (-12 (-5 *3 (-1135 (-1135 *4))) (-5 *2 (-1135 *4)) (-5 *1 (-1132 *4)) - (-4 *4 (-1192)))) - ((*1 *1 *2 *1) (-12 (-4 *1 (-1226 *2)) (-4 *2 (-1192)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1226 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*2 - (-2 (|:| -2770 (-630 *9)) (|:| -3361 *4) (|:| |ineq| (-630 *9)))) - (-5 *1 (-970 *6 *7 *8 *9 *4)) (-5 *3 (-630 *9)) - (-4 *4 (-1051 *6 *7 *8 *9)))) - ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-111)) (-4 *6 (-445)) (-4 *7 (-779)) - (-4 *8 (-833)) (-4 *9 (-1045 *6 *7 *8)) - (-5 *2 - (-2 (|:| -2770 (-630 *9)) (|:| -3361 *4) (|:| |ineq| (-630 *9)))) - (-5 *1 (-1086 *6 *7 *8 *9 *4)) (-5 *3 (-630 *9)) - (-4 *4 (-1051 *6 *7 *8 *9))))) + (-5 *2 (-630 (-2 (|:| |val| *3) (|:| -3233 *4)))) + (-5 *1 (-1087 *5 *6 *7 *3 *4)) (-4 *4 (-1051 *5 *6 *7 *3))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-778)) (-4 *2 (-1031)))) ((*1 *2 *1) (-12 (-4 *2 (-1031)) (-5 *1 (-50 *2 *3)) (-14 *3 (-630 (-1155))))) @@ -3249,10 +3553,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-376 *2 *3)) (-4 *3 (-1079)) (-4 *2 (-1031)))) ((*1 *2 *1) - (-12 (-14 *3 (-630 (-1155))) (-4 *5 (-233 (-2656 *3) (-757))) + (-12 (-14 *3 (-630 (-1155))) (-4 *5 (-233 (-2563 *3) (-757))) (-14 *6 - (-1 (-111) (-2 (|:| -2839 *4) (|:| -3503 *5)) - (-2 (|:| -2839 *4) (|:| -3503 *5)))) + (-1 (-111) (-2 (|:| -2735 *4) (|:| -2692 *5)) + (-2 (|:| -2735 *4) (|:| -2692 *5)))) (-4 *2 (-169)) (-5 *1 (-454 *3 *2 *4 *5 *6 *7)) (-4 *4 (-833)) (-4 *7 (-931 *2 *5 (-847 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-502 *2 *3)) (-4 *3 (-833)) (-4 *2 (-1079)))) @@ -3269,67 +3573,39 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1045 *3 *4 *2)) (-4 *3 (-1031)) (-4 *4 (-779)) (-4 *2 (-833))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-835 *2)) (-4 *2 (-1031)) (-4 *2 (-357))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-806)) (-14 *5 (-1155)) (-5 *2 (-630 (-1211 *5 *4))) - (-5 *1 (-1093 *4 *5)) (-5 *3 (-1211 *5 *4))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-674 *4)) (-5 *3 (-903)) (|has| *4 (-6 (-4371 "*"))) - (-4 *4 (-1031)) (-5 *1 (-1010 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-630 (-674 *4))) (-5 *3 (-903)) - (|has| *4 (-6 (-4371 "*"))) (-4 *4 (-1031)) (-5 *1 (-1010 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 (-111) *6)) (-4 *6 (-13 (-1079) (-1020 *5))) - (-4 *5 (-868 *4)) (-4 *4 (-1079)) 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*1 (-454 *3 *4 *5 *6 *7 *8)) (-4 *5 (-833)) (-4 *8 (-931 *4 *6 (-847 *3))))) ((*1 *2 *1) @@ -3338,217 +3614,169 @@ ((*1 *1 *1) (-12 (-4 *1 (-955 *2 *3 *4)) (-4 *2 (-1031)) (-4 *3 (-778)) (-4 *4 (-833))))) -(((*1 *1 *2) - (-12 - (-5 *2 - (-630 - (-2 - (|:| -2669 - (-2 (|:| |var| (-1155)) (|:| |fn| (-310 (-220))) - (|:| -2515 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) - (|:| |relerr| (-220)))) - (|:| -3359 - (-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| (-1135 (-220))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2515 - (-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 (-548))))) -(((*1 *2 *1) - (-12 (-4 *1 (-163 *3)) (-4 *3 (-169)) (-4 *3 (-538)) - (-5 *2 (-401 (-553))))) - ((*1 *2 *1) - (-12 (-5 *2 (-401 (-553))) (-5 *1 (-412 *3)) (-4 *3 (-538)) - (-4 *3 (-545)))) - ((*1 *2 *1) (-12 (-4 *1 (-538)) (-5 *2 (-401 (-553))))) - ((*1 *2 *1) - (-12 (-4 *1 (-783 *3)) (-4 *3 (-169)) (-4 *3 (-538)) - (-5 *2 (-401 (-553))))) - ((*1 *2 *1) - (-12 (-5 *2 (-401 (-553))) (-5 *1 (-819 *3)) (-4 *3 (-538)) - (-4 *3 (-1079)))) +(((*1 *2 *3 *4 *3) + (-12 (-5 *3 (-553)) (-5 *4 (-674 (-220))) (-5 *2 (-1017)) + (-5 *1 (-733))))) +(((*1 *1 *2) (-12 (-5 *2 (-401 (-553))) (-5 *1 (-480))))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-274)))) + ((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-874 *3)) (-4 *3 (-1079)))) ((*1 *2 *1) - (-12 (-5 *2 (-401 (-553))) (-5 *1 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*7 (-1045 *4 *5 *6)) + (-5 *2 (-630 (-2 (|:| -2498 *1) (|:| -2984 (-630 *7))))) + (-5 *3 (-630 *7)) (-4 *1 (-1185 *4 *5 *6 *7))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-779)) (-4 *6 (-833)) (-4 *3 (-545)) + (-4 *7 (-931 *3 *5 *6)) + (-5 *2 (-2 (|:| -2692 (-757)) (|:| -4120 *8) (|:| |radicand| *8))) + (-5 *1 (-935 *5 *6 *3 *7 *8)) (-5 *4 (-757)) + (-4 *8 + (-13 (-357) + (-10 -8 (-15 -3110 ($ *7)) (-15 -3963 (*7 $)) (-15 -3974 (*7 $)))))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-630 (-310 (-220)))) (|:| -1979 (-630 (-220))))) + (-2 (|:| |lfn| (-630 (-310 (-220)))) (|:| -1945 (-630 (-220))))) (-5 *2 (-630 (-1155))) (-5 *1 (-261)))) ((*1 *2 *3) (-12 (-5 *3 (-1151 *7)) (-4 *7 (-931 *6 *4 *5)) (-4 *4 (-779)) @@ -4085,7 +4455,7 @@ (-5 *1 (-932 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-357) - (-10 -8 (-15 -3212 ($ *7)) (-15 -4013 (*7 $)) (-15 -4024 (*7 $))))))) + (-10 -8 (-15 -3110 ($ *7)) (-15 -3963 (*7 $)) (-15 -3974 (*7 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1081 (-1155))) (-5 *1 (-948 *3)) (-4 *3 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+ (-5 *8 (-3 (|:| |fn| (-382)) (|:| |fp| (-85 FCN)))) + (-5 *9 (-3 (|:| |fn| (-382)) (|:| |fp| (-70 PEDERV)))) + (-5 *10 (-3 (|:| |fn| (-382)) (|:| |fp| (-87 OUTPUT)))) + (-5 *3 (-220)) (-5 *2 (-1017)) (-5 *1 (-735))))) +(((*1 *2 *3) + (-12 (-5 *2 (-553)) (-5 *1 (-438 *3)) (-4 *3 (-398)) (-4 *3 (-1031))))) (((*1 *1 *1) (-12 (-5 *1 (-333 *2 *3 *4)) (-14 *2 (-630 (-1155))) (-14 *3 (-630 (-1155))) (-4 *4 (-381)))) @@ -4644,65 +5363,33 @@ ((*1 *1 *2) (-12 (-5 *2 (-401 (-553))) (-4 *1 (-994)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-994)) (-5 *2 (-903)))) ((*1 *1 *1) (-4 *1 (-994)))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-553)) (-5 *2 (-1243)) (-5 *1 (-808))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5 - *7 *3 *8) - (-12 (-5 *5 (-674 (-220))) (-5 *6 (-111)) (-5 *7 (-674 (-553))) - (-5 *8 (-3 (|:| |fn| (-382)) (|:| |fp| (-64 QPHESS)))) - (-5 *3 (-553)) (-5 *4 (-220)) (-5 *2 (-1017)) (-5 *1 (-739))))) -(((*1 *2) - (-12 (-4 *3 (-545)) (-5 *2 (-630 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 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*1 (-392 *3 *4 *5 *6)) - (-14 *3 (-1155)) (-14 *4 (-3 (|:| |fst| (-428)) (|:| -1900 "void"))) + (-14 *3 (-1155)) (-14 *4 (-3 (|:| |fst| (-428)) (|:| -1875 "void"))) (-14 *5 (-630 (-1155))) (-14 *6 (-1159)))) ((*1 *1 *2) (-12 (-5 *2 (-324)) (-5 *1 (-392 *3 *4 *5 *6)) (-14 *3 (-1155)) - (-14 *4 (-3 (|:| |fst| (-428)) (|:| -1900 "void"))) + (-14 *4 (-3 (|:| |fst| (-428)) (|:| -1875 "void"))) (-14 *5 (-630 (-1155))) (-14 *6 (-1159)))) ((*1 *1 *2) (-12 (-5 *2 (-325 *4)) (-4 *4 (-13 (-833) (-21))) @@ -6619,17 +7062,16 @@ ((*1 *1 *2) (-12 (-5 *2 (-1155)) (-5 *1 (-428)))) ((*1 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-428)))) ((*1 *1 *2) (-12 (-5 *2 (-428)) (-5 *1 (-431)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-431)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1159)) (|:| -2149 (-630 (-324))))) + (-5 *2 (-2 (|:| |localSymbols| (-1159)) (|:| -2106 (-630 (-324))))) (-4 *1 (-433)))) ((*1 *1 *2) (-12 (-5 *2 (-324)) (-4 *1 (-433)))) ((*1 *1 *2) (-12 (-5 *2 (-630 (-324))) (-4 *1 (-433)))) ((*1 *1 *2) (-12 (-5 *2 (-1238 (-684))) (-4 *1 (-433)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1159)) (|:| -2149 (-630 (-324))))) + (-5 *2 (-2 (|:| |localSymbols| (-1159)) (|:| -2106 (-630 (-324))))) (-4 *1 (-434)))) ((*1 *1 *2) (-12 (-5 *2 (-324)) (-4 *1 (-434)))) ((*1 *1 *2) (-12 (-5 *2 (-630 (-324))) (-4 *1 (-434)))) @@ -6645,15 +7087,12 @@ ((*1 *1 *2) (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-467 *3 *4 *5)) (-4 *3 (-1031)) (-14 *5 *3))) - ((*1 *2 *1) (-12 (-5 *2 (-986 16)) (-5 *1 (-480)))) - ((*1 *2 *1) (-12 (-5 *2 (-401 (-553))) (-5 *1 (-480)))) ((*1 *1 *2) (-12 (-5 *2 (-1104 (-553) (-599 (-488)))) (-5 *1 (-488)))) ((*1 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-495)))) ((*1 *1 *2) (-12 (-5 *2 (-630 *6)) (-4 *6 (-931 *3 *4 *5)) (-4 *3 (-357)) (-4 *4 (-779)) (-4 *5 (-833)) (-5 *1 (-497 *3 *4 *5 *6)))) ((*1 *1 *2) (-12 (-5 *2 (-630 (-1191))) (-5 *1 (-517)))) - ((*1 *1 *2) (-12 (-5 *2 (-128)) (-5 *1 (-592)))) ((*1 *1 *2) (-12 (-5 *2 (-630 (-1191))) (-5 *1 (-593)))) ((*1 *1 *2) (-12 (-4 *3 (-169)) (-5 *1 (-594 *3 *2)) (-4 *2 (-730 *3)))) @@ -6693,27 +7132,17 @@ ((*1 *2 *1) (-12 (-5 *2 (-373)) (-5 *1 (-684)))) ((*1 *2 *3) (-12 (-5 *3 (-310 (-553))) (-5 *2 (-310 (-686))) (-5 *1 (-686)))) - ((*1 *1 *2) (-12 (-5 *1 (-688 *2)) (-4 *2 (-1079)))) ((*1 *2 *3) (-12 (-5 *3 (-845)) (-5 *2 (-1137)) (-5 *1 (-696)))) ((*1 *2 *1) (-12 (-4 *2 (-169)) (-5 *1 (-697 *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 (-4 *3 (-1031)) (-5 *1 (-698 *3 *2)) (-4 *2 (-1214 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -2839 *3) (|:| -3503 *4))) - (-5 *1 (-699 *3 *4 *5)) (-4 *3 (-833)) (-4 *4 (-1079)) - (-14 *5 (-1 (-111) *2 *2)))) - ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -2839 *3) (|:| -3503 *4))) (-4 *3 (-833)) - (-4 *4 (-1079)) (-5 *1 (-699 *3 *4 *5)) (-14 *5 (-1 (-111) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-169)) (-5 *1 (-701 *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 (-630 (-2 (|:| -4157 *3) (|:| -1728 *4)))) + (-12 (-5 *2 (-630 (-2 (|:| -4120 *3) (|:| -1718 *4)))) (-4 *3 (-1031)) (-4 *4 (-712)) (-5 *1 (-721 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-553)) (-4 *1 (-749)))) ((*1 *1 *2) @@ -6722,28 +7151,27 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1155)) (|:| |fn| (-310 (-220))) - (|:| -2515 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) + (|:| -1457 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) (|:| |relerr| (-220)))) (|:| |mdnia| (-2 (|:| |fn| (-310 (-220))) - (|:| -2515 (-630 (-1073 (-826 (-220))))) + (|:| -1457 (-630 (-1073 (-826 (-220))))) (|:| |abserr| (-220)) (|:| |relerr| (-220)))))) (-5 *1 (-755)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-310 (-220))) - (|:| -2515 (-630 (-1073 (-826 (-220))))) (|:| |abserr| (-220)) + (|:| -1457 (-630 (-1073 (-826 (-220))))) (|:| |abserr| (-220)) (|:| |relerr| (-220)))) (-5 *1 (-755)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1155)) (|:| |fn| (-310 (-220))) - (|:| -2515 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) + (|:| -1457 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) (|:| |relerr| (-220)))) (-5 *1 (-755)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-755)))) ((*1 *2 *3) (-12 (-5 *2 (-760)) (-5 *1 (-759 *3)) (-4 *3 (-1192)))) ((*1 *1 *2) (-12 @@ -6753,50 +7181,33 @@ (|:| |intvals| (-630 (-220))) (|:| |g| (-310 (-220))) (|:| |abserr| (-220)) (|:| |relerr| (-220)))) (-5 *1 (-794)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-794)))) - ((*1 *2 *1) - (-12 (-4 *2 (-882 *3)) (-5 *1 (-803 *3 *2 *4)) (-4 *3 (-1079)) - (-14 *4 *3))) - ((*1 *1 *2) - (-12 (-4 *3 (-1079)) (-14 *4 *3) (-5 *1 (-803 *3 *2 *4)) - (-4 *2 (-882 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1155)) (-5 *1 (-810)))) ((*1 *1 *2) (-12 (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-310 (-220))) (|:| -1979 (-630 (-220))) + (-2 (|:| |fn| (-310 (-220))) (|:| -1945 (-630 (-220))) (|:| |lb| (-630 (-826 (-220)))) (|:| |cf| (-630 (-310 (-220)))) (|:| |ub| (-630 (-826 (-220)))))) (|:| |lsa| (-2 (|:| |lfn| (-630 (-310 (-220)))) - (|:| -1979 (-630 (-220))))))) + (|:| -1945 (-630 (-220))))))) (-5 *1 (-824)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-630 (-310 (-220)))) (|:| -1979 (-630 (-220))))) + (-2 (|:| |lfn| (-630 (-310 (-220)))) (|:| -1945 (-630 (-220))))) (-5 *1 (-824)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-310 (-220))) (|:| -1979 (-630 (-220))) + (-2 (|:| |fn| (-310 (-220))) (|:| -1945 (-630 (-220))) (|:| |lb| (-630 (-826 (-220)))) (|:| |cf| (-630 (-310 (-220)))) (|:| |ub| (-630 (-826 (-220)))))) (-5 *1 (-824)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-824)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1234 *3)) (-14 *3 (-1155)) (-5 *1 (-838 *3 *4 *5 *6)) - (-4 *4 (-1031)) (-14 *5 (-98 *4)) (-14 *6 (-1 *4 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-553)) (-5 *1 (-841)))) - ((*1 *1 *2) - (-12 (-5 *2 (-934 *3)) (-4 *3 (-1031)) (-5 *1 (-848 *3 *4 *5 *6)) - (-14 *4 (-630 (-1155))) (-14 *5 (-630 (-757))) (-14 *6 (-757)))) - ((*1 *2 *1) - (-12 (-5 *2 (-934 *3)) (-5 *1 (-848 *3 *4 *5 *6)) (-4 *3 (-1031)) - (-14 *4 (-630 (-1155))) (-14 *5 (-630 (-757))) (-14 *6 (-757)))) ((*1 *1 *2) (-12 (-5 *2 (-154)) (-5 *1 (-856)))) ((*1 *2 *3) (-12 (-5 *3 (-934 (-48))) (-5 *2 (-310 (-553))) (-5 *1 (-857)))) @@ -6817,9 +7228,6 @@ (|:| |f| (-630 (-630 (-310 (-220))))) (|:| |st| (-1137)) (|:| |tol| (-220)))) (-5 *1 (-880)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-880)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1178 *3)) (-5 *1 (-883 *3)) (-4 *3 (-1079)))) ((*1 *1 *2) (-12 (-5 *2 (-630 (-887 *3))) (-4 *3 (-1079)) (-5 *1 (-886 *3)))) ((*1 *2 *1) @@ -6835,9 +7243,6 @@ (-4 *4 (-13 (-833) (-545))))) ((*1 *1 *2) (-12 (-5 *2 (-1155)) (-5 *1 (-948 *3)) (-4 *3 (-949)))) ((*1 *1 *2) (-12 (-5 *1 (-948 *2)) (-4 *2 (-949)))) - ((*1 *2 *1) (-12 (-5 *2 (-630 (-553))) (-5 *1 (-953)))) - ((*1 *2 *1) - (-12 (-5 *2 (-401 (-553))) (-5 *1 (-986 *3)) (-14 *3 (-553)))) ((*1 *2 *3) (-12 (-5 *2 (-1243)) (-5 *1 (-1015 *3)) (-4 *3 (-1192)))) ((*1 *2 *3) (-12 (-5 *3 (-306)) (-5 *1 (-1015 *2)) (-4 *2 (-1192)))) ((*1 *1 *2) @@ -6846,10 +7251,6 @@ (-14 *6 (-630 *2)))) ((*1 *2 *3) (-12 (-5 *2 (-401 (-934 *3))) (-5 *1 (-1025 *3)) (-4 *3 (-545)))) - ((*1 *1 *2) (-12 (-5 *2 (-553)) (-4 *1 (-1031)))) - ((*1 *2 *1) - (-12 (-5 *2 (-674 *5)) (-5 *1 (-1035 *3 *4 *5)) (-14 *3 (-757)) - (-14 *4 (-757)) (-4 *5 (-1031)))) ((*1 *1 *2) (-12 (-4 *3 (-1031)) (-4 *4 (-833)) (-5 *1 (-1105 *3 *4 *2)) (-4 *2 (-931 *3 (-524 *4) *4)))) @@ -6858,24 +7259,18 @@ (-4 *4 (-931 *3 (-524 *2) *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1113 *3)) (-4 *3 (-1031)) (-5 *2 (-845)))) ((*1 *1 *2) (-12 (-5 *2 (-141)) (-4 *1 (-1123)))) - ((*1 *1 *2) - (-12 (-5 *2 (-630 *3)) (-4 *3 (-1192)) (-5 *1 (-1135 *3)))) ((*1 *2 *3) (-12 (-5 *2 (-1135 *3)) (-5 *1 (-1139 *3)) (-4 *3 (-1031)))) ((*1 *1 *2) (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1146 *3 *4 *5)) (-4 *3 (-1031)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1152 *3 *4 *5)) - (-4 *3 (-1031)) (-14 *5 *3))) - ((*1 *1 *2) (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1153 *3 *4 *5)) (-4 *3 (-1031)) (-14 *5 *3))) ((*1 *1 *2) (-12 (-5 *2 (-1211 *4 *3)) (-4 *3 (-1031)) (-14 *4 (-1155)) (-14 *5 *3) (-5 *1 (-1153 *3 *4 *5)))) ((*1 *1 *2) (-12 (-5 *2 (-1155)) (-5 *1 (-1154)))) - ((*1 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-1155)))) ((*1 *2 *1) (-12 (-5 *2 (-1165 (-1155) (-431))) (-5 *1 (-1159)))) ((*1 *2 *1) (-12 (-5 *2 (-1137)) (-5 *1 (-1160)))) ((*1 *2 *1) (-12 (-5 *2 (-1155)) (-5 *1 (-1160)))) @@ -6883,28 +7278,15 @@ ((*1 *2 *1) (-12 (-5 *2 (-553)) (-5 *1 (-1160)))) ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-1164 *3)) (-4 *3 (-1079)))) ((*1 *2 *3) (-12 (-5 *2 (-1172)) (-5 *1 (-1171 *3)) (-4 *3 (-1079)))) - ((*1 *1 *2) (-12 (-5 *2 (-845)) (-5 *1 (-1172)))) ((*1 *1 *2) (-12 (-5 *2 (-934 *3)) (-4 *3 (-1031)) (-5 *1 (-1186 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1155)) (-5 *1 (-1186 *3)) (-4 *3 (-1031)))) ((*1 *1 *2) - (-12 (-5 *2 (-940 *3)) (-4 *3 (-1192)) (-5 *1 (-1189 *3)))) - ((*1 *1 *2) - (-12 (-4 *3 (-1031)) (-4 *1 (-1200 *3 *2)) (-4 *2 (-1229 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1202 *3 *4 *5)) (-4 *3 (-1031)) (-14 *5 *3))) ((*1 *1 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-1192)) (-5 *1 (-1205 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-1234 *3)) (-14 *3 (-1155)) (-5 *1 (-1211 *3 *4)) - (-4 *4 (-1031)))) - ((*1 *1 *2) - (-12 (-4 *3 (-1031)) (-4 *1 (-1221 *3 *2)) (-4 *2 (-1198 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1223 *3 *4 *5)) - (-4 *3 (-1031)) (-14 *5 *3))) - ((*1 *1 *2) (-12 (-5 *2 (-1234 *4)) (-14 *4 (-1155)) (-5 *1 (-1230 *3 *4 *5)) (-4 *3 (-1031)) (-14 *5 *3))) ((*1 *1 *2) @@ -6913,16 +7295,6 @@ ((*1 *2 *1) (-12 (-5 *2 (-1155)) (-5 *1 (-1234 *3)) (-14 *3 *2))) ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-1239)))) ((*1 *2 *3) (-12 (-5 *3 (-461)) (-5 *2 (-1239)) (-5 *1 (-1242)))) - ((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-1243)))) - ((*1 *1 *2) - (-12 (-4 *3 (-1031)) (-4 *4 (-833)) (-4 *5 (-779)) (-14 *6 (-630 *4)) - (-5 *1 (-1250 *3 *4 *5 *2 *6 *7 *8)) (-4 *2 (-931 *3 *5 *4)) - (-14 *7 (-630 (-757))) (-14 *8 (-757)))) - ((*1 *2 *1) - (-12 (-4 *2 (-931 *3 *5 *4)) (-5 *1 (-1250 *3 *4 *5 *2 *6 *7 *8)) - (-4 *3 (-1031)) (-4 *4 (-833)) (-4 *5 (-779)) (-14 *6 (-630 *4)) - (-14 *7 (-630 (-757))) (-14 *8 (-757)))) - ((*1 *1 *2) (-12 (-4 *1 (-1252 *2)) (-4 *2 (-1031)))) ((*1 *1 *2) (-12 (-4 *1 (-1255 *2 *3)) (-4 *2 (-833)) (-4 *3 (-1031)))) ((*1 *2 *1) @@ -6933,247 +7305,185 @@ (-4 *4 (-169)))) ((*1 *1 *2) (-12 (-5 *2 (-649 *3 *4)) (-4 *3 (-833)) (-4 *4 (-169)) - (-5 *1 (-1258 *3 *4)))) - ((*1 *1 *2) - (-12 (-5 *1 (-1261 *3 *2)) (-4 *3 (-1031)) (-4 *2 (-829))))) -(((*1 *2 *3) - (-12 (-5 *3 (-903)) - (-5 *2 - (-3 (-1151 *4) - (-1238 (-630 (-2 (|:| -2924 *4) (|:| -2839 (-1099))))))) - (-5 *1 (-340 *4)) (-4 *4 (-343))))) -(((*1 *2 *3 *4 *5 *6) - (-12 (-5 *5 (-757)) (-5 *6 (-111)) (-4 *7 (-445)) (-4 *8 (-779)) - (-4 *9 (-833)) (-4 *3 (-1045 *7 *8 *9)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1049 *7 *8 *9 *3 *4)) (-4 *4 (-1051 *7 *8 *9 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-757)) (-4 *6 (-445)) (-4 *7 (-779)) (-4 *8 (-833)) - (-4 *3 (-1045 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1049 *6 *7 *8 *3 *4)) (-4 *4 (-1051 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) - (-4 *3 (-1045 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1049 *5 *6 *7 *3 *4)) (-4 *4 (-1051 *5 *6 *7 *3)))) - ((*1 *2 *3 *4 *5 *6) - (-12 (-5 *5 (-757)) (-5 *6 (-111)) (-4 *7 (-445)) (-4 *8 (-779)) - (-4 *9 (-833)) (-4 *3 (-1045 *7 *8 *9)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1124 *7 *8 *9 *3 *4)) (-4 *4 (-1088 *7 *8 *9 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *5 (-757)) (-4 *6 (-445)) (-4 *7 (-779)) (-4 *8 (-833)) - (-4 *3 (-1045 *6 *7 *8)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1124 *6 *7 *8 *3 *4)) (-4 *4 (-1088 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) - (-4 *3 (-1045 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-630 *4)) - (|:| |todo| (-630 (-2 (|:| |val| (-630 *3)) (|:| -3361 *4)))))) - (-5 *1 (-1124 *5 *6 *7 *3 *4)) (-4 *4 (-1088 *5 *6 *7 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-630 *2)) (-4 *2 (-1214 *4)) (-5 *1 (-532 *4 *2 *5 *6)) - (-4 *4 (-301)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-757)))))) + (-5 *1 (-1258 *3 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1155)) - (-4 *5 (-13 (-545) (-833) (-1020 (-553)) (-626 (-553)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-630 (-599 *3))) - (|:| |vals| (-630 *3)))) - (-5 *1 (-271 *5 *3)) (-4 *3 (-13 (-27) (-1177) (-424 *5)))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4370)) (-4 *1 (-239 *2)) (-4 *2 (-1192))))) -(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-428))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *4 *4)) (-4 *4 (-1079)) (-4 *5 (-1079)) - (-5 *2 (-1 *5 *4)) (-5 *1 (-668 *4 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1155)) (-5 *2 (-529)) (-5 *1 (-528 *4)) - (-4 *4 (-1192))))) -(((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) - ((*1 *1) (-5 *1 (-128))) - ((*1 *1) - (-12 (-5 *1 (-134 *2 *3 *4)) (-14 *2 (-553)) (-14 *3 (-757)) - (-4 *4 (-169)))) - ((*1 *1) (-4 *1 (-712))) ((*1 *1) (-5 *1 (-1155)))) + (-12 (-5 *4 (-1 (-1135 *3))) (-5 *2 (-1135 *3)) (-5 *1 (-1139 *3)) + (-4 *3 (-38 (-401 (-553)))) (-4 *3 (-1031))))) +(((*1 *2 *1) (-12 (-5 *2 (-1135 *3)) (-5 *1 (-171 *3)) (-4 *3 (-301))))) +(((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-1155)) (-4 *4 (-1031)) (-4 *4 (-833)) + (-5 *2 (-2 (|:| |var| (-599 *1)) (|:| -2692 (-553)))) + (-4 *1 (-424 *4)))) + ((*1 *2 *1 *3) + (|partial| -12 (-5 *3 (-113)) (-4 *4 (-1031)) (-4 *4 (-833)) + (-5 *2 (-2 (|:| |var| (-599 *1)) (|:| -2692 (-553)))) + (-4 *1 (-424 *4)))) + ((*1 *2 *1) + 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continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1135 (-220))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1457 + (-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 *2 (-1017)) (-5 *1 (-299))))) +(((*1 *2 *3) (-12 (-5 *3 (-903)) (-5 *2 (-886 (-553))) (-5 *1 (-899)))) + ((*1 *2 *3) + (-12 (-5 *3 (-630 (-553))) (-5 *2 (-886 (-553))) (-5 *1 (-899))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-220)) (-5 *4 (-553)) (-5 *2 (-1017)) (-5 *1 (-744))))) (((*1 *2 *1) - (-12 (-4 *1 (-1020 (-553))) (-4 *1 (-296)) (-5 *2 (-111)))) - ((*1 *2 *1) (-12 (-4 *1 (-538)) (-5 *2 (-111)))) - ((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-887 *3)) (-4 *3 (-1079))))) + (-12 (-4 *3 (-1031)) (-4 *4 (-779)) (-4 *5 (-833)) (-5 *2 (-630 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(-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -10887,9 +10942,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 *3)) (-5 *1 (-273 *3 *4 *2 *5)) (-4 *2 (-1221 *3 *4)) (-4 *5 (-965 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-333 *2 *3 *4)) (-14 *2 (-630 (-1155))) - (-14 *3 (-630 (-1155))) (-4 *4 (-381)))) ((*1 *1 *1) (-4 *1 (-486))) ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) @@ -10897,46 +10949,72 @@ ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3))))) +(((*1 *2 *3 *2) (-12 (-5 *2 (-220)) (-5 *3 (-757)) (-5 *1 (-221)))) + ((*1 *2 *3 *2) + (-12 (-5 *2 (-166 (-220))) (-5 *3 (-757)) (-5 *1 (-221)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-425 *3 *2)) + (-4 *2 (-424 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1118)))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-274))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1151 *5)) (-4 *5 (-445)) (-5 *2 (-630 *6)) - (-5 *1 (-531 *5 *6 *4)) (-4 *6 (-357)) (-4 *4 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(-220)) (|:| |deltaY| (-220)))) + (-5 *3 (-630 (-257))) (-5 *1 (-255)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 (|:| |theta| (-220)) (|:| |phi| (-220)) (|:| -1731 (-220)) + (|:| |scaleX| (-220)) (|:| |scaleY| (-220)) (|:| |scaleZ| (-220)) + (|:| |deltaX| (-220)) (|:| |deltaY| (-220)))) + (-5 *1 (-257)))) + ((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240)))) ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-757)) (-5 *2 (-401 (-553))) (-5 *1 (-373)))) + (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240)))) + ((*1 *2 *1 *3 *3 *4 *4 *4) + (-12 (-5 *3 (-553)) (-5 *4 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240)))) ((*1 *2 *1 *3) - (-12 (-5 *3 (-757)) (-5 *2 (-401 (-553))) (-5 *1 (-373))))) -(((*1 *2 *3 *3 *4 *4 *3 *3 *5 *3) - (-12 (-5 *3 (-553)) (-5 *5 (-674 (-220))) (-5 *4 (-220)) - (-5 *2 (-1017)) (-5 *1 (-741))))) -(((*1 *1 *2 *3 *4) - (-12 (-5 *3 (-553)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) - (-5 *1 (-412 *2)) (-4 *2 (-545))))) + (-12 + (-5 *3 + (-2 (|:| |theta| (-220)) (|:| |phi| (-220)) (|:| -1731 (-220)) + (|:| |scaleX| (-220)) (|:| |scaleY| (-220)) (|:| |scaleZ| (-220)) + (|:| |deltaX| (-220)) (|:| |deltaY| (-220)))) + (-5 *2 (-1243)) (-5 *1 (-1240)))) + ((*1 *2 *1) + (-12 + (-5 *2 + (-2 (|:| |theta| (-220)) (|:| |phi| (-220)) (|:| -1731 (-220)) + (|:| |scaleX| (-220)) (|:| |scaleY| (-220)) (|:| |scaleZ| (-220)) + (|:| |deltaX| (-220)) (|:| |deltaY| (-220)))) + (-5 *1 (-1240)))) + ((*1 *2 *1 *3 *3 *3 *3 *3) + (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240))))) (((*1 *2 *1) - (-12 (-4 *1 (-323 *3)) (-4 *3 (-357)) (-4 *3 (-362)) - (-5 *2 (-1151 *3))))) -(((*1 *2) - (-12 (-4 *4 (-1196)) (-4 *5 (-1214 *4)) (-4 *6 (-1214 (-401 *5))) - (-5 *2 (-630 (-630 *4))) (-5 *1 (-335 *3 *4 *5 *6)) - (-4 *3 (-336 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *1 (-336 *3 *4 *5)) (-4 *3 (-1196)) (-4 *4 (-1214 *3)) - (-4 *5 (-1214 (-401 *4))) (-4 *3 (-362)) (-5 *2 (-630 (-630 *3)))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1137)) (-5 *2 (-373)) (-5 *1 (-96))))) -(((*1 *2 *2 *1) (-12 (-4 *1 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(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 (-630 *2))) (-5 *4 (-630 *5)) - (-4 *5 (-38 (-401 (-553)))) (-4 *2 (-1229 *5)) - (-5 *1 (-1231 *5 *2))))) + (-12 (-5 *3 (-401 (-934 *5))) (-5 *4 (-1155)) + (-4 *5 (-13 (-301) (-833) (-144))) (-5 *2 (-630 (-310 *5))) + (-5 *1 (-1108 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-630 (-401 (-934 *5)))) (-5 *4 (-630 (-1155))) + (-4 *5 (-13 (-301) (-833) (-144))) (-5 *2 (-630 (-630 (-310 *5)))) + (-5 *1 (-1108 *5))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-553)) (-5 *4 (-412 *2)) (-4 *2 (-931 *7 *5 *6)) - (-5 *1 (-728 *5 *6 *7 *2)) (-4 *5 (-779)) (-4 *6 (-833)) - (-4 *7 (-301))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-220)) (|:| |xend| (-220)) - (|:| |fn| (-1238 (-310 (-220)))) (|:| |yinit| (-630 (-220))) - (|:| |intvals| (-630 (-220))) (|:| |g| (-310 (-220))) - (|:| |abserr| (-220)) (|:| |relerr| (-220)))) - (-5 *2 - (-2 (|:| |stiffnessFactor| (-373)) (|:| |stabilityFactor| (-373)))) - (-5 *1 (-200))))) + (-12 (-5 *4 (-630 (-630 *8))) (-5 *3 (-630 *8)) + (-4 *8 (-931 *5 *7 *6)) (-4 *5 (-13 (-301) (-144))) + (-4 *6 (-13 (-833) (-601 (-1155)))) (-4 *7 (-779)) (-5 *2 (-111)) + (-5 *1 (-906 *5 *6 *7 *8))))) +(((*1 *1 *1 *1) (-5 *1 (-111))) ((*1 *1 *1 *1) (-4 *1 (-122))) + ((*1 *1 *1 *1) (-5 *1 (-1099)))) +(((*1 *1 *1) + (-12 (-4 *1 (-1045 *2 *3 *4)) (-4 *2 (-1031)) (-4 *3 (-779)) + (-4 *4 (-833))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -11050,50 +11092,9 @@ ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3))))) -(((*1 *2 *3) - (-12 (|has| *6 (-6 -4370)) (-4 *4 (-357)) (-4 *5 (-367 *4)) - (-4 *6 (-367 *4)) (-5 *2 (-630 *6)) (-5 *1 (-514 *4 *5 *6 *3)) - (-4 *3 (-672 *4 *5 *6)))) - ((*1 *2 *3) - (-12 (|has| *9 (-6 -4370)) (-4 *4 (-545)) (-4 *5 (-367 *4)) - (-4 *6 (-367 *4)) (-4 *7 (-974 *4)) (-4 *8 (-367 *7)) - (-4 *9 (-367 *7)) (-5 *2 (-630 *6)) - (-5 *1 (-515 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-672 *4 *5 *6)) - (-4 *10 (-672 *7 *8 *9)))) - ((*1 *2 *1) - (-12 (-4 *1 (-672 *3 *4 *5)) (-4 *3 (-1031)) (-4 *4 (-367 *3)) - (-4 *5 (-367 *3)) (-4 *3 (-545)) (-5 *2 (-630 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-545)) (-4 *4 (-169)) (-4 *5 (-367 *4)) - (-4 *6 (-367 *4)) (-5 *2 (-630 *6)) (-5 *1 (-673 *4 *5 *6 *3)) - (-4 *3 (-672 *4 *5 *6)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1034 *3 *4 *5 *6 *7)) (-4 *5 (-1031)) - (-4 *6 (-233 *4 *5)) (-4 *7 (-233 *3 *5)) (-4 *5 (-545)) - (-5 *2 (-630 *7))))) -(((*1 *2 *3 *4 *4 *4 *3 *3 *5 *5 *3) - (-12 (-5 *3 (-553)) (-5 *4 (-674 (-220))) (-5 *5 (-220)) - (-5 *2 (-1017)) (-5 *1 (-737))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-545)) (-5 *2 (-111))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-903)) (-5 *3 (-630 (-257))) (-5 *1 (-255)))) - ((*1 *1 *2) (-12 (-5 *2 (-903)) (-5 *1 (-257))))) -(((*1 *1 *1 *1) (-4 *1 (-296))) ((*1 *1 *1) (-4 *1 (-296)))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-553)) (-5 *1 (-412 *2)) (-4 *2 (-545))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-373)) (-5 *1 (-200)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-630 (-373))) (-5 *2 (-373)) (-5 *1 (-200))))) +(((*1 *1 *1) + (-12 (-5 *1 (-583 *2)) (-4 *2 (-38 (-401 (-553)))) (-4 *2 (-1031))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-833) (-445))) (-5 *1 (-1183 *3 *2)) - (-4 *2 (-13 (-424 *3) (-1177)))))) -(((*1 *2 *1) - (-12 (|has| *1 (-6 -4369)) (-4 *1 (-482 *3)) (-4 *3 (-1192)) - (-5 *2 (-630 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-630 *3)) (-5 *1 (-723 *3)) (-4 *3 (-1079))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-630 *3)) (-4 *3 (-301)) (-5 *1 (-176 *3))))) -(((*1 *1 *1) (-4 *1 (-94))) - ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) ((*1 *2 *2) @@ -11102,43 +11103,54 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 *3)) (-5 *1 (-273 *3 *4 *2 *5)) (-4 *2 (-1221 *3 *4)) (-4 *5 (-965 *4)))) + ((*1 *1 *1) (-4 *1 (-278))) + ((*1 *2 *3) + (-12 (-5 *3 (-412 *4)) (-4 *4 (-545)) + (-5 *2 (-630 (-2 (|:| -4120 (-757)) (|:| |logand| *4)))) + (-5 *1 (-314 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-333 *2 *3 *4)) (-14 *2 (-630 (-1155))) + (-14 *3 (-630 (-1155))) (-4 *4 (-381)))) + ((*1 *2 *1) + (-12 (-5 *2 (-649 *3 *4)) (-5 *1 (-614 *3 *4 *5)) (-4 *3 (-833)) + (-4 *4 (-13 (-169) (-703 (-401 (-553))))) (-14 *5 (-903)))) ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1140 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) - (-5 *1 (-1141 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-545) (-833))) - (-4 *2 (-13 (-424 *4) (-984) (-1177))) (-5 *1 (-587 *4 *2 *3)) - (-4 *3 (-13 (-424 (-166 *4)) (-984) (-1177)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1135 *3)) (-5 *1 (-171 *3)) (-4 *3 (-301))))) -(((*1 *1 *1) - (-12 (-5 *1 (-583 *2)) (-4 *2 (-38 (-401 (-553)))) (-4 *2 (-1031))))) -(((*1 *1) (-5 *1 (-138)))) -(((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-925 (-220))) (-5 *4 (-856)) (-5 *5 (-903)) - (-5 *2 (-1243)) (-5 *1 (-461)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-925 (-220))) (-5 *2 (-1243)) (-5 *1 (-461)))) - ((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-630 (-925 (-220)))) (-5 *4 (-856)) 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*6 (-672 *3 *4 *5)))) + ((*1 *2 *3 *3) + (-12 (-5 *2 (-2 (|:| -2666 *3) (|:| -1571 *3))) (-5 *1 (-685 *3)) + (-4 *3 (-301))))) +(((*1 *1) (-5 *1 (-154)))) +(((*1 *1 *1 *1 *2 *3) + (-12 (-5 *2 (-925 *5)) (-5 *3 (-757)) (-4 *5 (-1031)) + (-5 *1 (-1143 *4 *5)) (-14 *4 (-903))))) +(((*1 *2 *1) (-12 (-4 *1 (-659 *2)) (-4 *2 (-1192))))) +(((*1 *2 *2 *3) (-12 (-5 *3 (-553)) (-5 *1 (-1166 *2)) (-4 *2 (-357))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-553)) (-4 *1 (-56 *4 *5 *3)) (-4 *4 (-1192)) + (-4 *5 (-367 *4)) (-4 *3 (-367 *4))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *5 (-553)) (-4 *6 (-779)) (-4 *7 (-833)) (-4 *8 (-301)) + (-4 *9 (-931 *8 *6 *7)) + (-5 *2 (-2 (|:| -4252 (-1151 *9)) (|:| |polval| (-1151 *8)))) + (-5 *1 (-728 *6 *7 *8 *9)) (-5 *3 (-1151 *9)) (-5 *4 (-1151 *8))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-833) (-445))) (-5 *1 (-1183 *3 *2)) - (-4 *2 (-13 (-424 *3) (-1177)))))) -(((*1 *1 *1) (-4 *1 (-94))) - ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) ((*1 *2 *2) @@ -11147,6 +11159,10 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 *3)) (-5 *1 (-273 *3 *4 *2 *5)) (-4 *2 (-1221 *3 *4)) (-4 *5 (-965 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-333 *2 *3 *4)) (-14 *2 (-630 (-1155))) + (-14 *3 (-630 (-1155))) (-4 *4 (-381)))) + ((*1 *1 *1) (-4 *1 (-486))) ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1140 *3)))) @@ -11252,69 +11268,42 @@ ((*1 *2 *1 *3) (-12 (-4 *1 (-1216 *3 *4)) (-4 *3 (-1031)) (-4 *4 (-778)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1135 *3))))) -(((*1 *2 *1 *1 *3) - (-12 (-5 *3 (-1 (-111) *5 *5)) (-4 *5 (-13 (-1079) (-34))) - (-5 *2 (-111)) (-5 *1 (-1119 *4 *5)) (-4 *4 (-13 (-1079) (-34)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) - (-4 *2 (-13 (-424 *3) (-984))))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1229 *3)) - (-5 *1 (-272 *3 *4 *2)) (-4 *2 (-1200 *3 *4)))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 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(|partial| -12 (-4 *3 (-545)) (-4 *3 (-169)) (-4 *4 (-367 *3)) - (-4 *5 (-367 *3)) (-5 *1 (-673 *3 *4 *5 *2)) - (-4 *2 (-672 *3 *4 *5))))) -(((*1 *1 *2) (-12 (-5 *2 (-630 (-324))) (-5 *1 (-324))))) + (-12 (-4 *2 (-545)) (-5 *1 (-610 *2 *3)) (-4 *3 (-1214 *2))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) + (-4 *3 (-1045 *5 *6 *7)) + (-5 *2 (-630 (-2 (|:| |val| (-630 *3)) (|:| -3233 *4)))) + (-5 *1 (-1052 *5 *6 *7 *3 *4)) (-4 *4 (-1051 *5 *6 *7 *3))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-357) (-1020 (-401 *2)))) (-5 *2 (-553)) + (-5 *1 (-114 *4 *3)) (-4 *3 (-1214 *4))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-428)) + (-5 *2 + (-630 + (-3 (|:| -4298 (-1155)) + (|:| -1893 (-630 (-3 (|:| S (-1155)) (|:| P (-934 (-553))))))))) + (-5 *1 (-1159))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-958 *4 *5 *3 *6)) (-4 *4 (-1031)) (-4 *5 (-779)) + (-4 *3 (-833)) (-4 *6 (-1045 *4 *5 *3)) (-5 *2 (-111))))) +(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *5 *5 *5 *5 *4 *4 *6 *7) + (-12 (-5 *4 (-553)) (-5 *5 (-674 (-220))) + (-5 *6 (-3 (|:| |fn| (-382)) (|:| |fp| (-83 FCNF)))) + (-5 *7 (-3 (|:| |fn| (-382)) (|:| |fp| (-84 FCNG)))) (-5 *3 (-220)) + (-5 *2 (-1017)) (-5 *1 (-735))))) +(((*1 *2 *2 *3) + (|partial| -12 (-5 *3 (-757)) (-4 *4 (-13 (-545) (-144))) + (-5 *1 (-1208 *4 *2)) (-4 *2 (-1214 *4))))) +(((*1 *2 *1) + (-12 (-5 *2 (-1135 (-553))) (-5 *1 (-986 *3)) (-14 *3 (-553))))) +(((*1 *2 *3 *2) + (-12 (-4 *2 (-13 (-357) (-831))) (-5 *1 (-178 *2 *3)) + (-4 *3 (-1214 (-166 *2))))) + ((*1 *2 *3) + (-12 (-4 *2 (-13 (-357) (-831))) (-5 *1 (-178 *2 *3)) + (-4 *3 (-1214 (-166 *2)))))) (((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) @@ -11331,38 +11320,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-630 *6)) (-4 *6 (-1045 *3 *4 *5)) (-4 *3 (-445)) - (-4 *3 (-545)) (-4 *4 (-779)) (-4 *5 (-833)) - (-5 *1 (-959 *3 *4 *5 *6))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-553)) (-4 *2 (-424 *3)) (-5 *1 (-32 *3 *2)) - (-4 *3 (-1020 *4)) (-4 *3 (-13 (-833) (-545)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-757)) (-5 *2 (-1151 *4)) (-5 *1 (-521 *4)) - (-4 *4 (-343))))) -(((*1 *2 *3) - (-12 (-5 *3 (-674 (-310 (-220)))) - (-5 *2 - (-2 (|:| |stiffnessFactor| (-373)) (|:| |stabilityFactor| (-373)))) - (-5 *1 (-200))))) -(((*1 *2 *1) (-12 (-4 *1 (-783 *2)) (-4 *2 (-169))))) -(((*1 *2 *3) (-12 (-5 *3 (-1155)) (-5 *2 (-1243)) (-5 *1 (-1158)))) - ((*1 *2 *1) (-12 (-5 *2 (-1243)) (-5 *1 (-1159))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1155)) (-5 *4 (-934 (-553))) (-5 *2 (-324)) - (-5 *1 (-326))))) -(((*1 *2 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-745))))) +(((*1 *2 *1) (-12 (-4 *1 (-543 *2)) (-4 *2 (-13 (-398) (-1177))))) + ((*1 *1 *1 *1) (-4 *1 (-779)))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-674 *3)) (-4 *3 (-301)) (-5 *1 (-685 *3))))) (((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-545) (-833) (-1020 (-553)))) - (-4 *5 (-424 *4)) (-5 *2 (-412 (-1151 (-401 (-553))))) - (-5 *1 (-429 *4 *5 *3)) (-4 *3 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(-1031))))) +(((*1 *1 *1 *1) (-4 *1 (-140))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-155 *3 *2)) + (-4 *2 (-424 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-156 *2)) (-4 *2 (-538))))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-428)))) + ((*1 *2 *3) + (-12 (-5 *2 (-111)) (-5 *1 (-558 *3)) (-4 *3 (-1020 (-553))))) + ((*1 *2 *1) + (-12 (-4 *1 (-1082 *3 *4 *5 *6 *7)) (-4 *3 (-1079)) (-4 *4 (-1079)) + (-4 *5 (-1079)) (-4 *6 (-1079)) (-4 *7 (-1079)) (-5 *2 (-111))))) +(((*1 *2) + (-12 (-4 *3 (-1196)) (-4 *4 (-1214 *3)) (-4 *5 (-1214 (-401 *4))) + (-5 *2 (-1238 *1)) (-4 *1 (-336 *3 *4 *5))))) +(((*1 *1 *2) + (-12 (-5 *2 (-630 (-553))) (-5 *1 (-986 *3)) (-14 *3 (-553))))) +(((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -11372,10 +11368,6 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 *3)) (-5 *1 (-273 *3 *4 *2 *5)) (-4 *2 (-1221 *3 *4)) (-4 *5 (-965 *4)))) - ((*1 *1 *1) - (-12 (-5 *1 (-333 *2 *3 *4)) (-14 *2 (-630 (-1155))) - (-14 *3 (-630 (-1155))) (-4 *4 (-381)))) - ((*1 *1 *1 *1) (-5 *1 (-373))) ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1140 *3)))) @@ -11383,6 +11375,8 @@ (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3))))) (((*1 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-845))))) +(((*1 *2 *1) (-12 (-4 *1 (-974 *2)) (-4 *2 (-545)) (-4 *2 (-538)))) + ((*1 *1 *1) (-4 *1 (-1040)))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-630 (-1155))) (-5 *3 (-1155)) (-5 *1 (-529)))) ((*1 *2 *3 *2) @@ -11394,65 +11388,53 @@ ((*1 *2 *3 *2 *4) (-12 (-5 *4 (-630 (-1155))) (-5 *2 (-1155)) (-5 *1 (-690 *3)) (-4 *3 (-601 (-529)))))) -(((*1 *2) - (-12 (-4 *4 (-1196)) (-4 *5 (-1214 *4)) (-4 *6 (-1214 (-401 *5))) - (-5 *2 (-757)) (-5 *1 (-335 *3 *4 *5 *6)) (-4 *3 (-336 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *1 (-336 *3 *4 *5)) (-4 *3 (-1196)) (-4 *4 (-1214 *3)) - (-4 *5 (-1214 (-401 *4))) (-5 *2 (-757))))) -(((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 *3 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(-5 *1 (-119 *3)) (-4 *3 (-1214 (-553)))))) + (-12 (-4 *1 (-1113 *3)) (-4 *3 (-1031)) (-5 *2 (-630 (-925 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-630 (-925 *3))) (-4 *3 (-1031)) (-4 *1 (-1113 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-630 (-630 *3))) (-4 *1 (-1113 *3)) (-4 *3 (-1031)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-630 (-925 *3))) (-4 *1 (-1113 *3)) (-4 *3 (-1031))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-630 *3)) (-4 *3 (-833)) (-5 *1 (-725 *3))))) +(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) + (-12 (-5 *3 (-903)) (-5 *4 (-220)) (-5 *5 (-553)) (-5 *6 (-856)) + (-5 *2 (-1243)) (-5 *1 (-1239))))) (((*1 *2 *1) - (-12 (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1192)) (-4 *4 (-367 *3)) - (-4 *5 (-367 *3)) (-5 *2 (-757)))) + (-12 (-4 *3 (-169)) (-4 *2 (-23)) (-5 *1 (-283 *3 *4 *2 *5 *6 *7)) + (-4 *4 (-1214 *3)) (-14 *5 (-1 *4 *4 *2)) + (-14 *6 (-1 (-3 *2 "failed") *2 *2)) + (-14 *7 (-1 (-3 *4 "failed") *4 *4 *2)))) ((*1 *2 *1) - (-12 (-4 *1 (-1034 *3 *4 *5 *6 *7)) (-4 *5 (-1031)) - (-4 *6 (-233 *4 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(-553))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| -3278 (-373)) (|:| -4292 (-1137)) - (|:| |explanations| (-630 (-1137))))) - (-5 *2 (-1017)) (-5 *1 (-299)))) - ((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -3278 (-373)) (|:| -4292 (-1137)) - (|:| |explanations| (-630 (-1137))) (|:| |extra| (-1017)))) - (-5 *2 (-1017)) (-5 *1 (-299))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-630 *2)) (-4 *2 (-931 *4 *5 *6)) (-4 *4 (-357)) - (-4 *4 (-445)) (-4 *5 (-779)) (-4 *6 (-833)) - (-5 *1 (-443 *4 *5 *6 *2)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-98 *6)) (-5 *5 (-1 *6 *6)) (-4 *6 (-357)) - (-5 *2 - (-2 (|:| R (-674 *6)) (|:| A (-674 *6)) (|:| |Ainv| (-674 *6)))) - (-5 *1 (-960 *6)) (-5 *3 (-674 *6))))) + (-2 (|:| |var| (-1155)) (|:| |fn| (-310 (-220))) + (|:| -1457 (-1073 (-826 (-220)))) (|:| |abserr| (-220)) + (|:| |relerr| (-220)))) + (-5 *2 (-373)) (-5 *1 (-187))))) (((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) @@ -11463,46 +11445,98 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1198 *3)) (-5 *1 (-273 *3 *4 *2 *5)) (-4 *2 (-1221 *3 *4)) (-4 *5 (-965 *4)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) + (-5 *1 (-1140 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) + (-5 *1 (-1141 *3))))) +(((*1 *1 *2) + (-12 (-5 *2 (-674 *4)) (-4 *4 (-1031)) (-5 *1 (-1121 *3 *4)) + (-14 *3 (-757))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-630 (-1155))) (-5 *1 (-529))))) +(((*1 *2 *3) + (-12 (-4 *2 (-357)) (-4 *2 (-831)) (-5 *1 (-927 *2 *3)) + (-4 *3 (-1214 *2))))) +(((*1 *2 *3) + (-12 (-4 *4 (-545)) (-5 *2 (-1151 *3)) (-5 *1 (-41 *4 *3)) + (-4 *3 + (-13 (-357) (-296) + (-10 -8 (-15 -3963 ((-1104 *4 (-599 $)) $)) + (-15 -3974 ((-1104 *4 (-599 $)) $)) + (-15 -3110 ($ (-1104 *4 (-599 $)))))))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-630 (-1073 (-373)))) (-5 *3 (-630 (-257))) + (-5 *1 (-255)))) + ((*1 *1 *2) (-12 (-5 *2 (-630 (-1073 (-373)))) (-5 *1 (-257)))) + ((*1 *2 *1 *2) (-12 (-5 *2 (-630 (-1073 (-373)))) (-5 *1 (-461)))) + ((*1 *2 *1) (-12 (-5 *2 (-630 (-1073 (-373)))) (-5 *1 (-461))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1045 *2 *3 *4)) (-4 *2 (-1031)) (-4 *3 (-779)) + (-4 *4 (-833)) (-4 *2 (-445))))) +(((*1 *2 *3 *3 *1) + (|partial| -12 (-5 *3 (-1155)) (-5 *2 (-1083)) (-5 *1 (-285))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1185 *2 *3 *4 *5)) (-4 *2 (-545)) (-4 *3 (-779)) + (-4 *4 (-833)) (-4 *5 (-1045 *2 *3 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1164 (-630 *4))) (-4 *4 (-833)) + (-5 *2 (-630 (-630 *4))) (-5 *1 (-1163 *4))))) +(((*1 *1 *1 *2 *1) + (-12 (-5 *2 (-553)) (-5 *1 (-1135 *3)) (-4 *3 (-1192)))) + ((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4370)) (-4 *1 (-1226 *2)) (-4 *2 (-1192))))) +(((*1 *1 *1) (-4 *1 (-94))) ((*1 *1 *1 *1) (-5 *1 (-220))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) + (-4 *2 (-13 (-424 *3) (-984))))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1229 *3)) + (-5 *1 (-272 *3 *4 *2)) (-4 *2 (-1200 *3 *4)))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-401 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+(((*1 *2 *1 *1) + (-12 (-4 *3 (-357)) (-4 *3 (-1031)) + (-5 *2 (-2 (|:| -2666 *1) (|:| -1571 *1))) (-4 *1 (-835 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-98 *5)) (-4 *5 (-357)) (-4 *5 (-1031)) + (-5 *2 (-2 (|:| -2666 *3) (|:| -1571 *3))) (-5 *1 (-836 *5 *3)) + (-4 *3 (-835 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-553)) (-5 *1 (-856)))) + ((*1 *2 *3) (-12 (-5 *3 (-925 *2)) (-5 *1 (-964 *2)) (-4 *2 (-1031))))) (((*1 *2 *1) - (-12 (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1192)) (-4 *4 (-367 *3)) - (-4 *5 (-367 *3)) (-5 *2 (-757)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1034 *3 *4 *5 *6 *7)) (-4 *5 (-1031)) - (-4 *6 (-233 *4 *5)) (-4 *7 (-233 *3 *5)) (-5 *2 (-757))))) + (-12 (-5 *2 (-845)) (-5 *1 (-384 *3 *4 *5)) (-14 *3 (-757)) + (-14 *4 (-757)) (-4 *5 (-169))))) +(((*1 *2 *2) + (-12 (-4 *2 (-169)) (-4 *2 (-1031)) (-5 *1 (-700 *2 *3)) + (-4 *3 (-633 *2)))) + ((*1 *2 *2) (-12 (-5 *1 (-820 *2)) (-4 *2 (-169)) (-4 *2 (-1031))))) (((*1 *2 *3) (-12 (-5 *3 (-1137)) (-5 *2 (-1243)) (-5 *1 (-1162))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-1151 *3)) (-4 *3 (-362)) (-4 *1 (-323 *3)) - (-4 *3 (-357))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-553)) (-5 *4 (-674 (-220))) (-5 *2 (-1017)) - (-5 *1 (-738))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-111)) (-5 *1 (-634 *3 *4 *5)) (-4 *3 (-1079)) - (-4 *4 (-23)) (-14 *5 *4)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-630 *7)) (-4 *7 (-833)) (-4 *5 (-891)) (-4 *6 (-779)) + (-4 *8 (-931 *5 *6 *7)) (-5 *2 (-412 (-1151 *8))) + (-5 *1 (-888 *5 *6 *7 *8)) (-5 *4 (-1151 *8)))) + ((*1 *2 *3) + (-12 (-4 *4 (-891)) (-4 *5 (-1214 *4)) (-5 *2 (-412 (-1151 *5))) + (-5 *1 (-889 *4 *5)) (-5 *3 (-1151 *5))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-833) (-445))) (-5 *1 (-1183 *3 *2)) + (-4 *2 (-13 (-424 *3) (-1177)))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-111) *2)) (-4 *2 (-130)) (-5 *1 (-1063 *2)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-553) *2 *2)) (-4 *2 (-130)) (-5 *1 (-1063 *2))))) (((*1 *2 *1) (-12 (-4 *1 (-248 *3)) (-4 *3 (-1192)) (-5 *2 (-757)))) ((*1 *2 *1) (-12 (-4 *1 (-296)) (-5 *2 (-757)))) ((*1 *2 *3) @@ -11512,9 +11546,7 @@ ((*1 *2 *1) (-12 (-5 *2 (-757)) (-5 *1 (-599 *3)) (-4 *3 (-833)))) ((*1 *2) (-12 (-5 *2 (-553)) (-5 *1 (-845)))) ((*1 *2 *1) (-12 (-5 *2 (-553)) (-5 *1 (-845))))) -(((*1 *2 *3) - (-12 (-5 *3 (-630 (-630 (-630 *4)))) (-5 *2 (-630 (-630 *4))) - (-5 *1 (-1163 *4)) (-4 *4 (-833))))) +(((*1 *2 *2) (-12 (-5 *2 (-553)) (-5 *1 (-908))))) (((*1 *1 *1) (-4 *1 (-94))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) @@ -11534,71 +11566,46 @@ ((*1 *2 *2) (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1073 (-826 (-220)))) (-5 *2 (-220)) (-5 *1 (-187)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1073 (-826 (-220)))) (-5 *2 (-220)) (-5 *1 (-294)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1073 (-826 (-220)))) (-5 *2 (-220)) (-5 *1 (-299))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-871 *4 *5)) (-5 *3 (-871 *4 *6)) (-4 *4 (-1079)) - (-4 *5 (-1079)) (-4 *6 (-651 *5)) (-5 *1 (-867 *4 *5 *6))))) -(((*1 *2 *2) - (-12 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(-1192)))) + ((*1 *1 *1 *2) + (-12 (|has| *1 (-6 -4370)) (-4 *1 (-1226 *2)) (-4 *2 (-1192)))) + ((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4370)) (-4 *1 (-1226 *2)) (-4 *2 (-1192))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -11749,48 +11768,110 @@ ((*1 *1 *1) (-4 *1 (-1180)))) (((*1 *1 *1 *1) (-12 (-5 *1 (-493 *2)) (-14 *2 (-553)))) ((*1 *1 *1 *1) (-5 *1 (-1099)))) -(((*1 *1 *2) - (-12 (-5 *2 (-1151 *3)) (-4 *3 (-1031)) (-4 *1 (-1214 *3))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-357)) - (-5 *2 (-630 (-2 (|:| C (-674 *5)) (|:| |g| (-1238 *5))))) - (-5 *1 (-960 *5)) (-5 *3 (-674 *5)) (-5 *4 (-1238 *5))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-111)) (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) - (-4 *8 (-1045 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-630 *8)) - (|:| |towers| (-630 (-1009 *5 *6 *7 *8))))) - (-5 *1 (-1009 *5 *6 *7 *8)) (-5 *3 (-630 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-111)) (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) - 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(-5 *2 (-401 (-553))) (-5 *1 (-373))))) +(((*1 *2 *3 *3 *3 *4) + (-12 (-5 *3 (-220)) (-5 *4 (-553)) (-5 *2 (-1017)) (-5 *1 (-744))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1211 *5 *4)) (-4 *4 (-445)) (-4 *4 (-806)) + (-14 *5 (-1155)) (-5 *2 (-553)) (-5 *1 (-1093 *4 *5))))) +(((*1 *2) (-12 (-5 *2 (-903)) (-5 *1 (-154))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-1100 *2)) (-4 *2 (-1192))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1008 (-826 (-553)))) + (-5 *3 (-1135 (-2 (|:| |k| (-553)) (|:| |c| *4)))) (-4 *4 (-1031)) + (-5 *1 (-583 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-1243)) (-5 *1 (-324))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) - (-4 *2 (-13 (-424 *3) (-984)))))) -(((*1 *2 *2 *3 *4) - (|partial| -12 (-5 *3 (-757)) (-4 *4 (-13 (-545) (-144))) - (-5 *1 (-1208 *4 *2)) (-4 *2 (-1214 *4))))) + (-4 *2 (-13 (-424 *3) (-984))))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-401 (-553)))) (-4 *4 (-1229 *3)) + (-5 *1 (-272 *3 *4 *2)) (-4 *2 (-1200 *3 *4)))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-401 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(-630 (-220))) (|:| |g| (-310 (-220))) - (|:| |abserr| (-220)) (|:| |relerr| (-220)))) - (-5 *2 (-373)) (-5 *1 (-200))))) -(((*1 *1 *2) (-12 (-5 *2 (-630 (-845))) (-5 *1 (-845)))) - ((*1 *1 *1 *1) (-5 *1 (-845)))) + (-12 (-5 *2 (-2 (|:| -3165 (-553)) (|:| -3713 (-630 *3)))) + (-5 *1 (-435 *3)) (-4 *3 (-1214 (-553)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-630 (-52))) (-5 *1 (-874 *3)) (-4 *3 (-1079))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-934 (-166 *4))) (-4 *4 (-169)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-934 (-166 *5))) (-5 *4 (-903)) (-4 *5 (-169)) + (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-934 *4)) (-4 *4 (-1031)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-934 *5)) (-5 *4 (-903)) (-4 *5 (-1031)) + (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-401 (-934 *4))) (-4 *4 (-545)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-401 (-934 *5))) (-5 *4 (-903)) (-4 *5 (-545)) + (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-401 (-934 (-166 *4)))) (-4 *4 (-545)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-401 (-934 (-166 *5)))) (-5 *4 (-903)) + (-4 *5 (-545)) (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) + (-5 *1 (-771 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-310 *4)) (-4 *4 (-545)) (-4 *4 (-833)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-310 *5)) (-5 *4 (-903)) (-4 *5 (-545)) + (-4 *5 (-833)) (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) + (-5 *1 (-771 *5)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-310 (-166 *4))) (-4 *4 (-545)) (-4 *4 (-833)) + (-4 *4 (-601 (-373))) (-5 *2 (-166 (-373))) (-5 *1 (-771 *4)))) + ((*1 *2 *3 *4) + (|partial| -12 (-5 *3 (-310 (-166 *5))) (-5 *4 (-903)) (-4 *5 (-545)) + (-4 *5 (-833)) (-4 *5 (-601 (-373))) (-5 *2 (-166 (-373))) + (-5 *1 (-771 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-757)) (-5 *1 (-141))))) +(((*1 *2 *1) (-12 (-5 *2 (-845)) (-5 *1 (-52))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-373)) (-5 *2 (-1243)) (-5 *1 (-1240))))) +(((*1 *1 *2 *2) + (-12 (-5 *2 (-757)) (-4 *3 (-1031)) (-4 *1 (-672 *3 *4 *5)) + (-4 *4 (-367 *3)) (-4 *5 (-367 *3)))) + ((*1 *1 *2) + (-12 (-5 *2 (-757)) (-4 *1 (-1236 *3)) (-4 *3 (-23)) (-4 *3 (-1192))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -11810,55 +11891,27 @@ (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3)))) ((*1 *1 *1) (-4 *1 (-1180)))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-493 *2)) (-14 *2 (-553)))) - ((*1 *1 *1 *1) (-5 *1 (-1099)))) -(((*1 *2 *3) - (|partial| -12 (-5 *2 (-553)) (-5 *1 (-1174 *3)) (-4 *3 (-1031))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-401 (-934 *3))) (-5 *1 (-446 *3 *4 *5 *6)) - (-4 *3 (-545)) (-4 *3 (-169)) (-14 *4 (-903)) - (-14 *5 (-630 (-1155))) (-14 *6 (-1238 (-674 *3)))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-903)) (-5 *2 (-757)) (-5 *1 (-1080 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) +(((*1 *2 *1) (-12 (-5 *2 (-1155)) (-5 *1 (-808))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-630 *6)) (-5 *4 (-630 (-1135 *7))) (-4 *6 (-833)) + (-4 *7 (-931 *5 (-524 *6) *6)) (-4 *5 (-1031)) + (-5 *2 (-1 (-1135 *7) *7)) (-5 *1 (-1105 *5 *6 *7))))) +(((*1 *2 *2) (-12 (-5 *1 (-943 *2)) (-4 *2 (-538))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-320 *3 *4)) (-4 *3 (-1031)) + (-4 *4 (-778))))) (((*1 *2 *2 *3) - (-12 (-5 *2 (-674 *4)) (-5 *3 (-903)) (-4 *4 (-1031)) - (-5 *1 (-1010 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-630 (-674 *4))) (-5 *3 (-903)) (-4 *4 (-1031)) - (-5 *1 (-1010 *4))))) -(((*1 *2 *3 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-757)) (|:| |poli| *7) - (|:| |polj| *7))) - (-4 *5 (-779)) (-4 *7 (-931 *4 *5 *6)) (-4 *4 (-445)) (-4 *6 (-833)) - (-5 *2 (-111)) (-5 *1 (-442 *4 *5 *6 *7))))) + (-12 (-5 *3 (-630 (-242 *4 *5))) (-5 *2 (-242 *4 *5)) + (-14 *4 (-630 (-1155))) (-4 *5 (-445)) (-5 *1 (-618 *4 *5))))) (((*1 *2 *2) - (-12 (-5 *2 (-1135 *3)) (-4 *3 (-1031)) (-5 *1 (-1139 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1230 *2 *3 *4)) (-4 *2 (-1031)) (-14 *3 (-1155)) - (-14 *4 *2)))) -(((*1 *2 *1) (-12 (-4 *1 (-419 *3)) (-4 *3 (-1079)) (-5 *2 (-757))))) -(((*1 *1 *1 *2 *1) - (-12 (-5 *2 (-553)) (-5 *1 (-1135 *3)) (-4 *3 (-1192)))) - ((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4370)) (-4 *1 (-1226 *2)) (-4 *2 (-1192))))) -(((*1 *2 *1) - (-12 (-5 *2 (-630 (-630 (-925 (-220))))) (-5 *1 (-1187 *3)) - (-4 *3 (-956))))) -(((*1 *2 *1) (-12 (-5 *2 (-476)) (-5 *1 (-213)))) - ((*1 *1 *1) (-12 (-4 *1 (-239 *2)) (-4 *2 (-1192)))) - ((*1 *2 *1) (-12 (-5 *2 (-476)) (-5 *1 (-661)))) - ((*1 *1 *1) - (-12 (-4 *1 (-1045 *2 *3 *4)) (-4 *2 (-1031)) (-4 *3 (-779)) - (-4 *4 (-833))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-641 *2)) (-4 *2 (-1031)) (-4 *2 (-357)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-357)) (-5 *1 (-644 *4 *2)) - (-4 *2 (-641 *4))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-445)) (-4 *6 (-779)) (-4 *7 (-833)) - (-4 *3 (-1045 *5 *6 *7)) - (-5 *2 (-630 (-2 (|:| |val| (-111)) (|:| -3361 *4)))) - (-5 *1 (-1087 *5 *6 *7 *3 *4)) (-4 *4 (-1051 *5 *6 *7 *3))))) + (-12 (-5 *2 (-925 *3)) (-4 *3 (-13 (-357) (-1177) (-984))) + (-5 *1 (-173 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-948 *3)) (-4 *3 (-949))))) +(((*1 *2 *1) (-12 (-5 *2 (-208 4 (-128))) (-5 *1 (-568))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-220)) (-5 *2 (-1243)) (-5 *1 (-808))))) (((*1 *1) (-5 *1 (-324)))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) @@ -11880,56 +11933,32 @@ (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3)))) ((*1 *1 *1) (-4 *1 (-1180)))) -(((*1 *1 *2 *3 *4) - (-12 - (-5 *3 - (-630 - (-2 (|:| |scalar| (-401 (-553))) (|:| |coeff| (-1151 *2)) - (|:| |logand| (-1151 *2))))) - (-5 *4 (-630 (-2 (|:| |integrand| *2) (|:| |intvar| *2)))) - (-4 *2 (-357)) (-5 *1 (-574 *2))))) -(((*1 *2 *3) (-12 (-5 *3 (-1137)) (-5 *2 (-52)) (-5 *1 (-1170))))) (((*1 *2 *3) - (-12 (-5 *2 (-630 (-630 (-553)))) (-5 *1 (-953)) - (-5 *3 (-630 (-553)))))) -(((*1 *1) (-5 *1 (-1064)))) + (-12 (-5 *3 (-1137)) + (-4 *4 (-13 (-445) (-833) (-1020 (-553)) (-626 (-553)))) + (-5 *2 (-111)) (-5 *1 (-219 *4 *5)) (-4 *5 (-13 (-1177) (-29 *4)))))) (((*1 *2 *3) - (-12 (-4 *4 (-545)) - (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3488 *4))) - (-5 *1 (-951 *4 *3)) (-4 *3 (-1214 *4))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *3 (-1 *2 (-757) *2)) (-5 *4 (-757)) (-4 *2 (-1079)) - (-5 *1 (-663 *2)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1 *3 (-757) *3)) (-4 *3 (-1079)) (-5 *1 (-667 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1185 *3 *4 *5 *6)) (-4 *3 (-545)) (-4 *4 (-779)) - (-4 *5 (-833)) (-4 *6 (-1045 *3 *4 *5)) (-5 *2 (-630 *6))))) + (|partial| -12 (-4 *5 (-1020 (-48))) + (-4 *4 (-13 (-545) (-833) (-1020 (-553)))) (-4 *5 (-424 *4)) + (-5 *2 (-412 (-1151 (-48)))) (-5 *1 (-429 *4 *5 *3)) + (-4 *3 (-1214 *5))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1155)) (-5 *1 (-274))))) (((*1 *2 *3) - (|partial| -12 (-4 *4 (-1196)) (-4 *5 (-1214 *4)) - (-5 *2 (-2 (|:| |radicand| (-401 *5)) (|:| |deg| (-757)))) - (-5 *1 (-145 *4 *5 *3)) (-4 *3 (-1214 (-401 *5)))))) -(((*1 *1 *1) - (-12 (-5 *1 (-583 *2)) (-4 *2 (-38 (-401 (-553)))) (-4 *2 (-1031))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-903)) (-4 *4 (-362)) (-4 *4 (-357)) (-5 *2 (-1151 *1)) - (-4 *1 (-323 *4)))) - ((*1 *2 *1) (-12 (-4 *1 (-323 *3)) (-4 *3 (-357)) (-5 *2 (-1151 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-364 *3 *2)) (-4 *3 (-169)) (-4 *3 (-357)) - (-4 *2 (-1214 *3)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1238 *4)) (-4 *4 (-343)) (-5 *2 (-1151 *4)) - (-5 *1 (-521 *4))))) -(((*1 *2 *2 *2) - (|partial| -12 (-4 *3 (-357)) (-5 *1 (-752 *2 *3)) (-4 *2 (-694 *3)))) - ((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-835 *2)) (-4 *2 (-1031)) (-4 *2 (-357))))) -(((*1 *1 *2 *2) - (-12 (-5 *2 (-757)) (-4 *3 (-1031)) (-4 *1 (-672 *3 *4 *5)) - (-4 *4 (-367 *3)) (-4 *5 (-367 *3)))) - ((*1 *1 *2) - (-12 (-5 *2 (-757)) (-4 *1 (-1236 *3)) (-4 *3 (-23)) (-4 *3 (-1192))))) + (-12 (-4 *4 (-1031)) (-4 *5 (-1214 *4)) (-5 *2 (-1 *6 (-630 *6))) + (-5 *1 (-1232 *4 *5 *3 *6)) (-4 *3 (-641 *5)) (-4 *6 (-1229 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-630 (-847 *5))) (-14 *5 (-630 (-1155))) (-4 *6 (-445)) + (-5 *2 + (-2 (|:| |dpolys| (-630 (-242 *5 *6))) + (|:| |coords| (-630 (-553))))) + (-5 *1 (-464 *5 *6 *7)) (-5 *3 (-630 (-242 *5 *6))) (-4 *7 (-445))))) +(((*1 *2 *3) + (-12 (-5 *3 (-310 (-220))) (-5 *2 (-401 (-553))) (-5 *1 (-299))))) +(((*1 *2 *1) (-12 (-5 *2 (-111)) (-5 *1 (-428))))) +(((*1 *1) (-12 (-4 *1 (-163 *2)) (-4 *2 (-169))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) + (-4 *2 (-13 (-424 *3) (-984)))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-833) (-545))) (-5 *1 (-270 *3 *2)) (-4 *2 (-13 (-424 *3) (-984))))) @@ -11950,33 +11979,48 @@ (-12 (-5 *2 (-1135 *3)) (-4 *3 (-38 (-401 (-553)))) (-5 *1 (-1141 *3)))) ((*1 *1 *1) (-4 *1 (-1180)))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-757)) (-5 *3 (-925 *5)) (-4 *5 (-1031)) - (-5 *1 (-1143 *4 *5)) (-14 *4 (-903)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-630 (-757))) (-5 *3 (-757)) (-5 *1 (-1143 *4 *5)) - (-14 *4 (-903)) (-4 *5 (-1031)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-630 (-757))) (-5 *3 (-925 *5)) (-4 *5 (-1031)) - (-5 *1 (-1143 *4 *5)) (-14 *4 (-903))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1113 *3)) (-4 *3 (-1031)) (-5 *2 (-630 (-168)))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-630 (-757))) (-5 *1 (-1143 *3 *4)) (-14 *3 (-903)) - (-4 *4 (-1031))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1151 *9)) (-5 *4 (-630 *7)) (-5 *5 (-630 (-630 *8))) - (-4 *7 (-833)) (-4 *8 (-301)) (-4 *9 (-931 *8 *6 *7)) (-4 *6 (-779)) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-903)) (-5 *2 (-1243)) (-5 *1 (-1239)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-903)) (-5 *2 (-1243)) (-5 *1 (-1240))))) +(((*1 *2 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*6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3557 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2388 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-357)) (-4 *6 (-357)) - (-5 *2 (-2 (|:| -3557 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2388 *6) (|:| |coeff| *6))) (-5 *1 (-573 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -16402,7 +16277,7 @@ (-4 *8 (-1031)) (-4 *6 (-779)) (-4 *2 (-13 (-1079) - (-10 -8 (-15 -1699 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-757)))))) + (-10 -8 (-15 -1700 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-757)))))) (-5 *1 (-933 *6 *7 *8 *5 *2)) (-4 *5 (-931 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-940 *5)) (-4 *5 (-1192)) @@ -16415,8 +16290,8 @@ (-4 *2 (-931 (-934 *4) *5 *6)) (-4 *5 (-779)) (-4 *6 (-13 (-833) - (-10 -8 (-15 -1523 ((-1155) $)) - (-15 -1489 ((-3 $ "failed") (-1155)))))) + (-10 -8 (-15 -1524 ((-1155) $)) + (-15 -1509 ((-3 $ "failed") (-1155)))))) (-5 *1 (-966 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\ No newline at end of file |