diff options
Diffstat (limited to 'src/share/algebra/browse.daase')
| -rw-r--r-- | src/share/algebra/browse.daase | 106 |
1 files changed, 53 insertions, 53 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 447dc5ea..c93c135a 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2267858 . 3485461456) +(2267469 . 3485464570) (-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 @@ -88,7 +88,7 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3636 UP UPUP -2425) +(-40 -3636 UP UPUP -3163) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-3783 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-3783 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-3783 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-3783 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) @@ -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."))) ((-4454 . T) (-4455 . T)) -((-3783 (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|))))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|))))))) +((-3783 (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|))))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|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 @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4100 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4101 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-168 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."))) @@ -614,7 +614,7 @@ NIL NIL (-171 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}."))) -((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4100 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4447 -3783 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-4101 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-836)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1214)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-3783 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4453)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-356))))) (-172 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"))) @@ -838,7 +838,7 @@ NIL NIL (-227) ((|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}."))) -((-4090 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-228) ((|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{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * 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*\\%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*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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)}.}"))) @@ -859,7 +859,7 @@ NIL (-232 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}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) +((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -235) (|devaluate| |#2|)))) (-233 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) ((-4451 . T)) @@ -873,11 +873,11 @@ NIL NIL NIL (-236 S) -((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) +((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}."))) NIL NIL (-237) -((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) +((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}."))) ((-4451 . T)) NIL (-238 A S) @@ -959,7 +959,7 @@ NIL (-257 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL -((|HasCategory| |#2| (QUOTE (-237)))) +((|HasCategory| |#2| (LIST (QUOTE -235) (|devaluate| |#2|)))) (-258 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) @@ -1108,7 +1108,7 @@ 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 -(-295 S R |Mod| -4149 -1377 |exactQuo|) +(-295 S R |Mod| -4322 -4086 |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}")) (|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"))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -1135,7 +1135,7 @@ NIL (-301 |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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-302) ((|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 @@ -1231,7 +1231,7 @@ NIL (-325 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-326 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 @@ -1474,7 +1474,7 @@ NIL NIL (-386) ((|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{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}."))) -((-4437 . T) (-4445 . T) (-4090 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4437 . T) (-4445 . T) (-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-387 |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}."))) @@ -1578,7 +1578,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4437)) (|HasAttribute| |#1| (QUOTE -4445))) (-412) ((|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\"."))) -((-4090 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-413 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."))) @@ -1635,7 +1635,7 @@ NIL (-426 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."))) ((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -315) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1233))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-460)))) +((|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -315) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1233))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-460)))) (-427 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1859,11 +1859,11 @@ NIL (-482 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-483 |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."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111)))) (-484 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)}"))) ((-4455 . T) (-4454 . T)) @@ -1879,7 +1879,7 @@ NIL (-487 |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."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-488) ((|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 @@ -2163,7 +2163,7 @@ NIL (-558 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-559 R -3636) ((|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 @@ -2178,7 +2178,7 @@ NIL NIL (-562 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."))) -((-4090 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4091 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-563 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") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2246,7 +2246,7 @@ NIL NIL (-579 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-4090 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4091 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-580) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) @@ -2395,7 +2395,7 @@ NIL (-616 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-617 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 @@ -2491,7 +2491,7 @@ NIL (-640) ((|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}.")) (|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."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3762) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-1170) (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 (-52))) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-1170) (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 (-52))) (QUOTE (-1111)))) (-641 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 @@ -2515,7 +2515,7 @@ NIL (-646 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 -((-3795 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) +((-3796 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) (-647 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}."))) ((-4451 . T)) @@ -2592,7 +2592,7 @@ NIL ((|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)))) -(-666 A -2160) +(-666 A -3693) ((|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}}"))) ((-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) @@ -2738,7 +2738,7 @@ NIL NIL (-702) ((|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"))) -((-4447 . T) (-4452 |has| (-707) (-370)) (-4446 |has| (-707) (-370)) (-4100 . T) (-4453 |has| (-707) (-6 -4453)) (-4450 |has| (-707) (-6 -4450)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4447 . T) (-4452 |has| (-707) (-370)) (-4446 |has| (-707) (-370)) (-4101 . T) (-4453 |has| (-707) (-6 -4453)) (-4450 |has| (-707) (-6 -4450)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) ((|HasCategory| (-707) (QUOTE (-148))) (|HasCategory| (-707) (QUOTE (-146))) (|HasCategory| (-707) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-707) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-707) (QUOTE (-375))) (|HasCategory| (-707) (QUOTE (-370))) (-3783 (|HasCategory| (-707) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-707) (QUOTE (-370)))) (|HasCategory| (-707) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-707) (QUOTE (-237))) (-3783 (|HasCategory| (-707) (QUOTE (-370))) (|HasCategory| (-707) (QUOTE (-356)))) (|HasCategory| (-707) (QUOTE (-356))) (|HasCategory| (-707) (LIST (QUOTE -292) (QUOTE (-707)) (QUOTE (-707)))) (|HasCategory| (-707) (LIST (QUOTE -315) (QUOTE (-707)))) (|HasCategory| (-707) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-707)))) (|HasCategory| (-707) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-707) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-707) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-707) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (-3783 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-370))) (|HasCategory| (-707) (QUOTE (-356)))) (|HasCategory| (-707) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-707) (QUOTE (-1033))) (|HasCategory| (-707) (QUOTE (-1214))) (-12 (|HasCategory| (-707) (QUOTE (-1013))) (|HasCategory| (-707) (QUOTE (-1214)))) (-3783 (-12 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (|HasCategory| (-707) (QUOTE (-370))) (-12 (|HasCategory| (-707) (QUOTE (-356))) (|HasCategory| (-707) (QUOTE (-918))))) (-3783 (-12 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (-12 (|HasCategory| (-707) (QUOTE (-370))) (|HasCategory| (-707) (QUOTE (-918)))) (-12 (|HasCategory| (-707) (QUOTE (-356))) (|HasCategory| (-707) (QUOTE (-918))))) (|HasCategory| (-707) (QUOTE (-553))) (-12 (|HasCategory| (-707) (QUOTE (-1071))) (|HasCategory| (-707) (QUOTE (-1214)))) (|HasCategory| (-707) (QUOTE (-1071))) (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918))) (-3783 (-12 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (|HasCategory| (-707) (QUOTE (-370)))) (-3783 (-12 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (|HasCategory| (-707) (QUOTE (-564)))) (-12 (|HasCategory| (-707) (QUOTE (-237))) (|HasCategory| (-707) (QUOTE (-370)))) (-12 (|HasCategory| (-707) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-707) (QUOTE (-370)))) (|HasCategory| (-707) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-707) (QUOTE (-564))) (|HasAttribute| (-707) (QUOTE -4453)) (|HasAttribute| (-707) (QUOTE -4450)) (-12 (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (|HasCategory| (-707) (QUOTE (-146)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-707) (QUOTE (-313))) (|HasCategory| (-707) (QUOTE (-918)))) (|HasCategory| (-707) (QUOTE (-356))))) (-703 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}."))) @@ -2758,7 +2758,7 @@ NIL NIL (-707) ((|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}"))) -((-4090 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) +((-4091 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL (-708 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."))) @@ -2784,7 +2784,7 @@ 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 -(-714 S -4019 I) +(-714 S -4020 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 @@ -2804,7 +2804,7 @@ 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 -(-719 R |Mod| -4149 -1377 |exactQuo|) +(-719 R |Mod| -4322 -4086 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) NIL @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-723 R |Mod| -4149 -1377 |exactQuo|) +(-723 R |Mod| -4322 -4086 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4451 . T)) NIL @@ -3083,7 +3083,7 @@ NIL (-788 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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3795 (|HasCategory| |#1| (QUOTE (-553)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572))))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3795 (|HasCategory| |#1| (LIST (QUOTE -1003) (QUOTE (-572))))))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-918))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3796 (|HasCategory| |#1| (QUOTE (-553)))) (-3796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3796 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-572))))) (-3796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-1188)))) (-3796 (|HasCategory| |#1| (LIST (QUOTE -1003) (QUOTE (-572))))))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) (-789 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 @@ -3271,7 +3271,7 @@ NIL (-835 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) ((-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-237)))) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -235) (|devaluate| |#1|)))) (-836) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) NIL @@ -3515,7 +3515,7 @@ NIL (-896 |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 (-3795 (|HasCategory| |#2| (QUOTE (-1060)))) (-3795 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (-3795 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) +((-12 (-3796 (|HasCategory| |#2| (QUOTE (-1060)))) (-3796 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (-3796 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-897 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 @@ -3524,7 +3524,7 @@ 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 -(-899 R -4019) +(-899 R -4020) ((|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 @@ -3712,11 +3712,11 @@ 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 -895) (|devaluate| |#1|)))) -(-946 R -3636 -4019) +(-946 R -3636 -4020) ((|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 -(-947 -4019) +(-947 -4020) ((|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 @@ -3971,7 +3971,7 @@ NIL (-1010 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.}"))) ((-4447 |has| |#1| (-296)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553)))) (-1011 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}."))) ((-4454 . T) (-4455 . T)) @@ -4115,7 +4115,7 @@ NIL (-1046) ((|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.}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3762) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) (-1047) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4227,7 +4227,7 @@ NIL (-1074) ((|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}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3762) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3762 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -3763) (QUOTE (-52))))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1188)) (|:| -3763 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) (-1075 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 @@ -4575,7 +4575,7 @@ NIL (-1161 |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."))) ((-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111)))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111)))) (-1162) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4615,7 +4615,7 @@ NIL (-1171 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#1|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3762 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#1|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 (-1170)) (|:| -3763 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-1172 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 should be invertible.")) (|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,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 @@ -4647,7 +4647,7 @@ NIL (-1179 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) (((-4456 "*") -3783 (-3804 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-828))) (|has| |#1| (-174)) (-3804 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-918)))) (-4447 -3783 (-3804 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-828))) (|has| |#1| (-564)) (-3804 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-148)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370))))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-148)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370))))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1180 R -3636) ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL @@ -4671,11 +4671,11 @@ NIL (-1185 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1186 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1187) ((|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 @@ -4735,7 +4735,7 @@ NIL (-1201 |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}"))) ((-4454 . T) (-4455 . T)) -((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3762) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3762 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) +((-12 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1640) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3763) (|devaluate| |#2|)))))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-3783 (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -1640 |#1|) (|:| -3763 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) (-1202 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL @@ -4899,11 +4899,11 @@ NIL (-1242 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-146))))) (-3783 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-148))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858))))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-918))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-146)))))) +((-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-146))))) (-3783 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-148))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-3783 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858))))) (-3783 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-918))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-146)))))) (-1243 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) (((-4456 "*") -3783 (-3804 (|has| |#1| (-370)) (|has| (-1271 |#1| |#2| |#3|) (-828))) (|has| |#1| (-174)) (-3804 (|has| |#1| (-370)) (|has| (-1271 |#1| |#2| |#3|) (-918)))) (-4447 -3783 (-3804 (|has| |#1| (-370)) (|has| (-1271 |#1| |#2| |#3|) (-828))) (|has| |#1| (-564)) (-3804 (|has| |#1| (-370)) (|has| (-1271 |#1| |#2| |#3|) (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-148)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370))))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-148)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1123))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370))))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -315) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-3783 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1244 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4983,11 +4983,11 @@ NIL (-1263 |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)}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) +((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-1264 |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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-3783 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1265 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4456 "*") |has| (-1264 |#2| |#3| |#4|) (-174)) (-4447 |has| (-1264 |#2| |#3| |#4|) (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -5007,7 +5007,7 @@ NIL (-1269 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4161) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3270) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) (-1270 |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."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) @@ -5015,7 +5015,7 @@ NIL (-1271 |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|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|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}."))) (((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -4161) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2220) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-3783 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -3491) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-3783 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3270) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -2221) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) (-1272 |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 @@ -5180,4 +5180,4 @@ NIL NIL NIL NIL -((-3 NIL 2267838 2267843 2267848 2267853) (-2 NIL 2267818 2267823 2267828 2267833) (-1 NIL 2267798 2267803 2267808 2267813) (0 NIL 2267778 2267783 2267788 2267793) (-1308 "ZMOD.spad" 2267587 2267600 2267716 2267773) (-1307 "ZLINDEP.spad" 2266653 2266664 2267577 2267582) (-1306 "ZDSOLVE.spad" 2256598 2256620 2266643 2266648) (-1305 "YSTREAM.spad" 2256093 2256104 2256588 2256593) (-1304 "YDIAGRAM.spad" 2255727 2255736 2256083 2256088) (-1303 "XRPOLY.spad" 2254947 2254967 2255583 2255652) (-1302 "XPR.spad" 2252742 2252755 2254665 2254764) (-1301 "XPOLY.spad" 2252297 2252308 2252598 2252667) (-1300 "XPOLYC.spad" 2251616 2251632 2252223 2252292) (-1299 "XPBWPOLY.spad" 2250053 2250073 2251396 2251465) (-1298 "XF.spad" 2248516 2248531 2249955 2250048) (-1297 "XF.spad" 2246959 2246976 2248400 2248405) (-1296 "XFALG.spad" 2244007 2244023 2246885 2246954) (-1295 "XEXPPKG.spad" 2243258 2243284 2243997 2244002) (-1294 "XDPOLY.spad" 2242872 2242888 2243114 2243183) (-1293 "XALG.spad" 2242532 2242543 2242828 2242867) (-1292 "WUTSET.spad" 2238371 2238388 2242178 2242205) (-1291 "WP.spad" 2237570 2237614 2238229 2238296) (-1290 "WHILEAST.spad" 2237368 2237377 2237560 2237565) (-1289 "WHEREAST.spad" 2237039 2237048 2237358 2237363) (-1288 "WFFINTBS.spad" 2234702 2234724 2237029 2237034) (-1287 "WEIER.spad" 2232924 2232935 2234692 2234697) (-1286 "VSPACE.spad" 2232597 2232608 2232892 2232919) (-1285 "VSPACE.spad" 2232290 2232303 2232587 2232592) (-1284 "VOID.spad" 2231967 2231976 2232280 2232285) (-1283 "VIEW.spad" 2229647 2229656 2231957 2231962) (-1282 "VIEWDEF.spad" 2224848 2224857 2229637 2229642) (-1281 "VIEW3D.spad" 2208809 2208818 2224838 2224843) (-1280 "VIEW2D.spad" 2196700 2196709 2208799 2208804) (-1279 "VECTOR.spad" 2195374 2195385 2195625 2195652) (-1278 "VECTOR2.spad" 2194013 2194026 2195364 2195369) (-1277 "VECTCAT.spad" 2191917 2191928 2193981 2194008) (-1276 "VECTCAT.spad" 2189628 2189641 2191694 2191699) (-1275 "VARIABLE.spad" 2189408 2189423 2189618 2189623) (-1274 "UTYPE.spad" 2189052 2189061 2189398 2189403) (-1273 "UTSODETL.spad" 2188347 2188371 2189008 2189013) (-1272 "UTSODE.spad" 2186563 2186583 2188337 2188342) (-1271 "UTS.spad" 2181367 2181395 2185030 2185127) (-1270 "UTSCAT.spad" 2178846 2178862 2181265 2181362) (-1269 "UTSCAT.spad" 2175969 2175987 2178390 2178395) (-1268 "UTS2.spad" 2175564 2175599 2175959 2175964) (-1267 "URAGG.spad" 2170237 2170248 2175554 2175559) (-1266 "URAGG.spad" 2164874 2164887 2170193 2170198) (-1265 "UPXSSING.spad" 2162519 2162545 2163955 2164088) (-1264 "UPXS.spad" 2159673 2159701 2160651 2160800) (-1263 "UPXSCONS.spad" 2157432 2157452 2157805 2157954) (-1262 "UPXSCCA.spad" 2156003 2156023 2157278 2157427) (-1261 "UPXSCCA.spad" 2154716 2154738 2155993 2155998) (-1260 "UPXSCAT.spad" 2153305 2153321 2154562 2154711) (-1259 "UPXS2.spad" 2152848 2152901 2153295 2153300) (-1258 "UPSQFREE.spad" 2151262 2151276 2152838 2152843) (-1257 "UPSCAT.spad" 2149049 2149073 2151160 2151257) (-1256 "UPSCAT.spad" 2146542 2146568 2148655 2148660) (-1255 "UPOLYC.spad" 2141582 2141593 2146384 2146537) (-1254 "UPOLYC.spad" 2136514 2136527 2141318 2141323) (-1253 "UPOLYC2.spad" 2135985 2136004 2136504 2136509) (-1252 "UP.spad" 2133184 2133199 2133571 2133724) (-1251 "UPMP.spad" 2132084 2132097 2133174 2133179) (-1250 "UPDIVP.spad" 2131649 2131663 2132074 2132079) (-1249 "UPDECOMP.spad" 2129894 2129908 2131639 2131644) (-1248 "UPCDEN.spad" 2129103 2129119 2129884 2129889) (-1247 "UP2.spad" 2128467 2128488 2129093 2129098) (-1246 "UNISEG.spad" 2127820 2127831 2128386 2128391) (-1245 "UNISEG2.spad" 2127317 2127330 2127776 2127781) (-1244 "UNIFACT.spad" 2126420 2126432 2127307 2127312) (-1243 "ULS.spad" 2116978 2117006 2118065 2118494) (-1242 "ULSCONS.spad" 2109374 2109394 2109744 2109893) (-1241 "ULSCCAT.spad" 2107111 2107131 2109220 2109369) (-1240 "ULSCCAT.spad" 2104956 2104978 2107067 2107072) (-1239 "ULSCAT.spad" 2103188 2103204 2104802 2104951) (-1238 "ULS2.spad" 2102702 2102755 2103178 2103183) (-1237 "UINT8.spad" 2102579 2102588 2102692 2102697) (-1236 "UINT64.spad" 2102455 2102464 2102569 2102574) (-1235 "UINT32.spad" 2102331 2102340 2102445 2102450) (-1234 "UINT16.spad" 2102207 2102216 2102321 2102326) (-1233 "UFD.spad" 2101272 2101281 2102133 2102202) (-1232 "UFD.spad" 2100399 2100410 2101262 2101267) (-1231 "UDVO.spad" 2099280 2099289 2100389 2100394) (-1230 "UDPO.spad" 2096773 2096784 2099236 2099241) (-1229 "TYPE.spad" 2096705 2096714 2096763 2096768) (-1228 "TYPEAST.spad" 2096624 2096633 2096695 2096700) (-1227 "TWOFACT.spad" 2095276 2095291 2096614 2096619) (-1226 "TUPLE.spad" 2094762 2094773 2095175 2095180) (-1225 "TUBETOOL.spad" 2091629 2091638 2094752 2094757) (-1224 "TUBE.spad" 2090276 2090293 2091619 2091624) (-1223 "TS.spad" 2088875 2088891 2089841 2089938) (-1222 "TSETCAT.spad" 2076002 2076019 2088843 2088870) (-1221 "TSETCAT.spad" 2063115 2063134 2075958 2075963) (-1220 "TRMANIP.spad" 2057481 2057498 2062821 2062826) (-1219 "TRIMAT.spad" 2056444 2056469 2057471 2057476) (-1218 "TRIGMNIP.spad" 2054971 2054988 2056434 2056439) (-1217 "TRIGCAT.spad" 2054483 2054492 2054961 2054966) (-1216 "TRIGCAT.spad" 2053993 2054004 2054473 2054478) (-1215 "TREE.spad" 2052568 2052579 2053600 2053627) (-1214 "TRANFUN.spad" 2052407 2052416 2052558 2052563) (-1213 "TRANFUN.spad" 2052244 2052255 2052397 2052402) (-1212 "TOPSP.spad" 2051918 2051927 2052234 2052239) (-1211 "TOOLSIGN.spad" 2051581 2051592 2051908 2051913) (-1210 "TEXTFILE.spad" 2050142 2050151 2051571 2051576) (-1209 "TEX.spad" 2047288 2047297 2050132 2050137) (-1208 "TEX1.spad" 2046844 2046855 2047278 2047283) (-1207 "TEMUTL.spad" 2046399 2046408 2046834 2046839) (-1206 "TBCMPPK.spad" 2044492 2044515 2046389 2046394) (-1205 "TBAGG.spad" 2043542 2043565 2044472 2044487) (-1204 "TBAGG.spad" 2042600 2042625 2043532 2043537) (-1203 "TANEXP.spad" 2042008 2042019 2042590 2042595) (-1202 "TALGOP.spad" 2041732 2041743 2041998 2042003) (-1201 "TABLE.spad" 2040143 2040166 2040413 2040440) (-1200 "TABLEAU.spad" 2039624 2039635 2040133 2040138) (-1199 "TABLBUMP.spad" 2036427 2036438 2039614 2039619) (-1198 "SYSTEM.spad" 2035655 2035664 2036417 2036422) (-1197 "SYSSOLP.spad" 2033138 2033149 2035645 2035650) (-1196 "SYSPTR.spad" 2033037 2033046 2033128 2033133) (-1195 "SYSNNI.spad" 2032219 2032230 2033027 2033032) (-1194 "SYSINT.spad" 2031623 2031634 2032209 2032214) (-1193 "SYNTAX.spad" 2027829 2027838 2031613 2031618) (-1192 "SYMTAB.spad" 2025897 2025906 2027819 2027824) (-1191 "SYMS.spad" 2021920 2021929 2025887 2025892) (-1190 "SYMPOLY.spad" 2020927 2020938 2021009 2021136) (-1189 "SYMFUNC.spad" 2020428 2020439 2020917 2020922) (-1188 "SYMBOL.spad" 2017931 2017940 2020418 2020423) (-1187 "SWITCH.spad" 2014702 2014711 2017921 2017926) (-1186 "SUTS.spad" 2011607 2011635 2013169 2013266) (-1185 "SUPXS.spad" 2008748 2008776 2009739 2009888) (-1184 "SUP.spad" 2005561 2005572 2006334 2006487) (-1183 "SUPFRACF.spad" 2004666 2004684 2005551 2005556) (-1182 "SUP2.spad" 2004058 2004071 2004656 2004661) (-1181 "SUMRF.spad" 2003032 2003043 2004048 2004053) (-1180 "SUMFS.spad" 2002669 2002686 2003022 2003027) (-1179 "SULS.spad" 1993214 1993242 1994314 1994743) (-1178 "SUCHTAST.spad" 1992983 1992992 1993204 1993209) (-1177 "SUCH.spad" 1992665 1992680 1992973 1992978) (-1176 "SUBSPACE.spad" 1984780 1984795 1992655 1992660) (-1175 "SUBRESP.spad" 1983950 1983964 1984736 1984741) (-1174 "STTF.spad" 1980049 1980065 1983940 1983945) (-1173 "STTFNC.spad" 1976517 1976533 1980039 1980044) (-1172 "STTAYLOR.spad" 1969152 1969163 1976398 1976403) (-1171 "STRTBL.spad" 1967657 1967674 1967806 1967833) (-1170 "STRING.spad" 1967066 1967075 1967080 1967107) (-1169 "STRICAT.spad" 1966854 1966863 1967034 1967061) (-1168 "STREAM.spad" 1963772 1963783 1966379 1966394) (-1167 "STREAM3.spad" 1963345 1963360 1963762 1963767) (-1166 "STREAM2.spad" 1962473 1962486 1963335 1963340) (-1165 "STREAM1.spad" 1962179 1962190 1962463 1962468) (-1164 "STINPROD.spad" 1961115 1961131 1962169 1962174) (-1163 "STEP.spad" 1960316 1960325 1961105 1961110) (-1162 "STEPAST.spad" 1959550 1959559 1960306 1960311) (-1161 "STBL.spad" 1958076 1958104 1958243 1958258) (-1160 "STAGG.spad" 1957151 1957162 1958066 1958071) (-1159 "STAGG.spad" 1956224 1956237 1957141 1957146) (-1158 "STACK.spad" 1955581 1955592 1955831 1955858) (-1157 "SREGSET.spad" 1953285 1953302 1955227 1955254) (-1156 "SRDCMPK.spad" 1951846 1951866 1953275 1953280) (-1155 "SRAGG.spad" 1946989 1946998 1951814 1951841) (-1154 "SRAGG.spad" 1942152 1942163 1946979 1946984) (-1153 "SQMATRIX.spad" 1939768 1939786 1940684 1940771) (-1152 "SPLTREE.spad" 1934320 1934333 1939204 1939231) (-1151 "SPLNODE.spad" 1930908 1930921 1934310 1934315) (-1150 "SPFCAT.spad" 1929717 1929726 1930898 1930903) (-1149 "SPECOUT.spad" 1928269 1928278 1929707 1929712) (-1148 "SPADXPT.spad" 1919864 1919873 1928259 1928264) (-1147 "spad-parser.spad" 1919329 1919338 1919854 1919859) (-1146 "SPADAST.spad" 1919030 1919039 1919319 1919324) (-1145 "SPACEC.spad" 1903229 1903240 1919020 1919025) (-1144 "SPACE3.spad" 1903005 1903016 1903219 1903224) (-1143 "SORTPAK.spad" 1902554 1902567 1902961 1902966) (-1142 "SOLVETRA.spad" 1900317 1900328 1902544 1902549) (-1141 "SOLVESER.spad" 1898845 1898856 1900307 1900312) (-1140 "SOLVERAD.spad" 1894871 1894882 1898835 1898840) (-1139 "SOLVEFOR.spad" 1893333 1893351 1894861 1894866) (-1138 "SNTSCAT.spad" 1892933 1892950 1893301 1893328) (-1137 "SMTS.spad" 1891205 1891231 1892498 1892595) (-1136 "SMP.spad" 1888680 1888700 1889070 1889197) (-1135 "SMITH.spad" 1887525 1887550 1888670 1888675) (-1134 "SMATCAT.spad" 1885635 1885665 1887469 1887520) (-1133 "SMATCAT.spad" 1883677 1883709 1885513 1885518) (-1132 "SKAGG.spad" 1882640 1882651 1883645 1883672) (-1131 "SINT.spad" 1881580 1881589 1882506 1882635) (-1130 "SIMPAN.spad" 1881308 1881317 1881570 1881575) (-1129 "SIG.spad" 1880638 1880647 1881298 1881303) (-1128 "SIGNRF.spad" 1879756 1879767 1880628 1880633) (-1127 "SIGNEF.spad" 1879035 1879052 1879746 1879751) (-1126 "SIGAST.spad" 1878420 1878429 1879025 1879030) (-1125 "SHP.spad" 1876348 1876363 1878376 1878381) (-1124 "SHDP.spad" 1866059 1866086 1866568 1866699) (-1123 "SGROUP.spad" 1865667 1865676 1866049 1866054) (-1122 "SGROUP.spad" 1865273 1865284 1865657 1865662) (-1121 "SGCF.spad" 1858412 1858421 1865263 1865268) (-1120 "SFRTCAT.spad" 1857342 1857359 1858380 1858407) (-1119 "SFRGCD.spad" 1856405 1856425 1857332 1857337) (-1118 "SFQCMPK.spad" 1851042 1851062 1856395 1856400) (-1117 "SFORT.spad" 1850481 1850495 1851032 1851037) (-1116 "SEXOF.spad" 1850324 1850364 1850471 1850476) (-1115 "SEX.spad" 1850216 1850225 1850314 1850319) (-1114 "SEXCAT.spad" 1847997 1848037 1850206 1850211) (-1113 "SET.spad" 1846321 1846332 1847418 1847457) (-1112 "SETMN.spad" 1844771 1844788 1846311 1846316) (-1111 "SETCAT.spad" 1844093 1844102 1844761 1844766) (-1110 "SETCAT.spad" 1843413 1843424 1844083 1844088) (-1109 "SETAGG.spad" 1839962 1839973 1843393 1843408) (-1108 "SETAGG.spad" 1836519 1836532 1839952 1839957) (-1107 "SEQAST.spad" 1836222 1836231 1836509 1836514) (-1106 "SEGXCAT.spad" 1835378 1835391 1836212 1836217) (-1105 "SEG.spad" 1835191 1835202 1835297 1835302) (-1104 "SEGCAT.spad" 1834116 1834127 1835181 1835186) (-1103 "SEGBIND.spad" 1833874 1833885 1834063 1834068) (-1102 "SEGBIND2.spad" 1833572 1833585 1833864 1833869) (-1101 "SEGAST.spad" 1833286 1833295 1833562 1833567) (-1100 "SEG2.spad" 1832721 1832734 1833242 1833247) (-1099 "SDVAR.spad" 1831997 1832008 1832711 1832716) (-1098 "SDPOL.spad" 1829423 1829434 1829714 1829841) (-1097 "SCPKG.spad" 1827512 1827523 1829413 1829418) (-1096 "SCOPE.spad" 1826665 1826674 1827502 1827507) (-1095 "SCACHE.spad" 1825361 1825372 1826655 1826660) (-1094 "SASTCAT.spad" 1825270 1825279 1825351 1825356) (-1093 "SAOS.spad" 1825142 1825151 1825260 1825265) (-1092 "SAERFFC.spad" 1824855 1824875 1825132 1825137) (-1091 "SAE.spad" 1823030 1823046 1823641 1823776) (-1090 "SAEFACT.spad" 1822731 1822751 1823020 1823025) (-1089 "RURPK.spad" 1820390 1820406 1822721 1822726) (-1088 "RULESET.spad" 1819843 1819867 1820380 1820385) (-1087 "RULE.spad" 1818083 1818107 1819833 1819838) (-1086 "RULECOLD.spad" 1817935 1817948 1818073 1818078) (-1085 "RTVALUE.spad" 1817670 1817679 1817925 1817930) (-1084 "RSTRCAST.spad" 1817387 1817396 1817660 1817665) (-1083 "RSETGCD.spad" 1813765 1813785 1817377 1817382) (-1082 "RSETCAT.spad" 1803701 1803718 1813733 1813760) (-1081 "RSETCAT.spad" 1793657 1793676 1803691 1803696) (-1080 "RSDCMPK.spad" 1792109 1792129 1793647 1793652) (-1079 "RRCC.spad" 1790493 1790523 1792099 1792104) (-1078 "RRCC.spad" 1788875 1788907 1790483 1790488) (-1077 "RPTAST.spad" 1788577 1788586 1788865 1788870) (-1076 "RPOLCAT.spad" 1767937 1767952 1788445 1788572) (-1075 "RPOLCAT.spad" 1747010 1747027 1767520 1767525) (-1074 "ROUTINE.spad" 1742893 1742902 1745657 1745684) (-1073 "ROMAN.spad" 1742221 1742230 1742759 1742888) (-1072 "ROIRC.spad" 1741301 1741333 1742211 1742216) (-1071 "RNS.spad" 1740204 1740213 1741203 1741296) (-1070 "RNS.spad" 1739193 1739204 1740194 1740199) (-1069 "RNG.spad" 1738928 1738937 1739183 1739188) (-1068 "RNGBIND.spad" 1738088 1738102 1738883 1738888) (-1067 "RMODULE.spad" 1737853 1737864 1738078 1738083) (-1066 "RMCAT2.spad" 1737273 1737330 1737843 1737848) (-1065 "RMATRIX.spad" 1736097 1736116 1736440 1736479) (-1064 "RMATCAT.spad" 1731676 1731707 1736053 1736092) (-1063 "RMATCAT.spad" 1727145 1727178 1731524 1731529) (-1062 "RLINSET.spad" 1726539 1726550 1727135 1727140) (-1061 "RINTERP.spad" 1726427 1726447 1726529 1726534) (-1060 "RING.spad" 1725897 1725906 1726407 1726422) (-1059 "RING.spad" 1725375 1725386 1725887 1725892) (-1058 "RIDIST.spad" 1724767 1724776 1725365 1725370) (-1057 "RGCHAIN.spad" 1723350 1723366 1724252 1724279) (-1056 "RGBCSPC.spad" 1723131 1723143 1723340 1723345) (-1055 "RGBCMDL.spad" 1722661 1722673 1723121 1723126) (-1054 "RF.spad" 1720303 1720314 1722651 1722656) (-1053 "RFFACTOR.spad" 1719765 1719776 1720293 1720298) (-1052 "RFFACT.spad" 1719500 1719512 1719755 1719760) (-1051 "RFDIST.spad" 1718496 1718505 1719490 1719495) (-1050 "RETSOL.spad" 1717915 1717928 1718486 1718491) (-1049 "RETRACT.spad" 1717343 1717354 1717905 1717910) (-1048 "RETRACT.spad" 1716769 1716782 1717333 1717338) (-1047 "RETAST.spad" 1716581 1716590 1716759 1716764) (-1046 "RESULT.spad" 1714641 1714650 1715228 1715255) (-1045 "RESRING.spad" 1713988 1714035 1714579 1714636) (-1044 "RESLATC.spad" 1713312 1713323 1713978 1713983) (-1043 "REPSQ.spad" 1713043 1713054 1713302 1713307) (-1042 "REP.spad" 1710597 1710606 1713033 1713038) (-1041 "REPDB.spad" 1710304 1710315 1710587 1710592) (-1040 "REP2.spad" 1699962 1699973 1710146 1710151) (-1039 "REP1.spad" 1694158 1694169 1699912 1699917) (-1038 "REGSET.spad" 1691955 1691972 1693804 1693831) (-1037 "REF.spad" 1691290 1691301 1691910 1691915) (-1036 "REDORDER.spad" 1690496 1690513 1691280 1691285) (-1035 "RECLOS.spad" 1689279 1689299 1689983 1690076) (-1034 "REALSOLV.spad" 1688419 1688428 1689269 1689274) (-1033 "REAL.spad" 1688291 1688300 1688409 1688414) (-1032 "REAL0Q.spad" 1685589 1685604 1688281 1688286) (-1031 "REAL0.spad" 1682433 1682448 1685579 1685584) (-1030 "RDUCEAST.spad" 1682154 1682163 1682423 1682428) (-1029 "RDIV.spad" 1681809 1681834 1682144 1682149) (-1028 "RDIST.spad" 1681376 1681387 1681799 1681804) (-1027 "RDETRS.spad" 1680240 1680258 1681366 1681371) (-1026 "RDETR.spad" 1678379 1678397 1680230 1680235) (-1025 "RDEEFS.spad" 1677478 1677495 1678369 1678374) (-1024 "RDEEF.spad" 1676488 1676505 1677468 1677473) (-1023 "RCFIELD.spad" 1673674 1673683 1676390 1676483) (-1022 "RCFIELD.spad" 1670946 1670957 1673664 1673669) (-1021 "RCAGG.spad" 1668874 1668885 1670936 1670941) (-1020 "RCAGG.spad" 1666729 1666742 1668793 1668798) (-1019 "RATRET.spad" 1666089 1666100 1666719 1666724) (-1018 "RATFACT.spad" 1665781 1665793 1666079 1666084) (-1017 "RANDSRC.spad" 1665100 1665109 1665771 1665776) (-1016 "RADUTIL.spad" 1664856 1664865 1665090 1665095) (-1015 "RADIX.spad" 1661777 1661791 1663323 1663416) (-1014 "RADFF.spad" 1660190 1660227 1660309 1660465) (-1013 "RADCAT.spad" 1659785 1659794 1660180 1660185) (-1012 "RADCAT.spad" 1659378 1659389 1659775 1659780) (-1011 "QUEUE.spad" 1658726 1658737 1658985 1659012) (-1010 "QUAT.spad" 1657307 1657318 1657650 1657715) (-1009 "QUATCT2.spad" 1656927 1656946 1657297 1657302) (-1008 "QUATCAT.spad" 1655097 1655108 1656857 1656922) (-1007 "QUATCAT.spad" 1653018 1653031 1654780 1654785) (-1006 "QUAGG.spad" 1651845 1651856 1652986 1653013) (-1005 "QQUTAST.spad" 1651613 1651622 1651835 1651840) (-1004 "QFORM.spad" 1651231 1651246 1651603 1651608) (-1003 "QFCAT.spad" 1649933 1649944 1651133 1651226) (-1002 "QFCAT.spad" 1648226 1648239 1649428 1649433) (-1001 "QFCAT2.spad" 1647918 1647935 1648216 1648221) (-1000 "QEQUAT.spad" 1647476 1647485 1647908 1647913) (-999 "QCMPACK.spad" 1642223 1642242 1647466 1647471) (-998 "QALGSET.spad" 1638302 1638334 1642137 1642142) (-997 "QALGSET2.spad" 1636298 1636316 1638292 1638297) (-996 "PWFFINTB.spad" 1633714 1633735 1636288 1636293) (-995 "PUSHVAR.spad" 1633053 1633072 1633704 1633709) (-994 "PTRANFN.spad" 1629181 1629191 1633043 1633048) (-993 "PTPACK.spad" 1626269 1626279 1629171 1629176) (-992 "PTFUNC2.spad" 1626092 1626106 1626259 1626264) (-991 "PTCAT.spad" 1625347 1625357 1626060 1626087) (-990 "PSQFR.spad" 1624654 1624678 1625337 1625342) (-989 "PSEUDLIN.spad" 1623540 1623550 1624644 1624649) (-988 "PSETPK.spad" 1608973 1608989 1623418 1623423) (-987 "PSETCAT.spad" 1602893 1602916 1608953 1608968) (-986 "PSETCAT.spad" 1596787 1596812 1602849 1602854) (-985 "PSCURVE.spad" 1595770 1595778 1596777 1596782) (-984 "PSCAT.spad" 1594553 1594582 1595668 1595765) (-983 "PSCAT.spad" 1593426 1593457 1594543 1594548) (-982 "PRTITION.spad" 1592124 1592132 1593416 1593421) (-981 "PRTDAST.spad" 1591843 1591851 1592114 1592119) (-980 "PRS.spad" 1581405 1581422 1591799 1591804) (-979 "PRQAGG.spad" 1580840 1580850 1581373 1581400) (-978 "PROPLOG.spad" 1580412 1580420 1580830 1580835) (-977 "PROPFUN2.spad" 1580035 1580048 1580402 1580407) (-976 "PROPFUN1.spad" 1579433 1579444 1580025 1580030) (-975 "PROPFRML.spad" 1578001 1578012 1579423 1579428) (-974 "PROPERTY.spad" 1577489 1577497 1577991 1577996) (-973 "PRODUCT.spad" 1575171 1575183 1575455 1575510) (-972 "PR.spad" 1573563 1573575 1574262 1574389) (-971 "PRINT.spad" 1573315 1573323 1573553 1573558) (-970 "PRIMES.spad" 1571568 1571578 1573305 1573310) (-969 "PRIMELT.spad" 1569649 1569663 1571558 1571563) (-968 "PRIMCAT.spad" 1569276 1569284 1569639 1569644) (-967 "PRIMARR.spad" 1568281 1568291 1568459 1568486) (-966 "PRIMARR2.spad" 1567048 1567060 1568271 1568276) (-965 "PREASSOC.spad" 1566430 1566442 1567038 1567043) (-964 "PPCURVE.spad" 1565567 1565575 1566420 1566425) (-963 "PORTNUM.spad" 1565342 1565350 1565557 1565562) (-962 "POLYROOT.spad" 1564191 1564213 1565298 1565303) (-961 "POLY.spad" 1561526 1561536 1562041 1562168) (-960 "POLYLIFT.spad" 1560791 1560814 1561516 1561521) (-959 "POLYCATQ.spad" 1558909 1558931 1560781 1560786) (-958 "POLYCAT.spad" 1552379 1552400 1558777 1558904) (-957 "POLYCAT.spad" 1545187 1545210 1551587 1551592) (-956 "POLY2UP.spad" 1544639 1544653 1545177 1545182) (-955 "POLY2.spad" 1544236 1544248 1544629 1544634) (-954 "POLUTIL.spad" 1543177 1543206 1544192 1544197) (-953 "POLTOPOL.spad" 1541925 1541940 1543167 1543172) (-952 "POINT.spad" 1540763 1540773 1540850 1540877) (-951 "PNTHEORY.spad" 1537465 1537473 1540753 1540758) (-950 "PMTOOLS.spad" 1536240 1536254 1537455 1537460) (-949 "PMSYM.spad" 1535789 1535799 1536230 1536235) (-948 "PMQFCAT.spad" 1535380 1535394 1535779 1535784) (-947 "PMPRED.spad" 1534859 1534873 1535370 1535375) (-946 "PMPREDFS.spad" 1534313 1534335 1534849 1534854) (-945 "PMPLCAT.spad" 1533393 1533411 1534245 1534250) (-944 "PMLSAGG.spad" 1532978 1532992 1533383 1533388) (-943 "PMKERNEL.spad" 1532557 1532569 1532968 1532973) (-942 "PMINS.spad" 1532137 1532147 1532547 1532552) (-941 "PMFS.spad" 1531714 1531732 1532127 1532132) (-940 "PMDOWN.spad" 1531004 1531018 1531704 1531709) (-939 "PMASS.spad" 1530014 1530022 1530994 1530999) (-938 "PMASSFS.spad" 1528981 1528997 1530004 1530009) (-937 "PLOTTOOL.spad" 1528761 1528769 1528971 1528976) (-936 "PLOT.spad" 1523684 1523692 1528751 1528756) (-935 "PLOT3D.spad" 1520148 1520156 1523674 1523679) (-934 "PLOT1.spad" 1519305 1519315 1520138 1520143) (-933 "PLEQN.spad" 1506595 1506622 1519295 1519300) (-932 "PINTERP.spad" 1506217 1506236 1506585 1506590) (-931 "PINTERPA.spad" 1506001 1506017 1506207 1506212) (-930 "PI.spad" 1505610 1505618 1505975 1505996) (-929 "PID.spad" 1504580 1504588 1505536 1505605) (-928 "PICOERCE.spad" 1504237 1504247 1504570 1504575) (-927 "PGROEB.spad" 1502838 1502852 1504227 1504232) (-926 "PGE.spad" 1494455 1494463 1502828 1502833) (-925 "PGCD.spad" 1493345 1493362 1494445 1494450) (-924 "PFRPAC.spad" 1492494 1492504 1493335 1493340) (-923 "PFR.spad" 1489157 1489167 1492396 1492489) (-922 "PFOTOOLS.spad" 1488415 1488431 1489147 1489152) (-921 "PFOQ.spad" 1487785 1487803 1488405 1488410) (-920 "PFO.spad" 1487204 1487231 1487775 1487780) (-919 "PF.spad" 1486778 1486790 1487009 1487102) (-918 "PFECAT.spad" 1484460 1484468 1486704 1486773) (-917 "PFECAT.spad" 1482170 1482180 1484416 1484421) (-916 "PFBRU.spad" 1480058 1480070 1482160 1482165) (-915 "PFBR.spad" 1477618 1477641 1480048 1480053) (-914 "PERM.spad" 1473425 1473435 1477448 1477463) (-913 "PERMGRP.spad" 1468195 1468205 1473415 1473420) (-912 "PERMCAT.spad" 1466856 1466866 1468175 1468190) (-911 "PERMAN.spad" 1465388 1465402 1466846 1466851) (-910 "PENDTREE.spad" 1464729 1464739 1465017 1465022) (-909 "PDRING.spad" 1463280 1463290 1464709 1464724) (-908 "PDRING.spad" 1461839 1461851 1463270 1463275) (-907 "PDEPROB.spad" 1460854 1460862 1461829 1461834) (-906 "PDEPACK.spad" 1454894 1454902 1460844 1460849) (-905 "PDECOMP.spad" 1454364 1454381 1454884 1454889) (-904 "PDECAT.spad" 1452720 1452728 1454354 1454359) (-903 "PCOMP.spad" 1452573 1452586 1452710 1452715) (-902 "PBWLB.spad" 1451161 1451178 1452563 1452568) (-901 "PATTERN.spad" 1445700 1445710 1451151 1451156) (-900 "PATTERN2.spad" 1445438 1445450 1445690 1445695) (-899 "PATTERN1.spad" 1443774 1443790 1445428 1445433) (-898 "PATRES.spad" 1441349 1441361 1443764 1443769) (-897 "PATRES2.spad" 1441021 1441035 1441339 1441344) (-896 "PATMATCH.spad" 1439218 1439249 1440729 1440734) (-895 "PATMAB.spad" 1438647 1438657 1439208 1439213) (-894 "PATLRES.spad" 1437733 1437747 1438637 1438642) (-893 "PATAB.spad" 1437497 1437507 1437723 1437728) (-892 "PARTPERM.spad" 1435505 1435513 1437487 1437492) (-891 "PARSURF.spad" 1434939 1434967 1435495 1435500) (-890 "PARSU2.spad" 1434736 1434752 1434929 1434934) (-889 "script-parser.spad" 1434256 1434264 1434726 1434731) (-888 "PARSCURV.spad" 1433690 1433718 1434246 1434251) (-887 "PARSC2.spad" 1433481 1433497 1433680 1433685) (-886 "PARPCURV.spad" 1432943 1432971 1433471 1433476) (-885 "PARPC2.spad" 1432734 1432750 1432933 1432938) (-884 "PARAMAST.spad" 1431862 1431870 1432724 1432729) (-883 "PAN2EXPR.spad" 1431274 1431282 1431852 1431857) (-882 "PALETTE.spad" 1430244 1430252 1431264 1431269) (-881 "PAIR.spad" 1429231 1429244 1429832 1429837) (-880 "PADICRC.spad" 1426565 1426583 1427736 1427829) (-879 "PADICRAT.spad" 1424580 1424592 1424801 1424894) (-878 "PADIC.spad" 1424275 1424287 1424506 1424575) (-877 "PADICCT.spad" 1422824 1422836 1424201 1424270) (-876 "PADEPAC.spad" 1421513 1421532 1422814 1422819) (-875 "PADE.spad" 1420265 1420281 1421503 1421508) (-874 "OWP.spad" 1419505 1419535 1420123 1420190) (-873 "OVERSET.spad" 1419078 1419086 1419495 1419500) (-872 "OVAR.spad" 1418859 1418882 1419068 1419073) (-871 "OUT.spad" 1417945 1417953 1418849 1418854) (-870 "OUTFORM.spad" 1407337 1407345 1417935 1417940) (-869 "OUTBFILE.spad" 1406755 1406763 1407327 1407332) (-868 "OUTBCON.spad" 1405761 1405769 1406745 1406750) (-867 "OUTBCON.spad" 1404765 1404775 1405751 1405756) (-866 "OSI.spad" 1404240 1404248 1404755 1404760) (-865 "OSGROUP.spad" 1404158 1404166 1404230 1404235) (-864 "ORTHPOL.spad" 1402643 1402653 1404075 1404080) (-863 "OREUP.spad" 1402096 1402124 1402323 1402362) (-862 "ORESUP.spad" 1401397 1401421 1401776 1401815) (-861 "OREPCTO.spad" 1399254 1399266 1401317 1401322) (-860 "OREPCAT.spad" 1393401 1393411 1399210 1399249) (-859 "OREPCAT.spad" 1387438 1387450 1393249 1393254) (-858 "ORDSET.spad" 1386610 1386618 1387428 1387433) (-857 "ORDSET.spad" 1385780 1385790 1386600 1386605) (-856 "ORDRING.spad" 1385170 1385178 1385760 1385775) (-855 "ORDRING.spad" 1384568 1384578 1385160 1385165) (-854 "ORDMON.spad" 1384423 1384431 1384558 1384563) (-853 "ORDFUNS.spad" 1383555 1383571 1384413 1384418) (-852 "ORDFIN.spad" 1383375 1383383 1383545 1383550) (-851 "ORDCOMP.spad" 1381840 1381850 1382922 1382951) (-850 "ORDCOMP2.spad" 1381133 1381145 1381830 1381835) (-849 "OPTPROB.spad" 1379771 1379779 1381123 1381128) (-848 "OPTPACK.spad" 1372180 1372188 1379761 1379766) (-847 "OPTCAT.spad" 1369859 1369867 1372170 1372175) (-846 "OPSIG.spad" 1369513 1369521 1369849 1369854) (-845 "OPQUERY.spad" 1369062 1369070 1369503 1369508) (-844 "OP.spad" 1368804 1368814 1368884 1368951) (-843 "OPERCAT.spad" 1368270 1368280 1368794 1368799) (-842 "OPERCAT.spad" 1367734 1367746 1368260 1368265) (-841 "ONECOMP.spad" 1366479 1366489 1367281 1367310) (-840 "ONECOMP2.spad" 1365903 1365915 1366469 1366474) (-839 "OMSERVER.spad" 1364909 1364917 1365893 1365898) (-838 "OMSAGG.spad" 1364697 1364707 1364865 1364904) (-837 "OMPKG.spad" 1363313 1363321 1364687 1364692) (-836 "OM.spad" 1362286 1362294 1363303 1363308) (-835 "OMLO.spad" 1361711 1361723 1362172 1362211) (-834 "OMEXPR.spad" 1361545 1361555 1361701 1361706) (-833 "OMERR.spad" 1361090 1361098 1361535 1361540) (-832 "OMERRK.spad" 1360124 1360132 1361080 1361085) (-831 "OMENC.spad" 1359468 1359476 1360114 1360119) (-830 "OMDEV.spad" 1353777 1353785 1359458 1359463) (-829 "OMCONN.spad" 1353186 1353194 1353767 1353772) (-828 "OINTDOM.spad" 1352949 1352957 1353112 1353181) (-827 "OFMONOID.spad" 1351072 1351082 1352905 1352910) (-826 "ODVAR.spad" 1350333 1350343 1351062 1351067) (-825 "ODR.spad" 1349977 1350003 1350145 1350294) (-824 "ODPOL.spad" 1347359 1347369 1347699 1347826) (-823 "ODP.spad" 1337206 1337226 1337579 1337710) (-822 "ODETOOLS.spad" 1335855 1335874 1337196 1337201) (-821 "ODESYS.spad" 1333549 1333566 1335845 1335850) (-820 "ODERTRIC.spad" 1329558 1329575 1333506 1333511) (-819 "ODERED.spad" 1328957 1328981 1329548 1329553) (-818 "ODERAT.spad" 1326572 1326589 1328947 1328952) (-817 "ODEPRRIC.spad" 1323609 1323631 1326562 1326567) (-816 "ODEPROB.spad" 1322866 1322874 1323599 1323604) (-815 "ODEPRIM.spad" 1320200 1320222 1322856 1322861) (-814 "ODEPAL.spad" 1319586 1319610 1320190 1320195) (-813 "ODEPACK.spad" 1306252 1306260 1319576 1319581) (-812 "ODEINT.spad" 1305687 1305703 1306242 1306247) (-811 "ODEIFTBL.spad" 1303082 1303090 1305677 1305682) (-810 "ODEEF.spad" 1298573 1298589 1303072 1303077) (-809 "ODECONST.spad" 1298110 1298128 1298563 1298568) (-808 "ODECAT.spad" 1296708 1296716 1298100 1298105) (-807 "OCT.spad" 1294844 1294854 1295558 1295597) (-806 "OCTCT2.spad" 1294490 1294511 1294834 1294839) (-805 "OC.spad" 1292286 1292296 1294446 1294485) (-804 "OC.spad" 1289807 1289819 1291969 1291974) (-803 "OCAMON.spad" 1289655 1289663 1289797 1289802) (-802 "OASGP.spad" 1289470 1289478 1289645 1289650) (-801 "OAMONS.spad" 1288992 1289000 1289460 1289465) (-800 "OAMON.spad" 1288853 1288861 1288982 1288987) (-799 "OAGROUP.spad" 1288715 1288723 1288843 1288848) (-798 "NUMTUBE.spad" 1288306 1288322 1288705 1288710) (-797 "NUMQUAD.spad" 1276282 1276290 1288296 1288301) (-796 "NUMODE.spad" 1267636 1267644 1276272 1276277) (-795 "NUMINT.spad" 1265202 1265210 1267626 1267631) (-794 "NUMFMT.spad" 1264042 1264050 1265192 1265197) (-793 "NUMERIC.spad" 1256156 1256166 1263847 1263852) (-792 "NTSCAT.spad" 1254664 1254680 1256124 1256151) (-791 "NTPOLFN.spad" 1254215 1254225 1254581 1254586) (-790 "NSUP.spad" 1247261 1247271 1251801 1251954) (-789 "NSUP2.spad" 1246653 1246665 1247251 1247256) (-788 "NSMP.spad" 1242883 1242902 1243191 1243318) (-787 "NREP.spad" 1241261 1241275 1242873 1242878) (-786 "NPCOEF.spad" 1240507 1240527 1241251 1241256) (-785 "NORMRETR.spad" 1240105 1240144 1240497 1240502) (-784 "NORMPK.spad" 1238007 1238026 1240095 1240100) (-783 "NORMMA.spad" 1237695 1237721 1237997 1238002) (-782 "NONE.spad" 1237436 1237444 1237685 1237690) (-781 "NONE1.spad" 1237112 1237122 1237426 1237431) (-780 "NODE1.spad" 1236599 1236615 1237102 1237107) (-779 "NNI.spad" 1235494 1235502 1236573 1236594) (-778 "NLINSOL.spad" 1234120 1234130 1235484 1235489) (-777 "NIPROB.spad" 1232661 1232669 1234110 1234115) (-776 "NFINTBAS.spad" 1230221 1230238 1232651 1232656) (-775 "NETCLT.spad" 1230195 1230206 1230211 1230216) (-774 "NCODIV.spad" 1228411 1228427 1230185 1230190) (-773 "NCNTFRAC.spad" 1228053 1228067 1228401 1228406) (-772 "NCEP.spad" 1226219 1226233 1228043 1228048) (-771 "NASRING.spad" 1225815 1225823 1226209 1226214) (-770 "NASRING.spad" 1225409 1225419 1225805 1225810) (-769 "NARNG.spad" 1224761 1224769 1225399 1225404) (-768 "NARNG.spad" 1224111 1224121 1224751 1224756) (-767 "NAGSP.spad" 1223188 1223196 1224101 1224106) (-766 "NAGS.spad" 1212849 1212857 1223178 1223183) (-765 "NAGF07.spad" 1211280 1211288 1212839 1212844) (-764 "NAGF04.spad" 1205682 1205690 1211270 1211275) (-763 "NAGF02.spad" 1199751 1199759 1205672 1205677) (-762 "NAGF01.spad" 1195512 1195520 1199741 1199746) (-761 "NAGE04.spad" 1189212 1189220 1195502 1195507) (-760 "NAGE02.spad" 1179872 1179880 1189202 1189207) (-759 "NAGE01.spad" 1175874 1175882 1179862 1179867) (-758 "NAGD03.spad" 1173878 1173886 1175864 1175869) (-757 "NAGD02.spad" 1166625 1166633 1173868 1173873) (-756 "NAGD01.spad" 1160918 1160926 1166615 1166620) (-755 "NAGC06.spad" 1156793 1156801 1160908 1160913) (-754 "NAGC05.spad" 1155294 1155302 1156783 1156788) (-753 "NAGC02.spad" 1154561 1154569 1155284 1155289) (-752 "NAALG.spad" 1154102 1154112 1154529 1154556) (-751 "NAALG.spad" 1153663 1153675 1154092 1154097) (-750 "MULTSQFR.spad" 1150621 1150638 1153653 1153658) (-749 "MULTFACT.spad" 1150004 1150021 1150611 1150616) (-748 "MTSCAT.spad" 1148098 1148119 1149902 1149999) (-747 "MTHING.spad" 1147757 1147767 1148088 1148093) (-746 "MSYSCMD.spad" 1147191 1147199 1147747 1147752) (-745 "MSET.spad" 1145149 1145159 1146897 1146936) (-744 "MSETAGG.spad" 1144994 1145004 1145117 1145144) (-743 "MRING.spad" 1141971 1141983 1144702 1144769) (-742 "MRF2.spad" 1141541 1141555 1141961 1141966) (-741 "MRATFAC.spad" 1141087 1141104 1141531 1141536) (-740 "MPRFF.spad" 1139127 1139146 1141077 1141082) (-739 "MPOLY.spad" 1136598 1136613 1136957 1137084) (-738 "MPCPF.spad" 1135862 1135881 1136588 1136593) (-737 "MPC3.spad" 1135679 1135719 1135852 1135857) (-736 "MPC2.spad" 1135325 1135358 1135669 1135674) (-735 "MONOTOOL.spad" 1133676 1133693 1135315 1135320) (-734 "MONOID.spad" 1132995 1133003 1133666 1133671) (-733 "MONOID.spad" 1132312 1132322 1132985 1132990) (-732 "MONOGEN.spad" 1131060 1131073 1132172 1132307) (-731 "MONOGEN.spad" 1129830 1129845 1130944 1130949) (-730 "MONADWU.spad" 1127860 1127868 1129820 1129825) (-729 "MONADWU.spad" 1125888 1125898 1127850 1127855) (-728 "MONAD.spad" 1125048 1125056 1125878 1125883) (-727 "MONAD.spad" 1124206 1124216 1125038 1125043) (-726 "MOEBIUS.spad" 1122942 1122956 1124186 1124201) (-725 "MODULE.spad" 1122812 1122822 1122910 1122937) (-724 "MODULE.spad" 1122702 1122714 1122802 1122807) (-723 "MODRING.spad" 1122037 1122076 1122682 1122697) (-722 "MODOP.spad" 1120702 1120714 1121859 1121926) (-721 "MODMONOM.spad" 1120433 1120451 1120692 1120697) (-720 "MODMON.spad" 1117228 1117244 1117947 1118100) (-719 "MODFIELD.spad" 1116590 1116629 1117130 1117223) (-718 "MMLFORM.spad" 1115450 1115458 1116580 1116585) (-717 "MMAP.spad" 1115192 1115226 1115440 1115445) (-716 "MLO.spad" 1113651 1113661 1115148 1115187) (-715 "MLIFT.spad" 1112263 1112280 1113641 1113646) (-714 "MKUCFUNC.spad" 1111798 1111816 1112253 1112258) (-713 "MKRECORD.spad" 1111402 1111415 1111788 1111793) (-712 "MKFUNC.spad" 1110809 1110819 1111392 1111397) (-711 "MKFLCFN.spad" 1109777 1109787 1110799 1110804) (-710 "MKBCFUNC.spad" 1109272 1109290 1109767 1109772) (-709 "MINT.spad" 1108711 1108719 1109174 1109267) (-708 "MHROWRED.spad" 1107222 1107232 1108701 1108706) (-707 "MFLOAT.spad" 1105742 1105750 1107112 1107217) (-706 "MFINFACT.spad" 1105142 1105164 1105732 1105737) (-705 "MESH.spad" 1102924 1102932 1105132 1105137) (-704 "MDDFACT.spad" 1101135 1101145 1102914 1102919) (-703 "MDAGG.spad" 1100426 1100436 1101115 1101130) (-702 "MCMPLX.spad" 1096437 1096445 1097051 1097252) (-701 "MCDEN.spad" 1095647 1095659 1096427 1096432) (-700 "MCALCFN.spad" 1092769 1092795 1095637 1095642) (-699 "MAYBE.spad" 1092053 1092064 1092759 1092764) (-698 "MATSTOR.spad" 1089361 1089371 1092043 1092048) (-697 "MATRIX.spad" 1088065 1088075 1088549 1088576) (-696 "MATLIN.spad" 1085409 1085433 1087949 1087954) (-695 "MATCAT.spad" 1077138 1077160 1085377 1085404) (-694 "MATCAT.spad" 1068739 1068763 1076980 1076985) (-693 "MATCAT2.spad" 1068021 1068069 1068729 1068734) (-692 "MAPPKG3.spad" 1066936 1066950 1068011 1068016) (-691 "MAPPKG2.spad" 1066274 1066286 1066926 1066931) (-690 "MAPPKG1.spad" 1065102 1065112 1066264 1066269) (-689 "MAPPAST.spad" 1064417 1064425 1065092 1065097) (-688 "MAPHACK3.spad" 1064229 1064243 1064407 1064412) (-687 "MAPHACK2.spad" 1063998 1064010 1064219 1064224) (-686 "MAPHACK1.spad" 1063642 1063652 1063988 1063993) (-685 "MAGMA.spad" 1061432 1061449 1063632 1063637) (-684 "MACROAST.spad" 1061011 1061019 1061422 1061427) (-683 "M3D.spad" 1058731 1058741 1060389 1060394) (-682 "LZSTAGG.spad" 1055969 1055979 1058721 1058726) (-681 "LZSTAGG.spad" 1053205 1053217 1055959 1055964) (-680 "LWORD.spad" 1049910 1049927 1053195 1053200) (-679 "LSTAST.spad" 1049694 1049702 1049900 1049905) (-678 "LSQM.spad" 1047924 1047938 1048318 1048369) (-677 "LSPP.spad" 1047459 1047476 1047914 1047919) (-676 "LSMP.spad" 1046309 1046337 1047449 1047454) (-675 "LSMP1.spad" 1044127 1044141 1046299 1046304) (-674 "LSAGG.spad" 1043796 1043806 1044095 1044122) (-673 "LSAGG.spad" 1043485 1043497 1043786 1043791) (-672 "LPOLY.spad" 1042439 1042458 1043341 1043410) (-671 "LPEFRAC.spad" 1041710 1041720 1042429 1042434) (-670 "LO.spad" 1041111 1041125 1041644 1041671) (-669 "LOGIC.spad" 1040713 1040721 1041101 1041106) (-668 "LOGIC.spad" 1040313 1040323 1040703 1040708) (-667 "LODOOPS.spad" 1039243 1039255 1040303 1040308) (-666 "LODO.spad" 1038627 1038643 1038923 1038962) (-665 "LODOF.spad" 1037673 1037690 1038584 1038589) (-664 "LODOCAT.spad" 1036339 1036349 1037629 1037668) (-663 "LODOCAT.spad" 1035003 1035015 1036295 1036300) (-662 "LODO2.spad" 1034276 1034288 1034683 1034722) (-661 "LODO1.spad" 1033676 1033686 1033956 1033995) (-660 "LODEEF.spad" 1032478 1032496 1033666 1033671) (-659 "LNAGG.spad" 1028625 1028635 1032468 1032473) (-658 "LNAGG.spad" 1024736 1024748 1028581 1028586) (-657 "LMOPS.spad" 1021504 1021521 1024726 1024731) (-656 "LMODULE.spad" 1021272 1021282 1021494 1021499) (-655 "LMDICT.spad" 1020559 1020569 1020823 1020850) (-654 "LLINSET.spad" 1019956 1019966 1020549 1020554) (-653 "LITERAL.spad" 1019862 1019873 1019946 1019951) (-652 "LIST.spad" 1017597 1017607 1019009 1019036) (-651 "LIST3.spad" 1016908 1016922 1017587 1017592) (-650 "LIST2.spad" 1015610 1015622 1016898 1016903) (-649 "LIST2MAP.spad" 1012513 1012525 1015600 1015605) (-648 "LINSET.spad" 1012135 1012145 1012503 1012508) (-647 "LINEXP.spad" 1011569 1011579 1012115 1012130) (-646 "LINDEP.spad" 1010378 1010390 1011481 1011486) (-645 "LIMITRF.spad" 1008306 1008316 1010368 1010373) (-644 "LIMITPS.spad" 1007209 1007222 1008296 1008301) (-643 "LIE.spad" 1005225 1005237 1006499 1006644) (-642 "LIECAT.spad" 1004701 1004711 1005151 1005220) (-641 "LIECAT.spad" 1004205 1004217 1004657 1004662) (-640 "LIB.spad" 1002418 1002426 1002864 1002879) (-639 "LGROBP.spad" 999771 999790 1002408 1002413) (-638 "LF.spad" 998726 998742 999761 999766) (-637 "LFCAT.spad" 997785 997793 998716 998721) (-636 "LEXTRIPK.spad" 993288 993303 997775 997780) (-635 "LEXP.spad" 991291 991318 993268 993283) (-634 "LETAST.spad" 990990 990998 991281 991286) (-633 "LEADCDET.spad" 989388 989405 990980 990985) (-632 "LAZM3PK.spad" 988092 988114 989378 989383) (-631 "LAUPOL.spad" 986785 986798 987685 987754) (-630 "LAPLACE.spad" 986368 986384 986775 986780) (-629 "LA.spad" 985808 985822 986290 986329) (-628 "LALG.spad" 985584 985594 985788 985803) (-627 "LALG.spad" 985368 985380 985574 985579) (-626 "KVTFROM.spad" 985103 985113 985358 985363) (-625 "KTVLOGIC.spad" 984615 984623 985093 985098) (-624 "KRCFROM.spad" 984353 984363 984605 984610) (-623 "KOVACIC.spad" 983076 983093 984343 984348) (-622 "KONVERT.spad" 982798 982808 983066 983071) (-621 "KOERCE.spad" 982535 982545 982788 982793) (-620 "KERNEL.spad" 981190 981200 982319 982324) (-619 "KERNEL2.spad" 980893 980905 981180 981185) (-618 "KDAGG.spad" 980002 980024 980873 980888) (-617 "KDAGG.spad" 979119 979143 979992 979997) (-616 "KAFILE.spad" 978082 978098 978317 978344) (-615 "JORDAN.spad" 975911 975923 977372 977517) (-614 "JOINAST.spad" 975605 975613 975901 975906) (-613 "JAVACODE.spad" 975471 975479 975595 975600) (-612 "IXAGG.spad" 973604 973628 975461 975466) (-611 "IXAGG.spad" 971592 971618 973451 973456) (-610 "IVECTOR.spad" 970362 970377 970517 970544) (-609 "ITUPLE.spad" 969523 969533 970352 970357) (-608 "ITRIGMNP.spad" 968362 968381 969513 969518) (-607 "ITFUN3.spad" 967868 967882 968352 968357) (-606 "ITFUN2.spad" 967612 967624 967858 967863) (-605 "ITFORM.spad" 966967 966975 967602 967607) (-604 "ITAYLOR.spad" 964961 964976 966831 966928) (-603 "ISUPS.spad" 957398 957413 963935 964032) (-602 "ISUMP.spad" 956899 956915 957388 957393) (-601 "ISTRING.spad" 955987 956000 956068 956095) (-600 "ISAST.spad" 955706 955714 955977 955982) (-599 "IRURPK.spad" 954423 954442 955696 955701) (-598 "IRSN.spad" 952395 952403 954413 954418) (-597 "IRRF2F.spad" 950880 950890 952351 952356) (-596 "IRREDFFX.spad" 950481 950492 950870 950875) (-595 "IROOT.spad" 948820 948830 950471 950476) (-594 "IR.spad" 946621 946635 948675 948702) (-593 "IRFORM.spad" 945945 945953 946611 946616) (-592 "IR2.spad" 944973 944989 945935 945940) (-591 "IR2F.spad" 944179 944195 944963 944968) (-590 "IPRNTPK.spad" 943939 943947 944169 944174) (-589 "IPF.spad" 943504 943516 943744 943837) (-588 "IPADIC.spad" 943265 943291 943430 943499) (-587 "IP4ADDR.spad" 942822 942830 943255 943260) (-586 "IOMODE.spad" 942344 942352 942812 942817) (-585 "IOBFILE.spad" 941705 941713 942334 942339) (-584 "IOBCON.spad" 941570 941578 941695 941700) (-583 "INVLAPLA.spad" 941219 941235 941560 941565) (-582 "INTTR.spad" 934601 934618 941209 941214) (-581 "INTTOOLS.spad" 932356 932372 934175 934180) (-580 "INTSLPE.spad" 931676 931684 932346 932351) (-579 "INTRVL.spad" 931242 931252 931590 931671) (-578 "INTRF.spad" 929666 929680 931232 931237) (-577 "INTRET.spad" 929098 929108 929656 929661) (-576 "INTRAT.spad" 927825 927842 929088 929093) (-575 "INTPM.spad" 926210 926226 927468 927473) (-574 "INTPAF.spad" 924074 924092 926142 926147) (-573 "INTPACK.spad" 914448 914456 924064 924069) (-572 "INT.spad" 913896 913904 914302 914443) (-571 "INTHERTR.spad" 913170 913187 913886 913891) (-570 "INTHERAL.spad" 912840 912864 913160 913165) (-569 "INTHEORY.spad" 909279 909287 912830 912835) (-568 "INTG0.spad" 903012 903030 909211 909216) (-567 "INTFTBL.spad" 897041 897049 903002 903007) (-566 "INTFACT.spad" 896100 896110 897031 897036) (-565 "INTEF.spad" 894485 894501 896090 896095) (-564 "INTDOM.spad" 893108 893116 894411 894480) (-563 "INTDOM.spad" 891793 891803 893098 893103) (-562 "INTCAT.spad" 890052 890062 891707 891788) (-561 "INTBIT.spad" 889559 889567 890042 890047) (-560 "INTALG.spad" 888747 888774 889549 889554) (-559 "INTAF.spad" 888247 888263 888737 888742) (-558 "INTABL.spad" 886765 886796 886928 886955) (-557 "INT8.spad" 886645 886653 886755 886760) (-556 "INT64.spad" 886524 886532 886635 886640) (-555 "INT32.spad" 886403 886411 886514 886519) (-554 "INT16.spad" 886282 886290 886393 886398) (-553 "INS.spad" 883785 883793 886184 886277) (-552 "INS.spad" 881374 881384 883775 883780) (-551 "INPSIGN.spad" 880822 880835 881364 881369) (-550 "INPRODPF.spad" 879918 879937 880812 880817) (-549 "INPRODFF.spad" 879006 879030 879908 879913) (-548 "INNMFACT.spad" 877981 877998 878996 879001) (-547 "INMODGCD.spad" 877469 877499 877971 877976) (-546 "INFSP.spad" 875766 875788 877459 877464) (-545 "INFPROD0.spad" 874846 874865 875756 875761) (-544 "INFORM.spad" 872045 872053 874836 874841) (-543 "INFORM1.spad" 871670 871680 872035 872040) (-542 "INFINITY.spad" 871222 871230 871660 871665) (-541 "INETCLTS.spad" 871199 871207 871212 871217) (-540 "INEP.spad" 869737 869759 871189 871194) (-539 "INDE.spad" 869466 869483 869727 869732) (-538 "INCRMAPS.spad" 868887 868897 869456 869461) (-537 "INBFILE.spad" 867959 867967 868877 868882) (-536 "INBFF.spad" 863753 863764 867949 867954) (-535 "INBCON.spad" 862043 862051 863743 863748) (-534 "INBCON.spad" 860331 860341 862033 862038) (-533 "INAST.spad" 859992 860000 860321 860326) (-532 "IMPTAST.spad" 859700 859708 859982 859987) (-531 "IMATRIX.spad" 858645 858671 859157 859184) (-530 "IMATQF.spad" 857739 857783 858601 858606) (-529 "IMATLIN.spad" 856344 856368 857695 857700) (-528 "ILIST.spad" 855002 855017 855527 855554) (-527 "IIARRAY2.spad" 854390 854428 854609 854636) (-526 "IFF.spad" 853800 853816 854071 854164) (-525 "IFAST.spad" 853414 853422 853790 853795) (-524 "IFARRAY.spad" 850907 850922 852597 852624) (-523 "IFAMON.spad" 850769 850786 850863 850868) (-522 "IEVALAB.spad" 850174 850186 850759 850764) (-521 "IEVALAB.spad" 849577 849591 850164 850169) (-520 "IDPO.spad" 849375 849387 849567 849572) (-519 "IDPOAMS.spad" 849131 849143 849365 849370) (-518 "IDPOAM.spad" 848851 848863 849121 849126) (-517 "IDPC.spad" 847789 847801 848841 848846) (-516 "IDPAM.spad" 847534 847546 847779 847784) (-515 "IDPAG.spad" 847281 847293 847524 847529) (-514 "IDENT.spad" 846931 846939 847271 847276) (-513 "IDECOMP.spad" 844170 844188 846921 846926) (-512 "IDEAL.spad" 839119 839158 844105 844110) (-511 "ICDEN.spad" 838308 838324 839109 839114) (-510 "ICARD.spad" 837499 837507 838298 838303) (-509 "IBPTOOLS.spad" 836106 836123 837489 837494) (-508 "IBITS.spad" 835309 835322 835742 835769) (-507 "IBATOOL.spad" 832286 832305 835299 835304) (-506 "IBACHIN.spad" 830793 830808 832276 832281) (-505 "IARRAY2.spad" 829781 829807 830400 830427) (-504 "IARRAY1.spad" 828826 828841 828964 828991) (-503 "IAN.spad" 827049 827057 828642 828735) (-502 "IALGFACT.spad" 826652 826685 827039 827044) (-501 "HYPCAT.spad" 826076 826084 826642 826647) (-500 "HYPCAT.spad" 825498 825508 826066 826071) (-499 "HOSTNAME.spad" 825306 825314 825488 825493) (-498 "HOMOTOP.spad" 825049 825059 825296 825301) (-497 "HOAGG.spad" 822331 822341 825039 825044) (-496 "HOAGG.spad" 819388 819400 822098 822103) (-495 "HEXADEC.spad" 817490 817498 817855 817948) (-494 "HEUGCD.spad" 816525 816536 817480 817485) (-493 "HELLFDIV.spad" 816115 816139 816515 816520) (-492 "HEAP.spad" 815507 815517 815722 815749) (-491 "HEADAST.spad" 815040 815048 815497 815502) (-490 "HDP.spad" 804883 804899 805260 805391) (-489 "HDMP.spad" 802097 802112 802713 802840) (-488 "HB.spad" 800348 800356 802087 802092) (-487 "HASHTBL.spad" 798818 798849 799029 799056) (-486 "HASAST.spad" 798534 798542 798808 798813) (-485 "HACKPI.spad" 798025 798033 798436 798529) (-484 "GTSET.spad" 796964 796980 797671 797698) (-483 "GSTBL.spad" 795483 795518 795657 795672) (-482 "GSERIES.spad" 792654 792681 793615 793764) (-481 "GROUP.spad" 791927 791935 792634 792649) (-480 "GROUP.spad" 791208 791218 791917 791922) (-479 "GROEBSOL.spad" 789702 789723 791198 791203) (-478 "GRMOD.spad" 788273 788285 789692 789697) (-477 "GRMOD.spad" 786842 786856 788263 788268) (-476 "GRIMAGE.spad" 779731 779739 786832 786837) (-475 "GRDEF.spad" 778110 778118 779721 779726) (-474 "GRAY.spad" 776573 776581 778100 778105) (-473 "GRALG.spad" 775650 775662 776563 776568) (-472 "GRALG.spad" 774725 774739 775640 775645) (-471 "GPOLSET.spad" 774179 774202 774407 774434) (-470 "GOSPER.spad" 773448 773466 774169 774174) (-469 "GMODPOL.spad" 772596 772623 773416 773443) (-468 "GHENSEL.spad" 771679 771693 772586 772591) (-467 "GENUPS.spad" 767972 767985 771669 771674) (-466 "GENUFACT.spad" 767549 767559 767962 767967) (-465 "GENPGCD.spad" 767135 767152 767539 767544) (-464 "GENMFACT.spad" 766587 766606 767125 767130) (-463 "GENEEZ.spad" 764538 764551 766577 766582) (-462 "GDMP.spad" 761594 761611 762368 762495) (-461 "GCNAALG.spad" 755517 755544 761388 761455) (-460 "GCDDOM.spad" 754693 754701 755443 755512) (-459 "GCDDOM.spad" 753931 753941 754683 754688) (-458 "GB.spad" 751457 751495 753887 753892) (-457 "GBINTERN.spad" 747477 747515 751447 751452) (-456 "GBF.spad" 743244 743282 747467 747472) (-455 "GBEUCLID.spad" 741126 741164 743234 743239) (-454 "GAUSSFAC.spad" 740439 740447 741116 741121) (-453 "GALUTIL.spad" 738765 738775 740395 740400) (-452 "GALPOLYU.spad" 737219 737232 738755 738760) (-451 "GALFACTU.spad" 735392 735411 737209 737214) (-450 "GALFACT.spad" 725581 725592 735382 735387) (-449 "FVFUN.spad" 722604 722612 725571 725576) (-448 "FVC.spad" 721656 721664 722594 722599) (-447 "FUNDESC.spad" 721334 721342 721646 721651) (-446 "FUNCTION.spad" 721183 721195 721324 721329) (-445 "FT.spad" 719480 719488 721173 721178) (-444 "FTEM.spad" 718645 718653 719470 719475) (-443 "FSUPFACT.spad" 717545 717564 718581 718586) (-442 "FST.spad" 715631 715639 717535 717540) (-441 "FSRED.spad" 715111 715127 715621 715626) (-440 "FSPRMELT.spad" 713993 714009 715068 715073) (-439 "FSPECF.spad" 712084 712100 713983 713988) (-438 "FS.spad" 706352 706362 711859 712079) (-437 "FS.spad" 700398 700410 705907 705912) (-436 "FSINT.spad" 700058 700074 700388 700393) (-435 "FSERIES.spad" 699249 699261 699878 699977) (-434 "FSCINT.spad" 698566 698582 699239 699244) (-433 "FSAGG.spad" 697683 697693 698522 698561) (-432 "FSAGG.spad" 696762 696774 697603 697608) (-431 "FSAGG2.spad" 695505 695521 696752 696757) (-430 "FS2UPS.spad" 689996 690030 695495 695500) (-429 "FS2.spad" 689643 689659 689986 689991) (-428 "FS2EXPXP.spad" 688768 688791 689633 689638) (-427 "FRUTIL.spad" 687722 687732 688758 688763) (-426 "FR.spad" 681290 681300 686598 686667) (-425 "FRNAALG.spad" 676559 676569 681232 681285) (-424 "FRNAALG.spad" 671840 671852 676515 676520) (-423 "FRNAAF2.spad" 671296 671314 671830 671835) (-422 "FRMOD.spad" 670706 670736 671227 671232) (-421 "FRIDEAL.spad" 669931 669952 670686 670701) (-420 "FRIDEAL2.spad" 669535 669567 669921 669926) (-419 "FRETRCT.spad" 669046 669056 669525 669530) (-418 "FRETRCT.spad" 668423 668435 668904 668909) (-417 "FRAMALG.spad" 666771 666784 668379 668418) (-416 "FRAMALG.spad" 665151 665166 666761 666766) (-415 "FRAC.spad" 662250 662260 662653 662826) (-414 "FRAC2.spad" 661855 661867 662240 662245) (-413 "FR2.spad" 661191 661203 661845 661850) (-412 "FPS.spad" 658006 658014 661081 661186) (-411 "FPS.spad" 654849 654859 657926 657931) (-410 "FPC.spad" 653895 653903 654751 654844) (-409 "FPC.spad" 653027 653037 653885 653890) (-408 "FPATMAB.spad" 652789 652799 653017 653022) (-407 "FPARFRAC.spad" 651276 651293 652779 652784) (-406 "FORTRAN.spad" 649782 649825 651266 651271) (-405 "FORT.spad" 648731 648739 649772 649777) (-404 "FORTFN.spad" 645901 645909 648721 648726) (-403 "FORTCAT.spad" 645585 645593 645891 645896) (-402 "FORMULA.spad" 643059 643067 645575 645580) (-401 "FORMULA1.spad" 642538 642548 643049 643054) (-400 "FORDER.spad" 642229 642253 642528 642533) (-399 "FOP.spad" 641430 641438 642219 642224) (-398 "FNLA.spad" 640854 640876 641398 641425) (-397 "FNCAT.spad" 639449 639457 640844 640849) (-396 "FNAME.spad" 639341 639349 639439 639444) (-395 "FMTC.spad" 639139 639147 639267 639336) (-394 "FMONOID.spad" 638804 638814 639095 639100) (-393 "FMONCAT.spad" 635957 635967 638794 638799) (-392 "FM.spad" 635652 635664 635891 635918) (-391 "FMFUN.spad" 632682 632690 635642 635647) (-390 "FMC.spad" 631734 631742 632672 632677) (-389 "FMCAT.spad" 629402 629420 631702 631729) (-388 "FM1.spad" 628759 628771 629336 629363) (-387 "FLOATRP.spad" 626494 626508 628749 628754) (-386 "FLOAT.spad" 619808 619816 626360 626489) (-385 "FLOATCP.spad" 617239 617253 619798 619803) (-384 "FLINEXP.spad" 616951 616961 617219 617234) (-383 "FLINEXP.spad" 616617 616629 616887 616892) (-382 "FLASORT.spad" 615943 615955 616607 616612) (-381 "FLALG.spad" 613589 613608 615869 615938) (-380 "FLAGG.spad" 610631 610641 613569 613584) (-379 "FLAGG.spad" 607574 607586 610514 610519) (-378 "FLAGG2.spad" 606299 606315 607564 607569) (-377 "FINRALG.spad" 604360 604373 606255 606294) (-376 "FINRALG.spad" 602347 602362 604244 604249) (-375 "FINITE.spad" 601499 601507 602337 602342) (-374 "FINAALG.spad" 590620 590630 601441 601494) (-373 "FINAALG.spad" 579753 579765 590576 590581) (-372 "FILE.spad" 579336 579346 579743 579748) (-371 "FILECAT.spad" 577862 577879 579326 579331) (-370 "FIELD.spad" 577268 577276 577764 577857) (-369 "FIELD.spad" 576760 576770 577258 577263) (-368 "FGROUP.spad" 575407 575417 576740 576755) (-367 "FGLMICPK.spad" 574194 574209 575397 575402) (-366 "FFX.spad" 573569 573584 573910 574003) (-365 "FFSLPE.spad" 573072 573093 573559 573564) (-364 "FFPOLY.spad" 564334 564345 573062 573067) (-363 "FFPOLY2.spad" 563394 563411 564324 564329) (-362 "FFP.spad" 562791 562811 563110 563203) (-361 "FF.spad" 562239 562255 562472 562565) (-360 "FFNBX.spad" 560751 560771 561955 562048) (-359 "FFNBP.spad" 559264 559281 560467 560560) (-358 "FFNB.spad" 557729 557750 558945 559038) (-357 "FFINTBAS.spad" 555243 555262 557719 557724) (-356 "FFIELDC.spad" 552820 552828 555145 555238) (-355 "FFIELDC.spad" 550483 550493 552810 552815) (-354 "FFHOM.spad" 549231 549248 550473 550478) (-353 "FFF.spad" 546666 546677 549221 549226) (-352 "FFCGX.spad" 545513 545533 546382 546475) (-351 "FFCGP.spad" 544402 544422 545229 545322) (-350 "FFCG.spad" 543194 543215 544083 544176) (-349 "FFCAT.spad" 536367 536389 543033 543189) (-348 "FFCAT.spad" 529619 529643 536287 536292) (-347 "FFCAT2.spad" 529366 529406 529609 529614) (-346 "FEXPR.spad" 521083 521129 529122 529161) (-345 "FEVALAB.spad" 520791 520801 521073 521078) (-344 "FEVALAB.spad" 520284 520296 520568 520573) (-343 "FDIV.spad" 519726 519750 520274 520279) (-342 "FDIVCAT.spad" 517790 517814 519716 519721) (-341 "FDIVCAT.spad" 515852 515878 517780 517785) (-340 "FDIV2.spad" 515508 515548 515842 515847) (-339 "FCTRDATA.spad" 514516 514524 515498 515503) (-338 "FCPAK1.spad" 513083 513091 514506 514511) (-337 "FCOMP.spad" 512462 512472 513073 513078) (-336 "FC.spad" 502469 502477 512452 512457) (-335 "FAXF.spad" 495440 495454 502371 502464) (-334 "FAXF.spad" 488463 488479 495396 495401) (-333 "FARRAY.spad" 486613 486623 487646 487673) (-332 "FAMR.spad" 484749 484761 486511 486608) (-331 "FAMR.spad" 482869 482883 484633 484638) (-330 "FAMONOID.spad" 482537 482547 482823 482828) (-329 "FAMONC.spad" 480833 480845 482527 482532) (-328 "FAGROUP.spad" 480457 480467 480729 480756) (-327 "FACUTIL.spad" 478661 478678 480447 480452) (-326 "FACTFUNC.spad" 477855 477865 478651 478656) (-325 "EXPUPXS.spad" 474688 474711 475987 476136) (-324 "EXPRTUBE.spad" 471976 471984 474678 474683) (-323 "EXPRODE.spad" 469136 469152 471966 471971) (-322 "EXPR.spad" 464411 464421 465125 465532) (-321 "EXPR2UPS.spad" 460533 460546 464401 464406) (-320 "EXPR2.spad" 460238 460250 460523 460528) (-319 "EXPEXPAN.spad" 457178 457203 457810 457903) (-318 "EXIT.spad" 456849 456857 457168 457173) (-317 "EXITAST.spad" 456585 456593 456839 456844) (-316 "EVALCYC.spad" 456045 456059 456575 456580) (-315 "EVALAB.spad" 455617 455627 456035 456040) (-314 "EVALAB.spad" 455187 455199 455607 455612) (-313 "EUCDOM.spad" 452761 452769 455113 455182) (-312 "EUCDOM.spad" 450397 450407 452751 452756) (-311 "ESTOOLS.spad" 442243 442251 450387 450392) (-310 "ESTOOLS2.spad" 441846 441860 442233 442238) (-309 "ESTOOLS1.spad" 441531 441542 441836 441841) (-308 "ES.spad" 434346 434354 441521 441526) (-307 "ES.spad" 427067 427077 434244 434249) (-306 "ESCONT.spad" 423860 423868 427057 427062) (-305 "ESCONT1.spad" 423609 423621 423850 423855) (-304 "ES2.spad" 423114 423130 423599 423604) (-303 "ES1.spad" 422684 422700 423104 423109) (-302 "ERROR.spad" 420011 420019 422674 422679) (-301 "EQTBL.spad" 418483 418505 418692 418719) (-300 "EQ.spad" 413288 413298 416075 416187) (-299 "EQ2.spad" 413006 413018 413278 413283) (-298 "EP.spad" 409332 409342 412996 413001) (-297 "ENV.spad" 408010 408018 409322 409327) (-296 "ENTIRER.spad" 407678 407686 407954 408005) (-295 "EMR.spad" 406966 407007 407604 407673) (-294 "ELTAGG.spad" 405220 405239 406956 406961) (-293 "ELTAGG.spad" 403438 403459 405176 405181) (-292 "ELTAB.spad" 402913 402926 403428 403433) (-291 "ELFUTS.spad" 402300 402319 402903 402908) (-290 "ELEMFUN.spad" 401989 401997 402290 402295) (-289 "ELEMFUN.spad" 401676 401686 401979 401984) (-288 "ELAGG.spad" 399647 399657 401656 401671) (-287 "ELAGG.spad" 397555 397567 399566 399571) (-286 "ELABOR.spad" 396901 396909 397545 397550) (-285 "ELABEXPR.spad" 395833 395841 396891 396896) (-284 "EFUPXS.spad" 392609 392639 395789 395794) (-283 "EFULS.spad" 389445 389468 392565 392570) (-282 "EFSTRUC.spad" 387460 387476 389435 389440) (-281 "EF.spad" 382236 382252 387450 387455) (-280 "EAB.spad" 380512 380520 382226 382231) (-279 "E04UCFA.spad" 380048 380056 380502 380507) (-278 "E04NAFA.spad" 379625 379633 380038 380043) (-277 "E04MBFA.spad" 379205 379213 379615 379620) (-276 "E04JAFA.spad" 378741 378749 379195 379200) (-275 "E04GCFA.spad" 378277 378285 378731 378736) (-274 "E04FDFA.spad" 377813 377821 378267 378272) (-273 "E04DGFA.spad" 377349 377357 377803 377808) (-272 "E04AGNT.spad" 373199 373207 377339 377344) (-271 "DVARCAT.spad" 369888 369898 373189 373194) (-270 "DVARCAT.spad" 366575 366587 369878 369883) (-269 "DSMP.spad" 364042 364056 364347 364474) (-268 "DROPT.spad" 358001 358009 364032 364037) (-267 "DROPT1.spad" 357666 357676 357991 357996) (-266 "DROPT0.spad" 352523 352531 357656 357661) (-265 "DRAWPT.spad" 350696 350704 352513 352518) (-264 "DRAW.spad" 343572 343585 350686 350691) (-263 "DRAWHACK.spad" 342880 342890 343562 343567) (-262 "DRAWCX.spad" 340350 340358 342870 342875) (-261 "DRAWCURV.spad" 339897 339912 340340 340345) (-260 "DRAWCFUN.spad" 329429 329437 339887 339892) (-259 "DQAGG.spad" 327607 327617 329397 329424) (-258 "DPOLCAT.spad" 322956 322972 327475 327602) (-257 "DPOLCAT.spad" 318391 318409 322912 322917) (-256 "DPMO.spad" 310617 310633 310755 311056) (-255 "DPMM.spad" 302856 302874 302981 303282) (-254 "DOMTMPLT.spad" 302627 302635 302846 302851) (-253 "DOMCTOR.spad" 302382 302390 302617 302622) (-252 "DOMAIN.spad" 301469 301477 302372 302377) (-251 "DMP.spad" 298729 298744 299299 299426) (-250 "DLP.spad" 298081 298091 298719 298724) (-249 "DLIST.spad" 296660 296670 297264 297291) (-248 "DLAGG.spad" 295077 295087 296650 296655) (-247 "DIVRING.spad" 294619 294627 295021 295072) (-246 "DIVRING.spad" 294205 294215 294609 294614) (-245 "DISPLAY.spad" 292395 292403 294195 294200) (-244 "DIRPROD.spad" 281975 281991 282615 282746) (-243 "DIRPROD2.spad" 280793 280811 281965 281970) (-242 "DIRPCAT.spad" 279737 279753 280657 280788) (-241 "DIRPCAT.spad" 278410 278428 279332 279337) (-240 "DIOSP.spad" 277235 277243 278400 278405) (-239 "DIOPS.spad" 276231 276241 277215 277230) (-238 "DIOPS.spad" 275201 275213 276187 276192) (-237 "DIFRING.spad" 274497 274505 275181 275196) (-236 "DIFRING.spad" 273801 273811 274487 274492) (-235 "DIFFDOM.spad" 272966 272977 273791 273796) (-234 "DIFFDOM.spad" 272129 272142 272956 272961) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2267449 2267454 2267459 2267464) (-2 NIL 2267429 2267434 2267439 2267444) (-1 NIL 2267409 2267414 2267419 2267424) (0 NIL 2267389 2267394 2267399 2267404) (-1308 "ZMOD.spad" 2267198 2267211 2267327 2267384) (-1307 "ZLINDEP.spad" 2266264 2266275 2267188 2267193) (-1306 "ZDSOLVE.spad" 2256209 2256231 2266254 2266259) (-1305 "YSTREAM.spad" 2255704 2255715 2256199 2256204) (-1304 "YDIAGRAM.spad" 2255338 2255347 2255694 2255699) (-1303 "XRPOLY.spad" 2254558 2254578 2255194 2255263) (-1302 "XPR.spad" 2252353 2252366 2254276 2254375) (-1301 "XPOLY.spad" 2251908 2251919 2252209 2252278) (-1300 "XPOLYC.spad" 2251227 2251243 2251834 2251903) (-1299 "XPBWPOLY.spad" 2249664 2249684 2251007 2251076) (-1298 "XF.spad" 2248127 2248142 2249566 2249659) (-1297 "XF.spad" 2246570 2246587 2248011 2248016) (-1296 "XFALG.spad" 2243618 2243634 2246496 2246565) (-1295 "XEXPPKG.spad" 2242869 2242895 2243608 2243613) (-1294 "XDPOLY.spad" 2242483 2242499 2242725 2242794) (-1293 "XALG.spad" 2242143 2242154 2242439 2242478) (-1292 "WUTSET.spad" 2237982 2237999 2241789 2241816) (-1291 "WP.spad" 2237181 2237225 2237840 2237907) (-1290 "WHILEAST.spad" 2236979 2236988 2237171 2237176) (-1289 "WHEREAST.spad" 2236650 2236659 2236969 2236974) (-1288 "WFFINTBS.spad" 2234313 2234335 2236640 2236645) (-1287 "WEIER.spad" 2232535 2232546 2234303 2234308) (-1286 "VSPACE.spad" 2232208 2232219 2232503 2232530) (-1285 "VSPACE.spad" 2231901 2231914 2232198 2232203) (-1284 "VOID.spad" 2231578 2231587 2231891 2231896) (-1283 "VIEW.spad" 2229258 2229267 2231568 2231573) (-1282 "VIEWDEF.spad" 2224459 2224468 2229248 2229253) (-1281 "VIEW3D.spad" 2208420 2208429 2224449 2224454) (-1280 "VIEW2D.spad" 2196311 2196320 2208410 2208415) (-1279 "VECTOR.spad" 2194985 2194996 2195236 2195263) (-1278 "VECTOR2.spad" 2193624 2193637 2194975 2194980) (-1277 "VECTCAT.spad" 2191528 2191539 2193592 2193619) (-1276 "VECTCAT.spad" 2189239 2189252 2191305 2191310) (-1275 "VARIABLE.spad" 2189019 2189034 2189229 2189234) (-1274 "UTYPE.spad" 2188663 2188672 2189009 2189014) (-1273 "UTSODETL.spad" 2187958 2187982 2188619 2188624) (-1272 "UTSODE.spad" 2186174 2186194 2187948 2187953) (-1271 "UTS.spad" 2180978 2181006 2184641 2184738) (-1270 "UTSCAT.spad" 2178457 2178473 2180876 2180973) (-1269 "UTSCAT.spad" 2175580 2175598 2178001 2178006) (-1268 "UTS2.spad" 2175175 2175210 2175570 2175575) (-1267 "URAGG.spad" 2169848 2169859 2175165 2175170) (-1266 "URAGG.spad" 2164485 2164498 2169804 2169809) (-1265 "UPXSSING.spad" 2162130 2162156 2163566 2163699) (-1264 "UPXS.spad" 2159284 2159312 2160262 2160411) (-1263 "UPXSCONS.spad" 2157043 2157063 2157416 2157565) (-1262 "UPXSCCA.spad" 2155614 2155634 2156889 2157038) (-1261 "UPXSCCA.spad" 2154327 2154349 2155604 2155609) (-1260 "UPXSCAT.spad" 2152916 2152932 2154173 2154322) (-1259 "UPXS2.spad" 2152459 2152512 2152906 2152911) (-1258 "UPSQFREE.spad" 2150873 2150887 2152449 2152454) (-1257 "UPSCAT.spad" 2148660 2148684 2150771 2150868) (-1256 "UPSCAT.spad" 2146153 2146179 2148266 2148271) (-1255 "UPOLYC.spad" 2141193 2141204 2145995 2146148) (-1254 "UPOLYC.spad" 2136125 2136138 2140929 2140934) (-1253 "UPOLYC2.spad" 2135596 2135615 2136115 2136120) (-1252 "UP.spad" 2132795 2132810 2133182 2133335) (-1251 "UPMP.spad" 2131695 2131708 2132785 2132790) (-1250 "UPDIVP.spad" 2131260 2131274 2131685 2131690) (-1249 "UPDECOMP.spad" 2129505 2129519 2131250 2131255) (-1248 "UPCDEN.spad" 2128714 2128730 2129495 2129500) (-1247 "UP2.spad" 2128078 2128099 2128704 2128709) (-1246 "UNISEG.spad" 2127431 2127442 2127997 2128002) (-1245 "UNISEG2.spad" 2126928 2126941 2127387 2127392) (-1244 "UNIFACT.spad" 2126031 2126043 2126918 2126923) (-1243 "ULS.spad" 2116589 2116617 2117676 2118105) (-1242 "ULSCONS.spad" 2108985 2109005 2109355 2109504) (-1241 "ULSCCAT.spad" 2106722 2106742 2108831 2108980) (-1240 "ULSCCAT.spad" 2104567 2104589 2106678 2106683) (-1239 "ULSCAT.spad" 2102799 2102815 2104413 2104562) (-1238 "ULS2.spad" 2102313 2102366 2102789 2102794) (-1237 "UINT8.spad" 2102190 2102199 2102303 2102308) (-1236 "UINT64.spad" 2102066 2102075 2102180 2102185) (-1235 "UINT32.spad" 2101942 2101951 2102056 2102061) (-1234 "UINT16.spad" 2101818 2101827 2101932 2101937) (-1233 "UFD.spad" 2100883 2100892 2101744 2101813) (-1232 "UFD.spad" 2100010 2100021 2100873 2100878) (-1231 "UDVO.spad" 2098891 2098900 2100000 2100005) (-1230 "UDPO.spad" 2096384 2096395 2098847 2098852) (-1229 "TYPE.spad" 2096316 2096325 2096374 2096379) (-1228 "TYPEAST.spad" 2096235 2096244 2096306 2096311) (-1227 "TWOFACT.spad" 2094887 2094902 2096225 2096230) (-1226 "TUPLE.spad" 2094373 2094384 2094786 2094791) (-1225 "TUBETOOL.spad" 2091240 2091249 2094363 2094368) (-1224 "TUBE.spad" 2089887 2089904 2091230 2091235) (-1223 "TS.spad" 2088486 2088502 2089452 2089549) (-1222 "TSETCAT.spad" 2075613 2075630 2088454 2088481) (-1221 "TSETCAT.spad" 2062726 2062745 2075569 2075574) (-1220 "TRMANIP.spad" 2057092 2057109 2062432 2062437) (-1219 "TRIMAT.spad" 2056055 2056080 2057082 2057087) (-1218 "TRIGMNIP.spad" 2054582 2054599 2056045 2056050) (-1217 "TRIGCAT.spad" 2054094 2054103 2054572 2054577) (-1216 "TRIGCAT.spad" 2053604 2053615 2054084 2054089) (-1215 "TREE.spad" 2052179 2052190 2053211 2053238) (-1214 "TRANFUN.spad" 2052018 2052027 2052169 2052174) (-1213 "TRANFUN.spad" 2051855 2051866 2052008 2052013) (-1212 "TOPSP.spad" 2051529 2051538 2051845 2051850) (-1211 "TOOLSIGN.spad" 2051192 2051203 2051519 2051524) (-1210 "TEXTFILE.spad" 2049753 2049762 2051182 2051187) (-1209 "TEX.spad" 2046899 2046908 2049743 2049748) (-1208 "TEX1.spad" 2046455 2046466 2046889 2046894) (-1207 "TEMUTL.spad" 2046010 2046019 2046445 2046450) (-1206 "TBCMPPK.spad" 2044103 2044126 2046000 2046005) (-1205 "TBAGG.spad" 2043153 2043176 2044083 2044098) (-1204 "TBAGG.spad" 2042211 2042236 2043143 2043148) (-1203 "TANEXP.spad" 2041619 2041630 2042201 2042206) (-1202 "TALGOP.spad" 2041343 2041354 2041609 2041614) (-1201 "TABLE.spad" 2039754 2039777 2040024 2040051) (-1200 "TABLEAU.spad" 2039235 2039246 2039744 2039749) (-1199 "TABLBUMP.spad" 2036038 2036049 2039225 2039230) (-1198 "SYSTEM.spad" 2035266 2035275 2036028 2036033) (-1197 "SYSSOLP.spad" 2032749 2032760 2035256 2035261) (-1196 "SYSPTR.spad" 2032648 2032657 2032739 2032744) (-1195 "SYSNNI.spad" 2031830 2031841 2032638 2032643) (-1194 "SYSINT.spad" 2031234 2031245 2031820 2031825) (-1193 "SYNTAX.spad" 2027440 2027449 2031224 2031229) (-1192 "SYMTAB.spad" 2025508 2025517 2027430 2027435) (-1191 "SYMS.spad" 2021531 2021540 2025498 2025503) (-1190 "SYMPOLY.spad" 2020538 2020549 2020620 2020747) (-1189 "SYMFUNC.spad" 2020039 2020050 2020528 2020533) (-1188 "SYMBOL.spad" 2017542 2017551 2020029 2020034) (-1187 "SWITCH.spad" 2014313 2014322 2017532 2017537) (-1186 "SUTS.spad" 2011218 2011246 2012780 2012877) (-1185 "SUPXS.spad" 2008359 2008387 2009350 2009499) (-1184 "SUP.spad" 2005172 2005183 2005945 2006098) (-1183 "SUPFRACF.spad" 2004277 2004295 2005162 2005167) (-1182 "SUP2.spad" 2003669 2003682 2004267 2004272) (-1181 "SUMRF.spad" 2002643 2002654 2003659 2003664) (-1180 "SUMFS.spad" 2002280 2002297 2002633 2002638) (-1179 "SULS.spad" 1992825 1992853 1993925 1994354) (-1178 "SUCHTAST.spad" 1992594 1992603 1992815 1992820) (-1177 "SUCH.spad" 1992276 1992291 1992584 1992589) (-1176 "SUBSPACE.spad" 1984391 1984406 1992266 1992271) (-1175 "SUBRESP.spad" 1983561 1983575 1984347 1984352) (-1174 "STTF.spad" 1979660 1979676 1983551 1983556) (-1173 "STTFNC.spad" 1976128 1976144 1979650 1979655) (-1172 "STTAYLOR.spad" 1968763 1968774 1976009 1976014) (-1171 "STRTBL.spad" 1967268 1967285 1967417 1967444) (-1170 "STRING.spad" 1966677 1966686 1966691 1966718) (-1169 "STRICAT.spad" 1966465 1966474 1966645 1966672) (-1168 "STREAM.spad" 1963383 1963394 1965990 1966005) (-1167 "STREAM3.spad" 1962956 1962971 1963373 1963378) (-1166 "STREAM2.spad" 1962084 1962097 1962946 1962951) (-1165 "STREAM1.spad" 1961790 1961801 1962074 1962079) (-1164 "STINPROD.spad" 1960726 1960742 1961780 1961785) (-1163 "STEP.spad" 1959927 1959936 1960716 1960721) (-1162 "STEPAST.spad" 1959161 1959170 1959917 1959922) (-1161 "STBL.spad" 1957687 1957715 1957854 1957869) (-1160 "STAGG.spad" 1956762 1956773 1957677 1957682) (-1159 "STAGG.spad" 1955835 1955848 1956752 1956757) (-1158 "STACK.spad" 1955192 1955203 1955442 1955469) (-1157 "SREGSET.spad" 1952896 1952913 1954838 1954865) (-1156 "SRDCMPK.spad" 1951457 1951477 1952886 1952891) (-1155 "SRAGG.spad" 1946600 1946609 1951425 1951452) (-1154 "SRAGG.spad" 1941763 1941774 1946590 1946595) (-1153 "SQMATRIX.spad" 1939379 1939397 1940295 1940382) (-1152 "SPLTREE.spad" 1933931 1933944 1938815 1938842) (-1151 "SPLNODE.spad" 1930519 1930532 1933921 1933926) (-1150 "SPFCAT.spad" 1929328 1929337 1930509 1930514) (-1149 "SPECOUT.spad" 1927880 1927889 1929318 1929323) (-1148 "SPADXPT.spad" 1919475 1919484 1927870 1927875) (-1147 "spad-parser.spad" 1918940 1918949 1919465 1919470) (-1146 "SPADAST.spad" 1918641 1918650 1918930 1918935) (-1145 "SPACEC.spad" 1902840 1902851 1918631 1918636) (-1144 "SPACE3.spad" 1902616 1902627 1902830 1902835) (-1143 "SORTPAK.spad" 1902165 1902178 1902572 1902577) (-1142 "SOLVETRA.spad" 1899928 1899939 1902155 1902160) (-1141 "SOLVESER.spad" 1898456 1898467 1899918 1899923) (-1140 "SOLVERAD.spad" 1894482 1894493 1898446 1898451) (-1139 "SOLVEFOR.spad" 1892944 1892962 1894472 1894477) (-1138 "SNTSCAT.spad" 1892544 1892561 1892912 1892939) (-1137 "SMTS.spad" 1890816 1890842 1892109 1892206) (-1136 "SMP.spad" 1888291 1888311 1888681 1888808) (-1135 "SMITH.spad" 1887136 1887161 1888281 1888286) (-1134 "SMATCAT.spad" 1885246 1885276 1887080 1887131) (-1133 "SMATCAT.spad" 1883288 1883320 1885124 1885129) (-1132 "SKAGG.spad" 1882251 1882262 1883256 1883283) (-1131 "SINT.spad" 1881191 1881200 1882117 1882246) (-1130 "SIMPAN.spad" 1880919 1880928 1881181 1881186) (-1129 "SIG.spad" 1880249 1880258 1880909 1880914) (-1128 "SIGNRF.spad" 1879367 1879378 1880239 1880244) (-1127 "SIGNEF.spad" 1878646 1878663 1879357 1879362) (-1126 "SIGAST.spad" 1878031 1878040 1878636 1878641) (-1125 "SHP.spad" 1875959 1875974 1877987 1877992) (-1124 "SHDP.spad" 1865670 1865697 1866179 1866310) (-1123 "SGROUP.spad" 1865278 1865287 1865660 1865665) (-1122 "SGROUP.spad" 1864884 1864895 1865268 1865273) (-1121 "SGCF.spad" 1858023 1858032 1864874 1864879) (-1120 "SFRTCAT.spad" 1856953 1856970 1857991 1858018) (-1119 "SFRGCD.spad" 1856016 1856036 1856943 1856948) (-1118 "SFQCMPK.spad" 1850653 1850673 1856006 1856011) (-1117 "SFORT.spad" 1850092 1850106 1850643 1850648) (-1116 "SEXOF.spad" 1849935 1849975 1850082 1850087) (-1115 "SEX.spad" 1849827 1849836 1849925 1849930) (-1114 "SEXCAT.spad" 1847608 1847648 1849817 1849822) (-1113 "SET.spad" 1845932 1845943 1847029 1847068) (-1112 "SETMN.spad" 1844382 1844399 1845922 1845927) (-1111 "SETCAT.spad" 1843704 1843713 1844372 1844377) (-1110 "SETCAT.spad" 1843024 1843035 1843694 1843699) (-1109 "SETAGG.spad" 1839573 1839584 1843004 1843019) (-1108 "SETAGG.spad" 1836130 1836143 1839563 1839568) (-1107 "SEQAST.spad" 1835833 1835842 1836120 1836125) (-1106 "SEGXCAT.spad" 1834989 1835002 1835823 1835828) (-1105 "SEG.spad" 1834802 1834813 1834908 1834913) (-1104 "SEGCAT.spad" 1833727 1833738 1834792 1834797) (-1103 "SEGBIND.spad" 1833485 1833496 1833674 1833679) (-1102 "SEGBIND2.spad" 1833183 1833196 1833475 1833480) (-1101 "SEGAST.spad" 1832897 1832906 1833173 1833178) (-1100 "SEG2.spad" 1832332 1832345 1832853 1832858) (-1099 "SDVAR.spad" 1831608 1831619 1832322 1832327) (-1098 "SDPOL.spad" 1829034 1829045 1829325 1829452) (-1097 "SCPKG.spad" 1827123 1827134 1829024 1829029) (-1096 "SCOPE.spad" 1826276 1826285 1827113 1827118) (-1095 "SCACHE.spad" 1824972 1824983 1826266 1826271) (-1094 "SASTCAT.spad" 1824881 1824890 1824962 1824967) (-1093 "SAOS.spad" 1824753 1824762 1824871 1824876) (-1092 "SAERFFC.spad" 1824466 1824486 1824743 1824748) (-1091 "SAE.spad" 1822641 1822657 1823252 1823387) (-1090 "SAEFACT.spad" 1822342 1822362 1822631 1822636) (-1089 "RURPK.spad" 1820001 1820017 1822332 1822337) (-1088 "RULESET.spad" 1819454 1819478 1819991 1819996) (-1087 "RULE.spad" 1817694 1817718 1819444 1819449) (-1086 "RULECOLD.spad" 1817546 1817559 1817684 1817689) (-1085 "RTVALUE.spad" 1817281 1817290 1817536 1817541) (-1084 "RSTRCAST.spad" 1816998 1817007 1817271 1817276) (-1083 "RSETGCD.spad" 1813376 1813396 1816988 1816993) (-1082 "RSETCAT.spad" 1803312 1803329 1813344 1813371) (-1081 "RSETCAT.spad" 1793268 1793287 1803302 1803307) (-1080 "RSDCMPK.spad" 1791720 1791740 1793258 1793263) (-1079 "RRCC.spad" 1790104 1790134 1791710 1791715) (-1078 "RRCC.spad" 1788486 1788518 1790094 1790099) (-1077 "RPTAST.spad" 1788188 1788197 1788476 1788481) (-1076 "RPOLCAT.spad" 1767548 1767563 1788056 1788183) (-1075 "RPOLCAT.spad" 1746621 1746638 1767131 1767136) (-1074 "ROUTINE.spad" 1742504 1742513 1745268 1745295) (-1073 "ROMAN.spad" 1741832 1741841 1742370 1742499) (-1072 "ROIRC.spad" 1740912 1740944 1741822 1741827) (-1071 "RNS.spad" 1739815 1739824 1740814 1740907) (-1070 "RNS.spad" 1738804 1738815 1739805 1739810) (-1069 "RNG.spad" 1738539 1738548 1738794 1738799) (-1068 "RNGBIND.spad" 1737699 1737713 1738494 1738499) (-1067 "RMODULE.spad" 1737464 1737475 1737689 1737694) (-1066 "RMCAT2.spad" 1736884 1736941 1737454 1737459) (-1065 "RMATRIX.spad" 1735708 1735727 1736051 1736090) (-1064 "RMATCAT.spad" 1731287 1731318 1735664 1735703) (-1063 "RMATCAT.spad" 1726756 1726789 1731135 1731140) (-1062 "RLINSET.spad" 1726150 1726161 1726746 1726751) (-1061 "RINTERP.spad" 1726038 1726058 1726140 1726145) (-1060 "RING.spad" 1725508 1725517 1726018 1726033) (-1059 "RING.spad" 1724986 1724997 1725498 1725503) (-1058 "RIDIST.spad" 1724378 1724387 1724976 1724981) (-1057 "RGCHAIN.spad" 1722961 1722977 1723863 1723890) (-1056 "RGBCSPC.spad" 1722742 1722754 1722951 1722956) (-1055 "RGBCMDL.spad" 1722272 1722284 1722732 1722737) (-1054 "RF.spad" 1719914 1719925 1722262 1722267) (-1053 "RFFACTOR.spad" 1719376 1719387 1719904 1719909) (-1052 "RFFACT.spad" 1719111 1719123 1719366 1719371) (-1051 "RFDIST.spad" 1718107 1718116 1719101 1719106) (-1050 "RETSOL.spad" 1717526 1717539 1718097 1718102) (-1049 "RETRACT.spad" 1716954 1716965 1717516 1717521) (-1048 "RETRACT.spad" 1716380 1716393 1716944 1716949) (-1047 "RETAST.spad" 1716192 1716201 1716370 1716375) (-1046 "RESULT.spad" 1714252 1714261 1714839 1714866) (-1045 "RESRING.spad" 1713599 1713646 1714190 1714247) (-1044 "RESLATC.spad" 1712923 1712934 1713589 1713594) (-1043 "REPSQ.spad" 1712654 1712665 1712913 1712918) (-1042 "REP.spad" 1710208 1710217 1712644 1712649) (-1041 "REPDB.spad" 1709915 1709926 1710198 1710203) (-1040 "REP2.spad" 1699573 1699584 1709757 1709762) (-1039 "REP1.spad" 1693769 1693780 1699523 1699528) (-1038 "REGSET.spad" 1691566 1691583 1693415 1693442) (-1037 "REF.spad" 1690901 1690912 1691521 1691526) (-1036 "REDORDER.spad" 1690107 1690124 1690891 1690896) (-1035 "RECLOS.spad" 1688890 1688910 1689594 1689687) (-1034 "REALSOLV.spad" 1688030 1688039 1688880 1688885) (-1033 "REAL.spad" 1687902 1687911 1688020 1688025) (-1032 "REAL0Q.spad" 1685200 1685215 1687892 1687897) (-1031 "REAL0.spad" 1682044 1682059 1685190 1685195) (-1030 "RDUCEAST.spad" 1681765 1681774 1682034 1682039) (-1029 "RDIV.spad" 1681420 1681445 1681755 1681760) (-1028 "RDIST.spad" 1680987 1680998 1681410 1681415) (-1027 "RDETRS.spad" 1679851 1679869 1680977 1680982) (-1026 "RDETR.spad" 1677990 1678008 1679841 1679846) (-1025 "RDEEFS.spad" 1677089 1677106 1677980 1677985) (-1024 "RDEEF.spad" 1676099 1676116 1677079 1677084) (-1023 "RCFIELD.spad" 1673285 1673294 1676001 1676094) (-1022 "RCFIELD.spad" 1670557 1670568 1673275 1673280) (-1021 "RCAGG.spad" 1668485 1668496 1670547 1670552) (-1020 "RCAGG.spad" 1666340 1666353 1668404 1668409) (-1019 "RATRET.spad" 1665700 1665711 1666330 1666335) (-1018 "RATFACT.spad" 1665392 1665404 1665690 1665695) (-1017 "RANDSRC.spad" 1664711 1664720 1665382 1665387) (-1016 "RADUTIL.spad" 1664467 1664476 1664701 1664706) (-1015 "RADIX.spad" 1661388 1661402 1662934 1663027) (-1014 "RADFF.spad" 1659801 1659838 1659920 1660076) (-1013 "RADCAT.spad" 1659396 1659405 1659791 1659796) (-1012 "RADCAT.spad" 1658989 1659000 1659386 1659391) (-1011 "QUEUE.spad" 1658337 1658348 1658596 1658623) (-1010 "QUAT.spad" 1656795 1656806 1657138 1657203) (-1009 "QUATCT2.spad" 1656415 1656434 1656785 1656790) (-1008 "QUATCAT.spad" 1654585 1654596 1656345 1656410) (-1007 "QUATCAT.spad" 1652506 1652519 1654268 1654273) (-1006 "QUAGG.spad" 1651333 1651344 1652474 1652501) (-1005 "QQUTAST.spad" 1651101 1651110 1651323 1651328) (-1004 "QFORM.spad" 1650719 1650734 1651091 1651096) (-1003 "QFCAT.spad" 1649421 1649432 1650621 1650714) (-1002 "QFCAT.spad" 1647714 1647727 1648916 1648921) (-1001 "QFCAT2.spad" 1647406 1647423 1647704 1647709) (-1000 "QEQUAT.spad" 1646964 1646973 1647396 1647401) (-999 "QCMPACK.spad" 1641711 1641730 1646954 1646959) (-998 "QALGSET.spad" 1637790 1637822 1641625 1641630) (-997 "QALGSET2.spad" 1635786 1635804 1637780 1637785) (-996 "PWFFINTB.spad" 1633202 1633223 1635776 1635781) (-995 "PUSHVAR.spad" 1632541 1632560 1633192 1633197) (-994 "PTRANFN.spad" 1628669 1628679 1632531 1632536) (-993 "PTPACK.spad" 1625757 1625767 1628659 1628664) (-992 "PTFUNC2.spad" 1625580 1625594 1625747 1625752) (-991 "PTCAT.spad" 1624835 1624845 1625548 1625575) (-990 "PSQFR.spad" 1624142 1624166 1624825 1624830) (-989 "PSEUDLIN.spad" 1623028 1623038 1624132 1624137) (-988 "PSETPK.spad" 1608461 1608477 1622906 1622911) (-987 "PSETCAT.spad" 1602381 1602404 1608441 1608456) (-986 "PSETCAT.spad" 1596275 1596300 1602337 1602342) (-985 "PSCURVE.spad" 1595258 1595266 1596265 1596270) (-984 "PSCAT.spad" 1594041 1594070 1595156 1595253) (-983 "PSCAT.spad" 1592914 1592945 1594031 1594036) (-982 "PRTITION.spad" 1591612 1591620 1592904 1592909) (-981 "PRTDAST.spad" 1591331 1591339 1591602 1591607) (-980 "PRS.spad" 1580893 1580910 1591287 1591292) (-979 "PRQAGG.spad" 1580328 1580338 1580861 1580888) (-978 "PROPLOG.spad" 1579900 1579908 1580318 1580323) (-977 "PROPFUN2.spad" 1579523 1579536 1579890 1579895) (-976 "PROPFUN1.spad" 1578921 1578932 1579513 1579518) (-975 "PROPFRML.spad" 1577489 1577500 1578911 1578916) (-974 "PROPERTY.spad" 1576977 1576985 1577479 1577484) (-973 "PRODUCT.spad" 1574659 1574671 1574943 1574998) (-972 "PR.spad" 1573051 1573063 1573750 1573877) (-971 "PRINT.spad" 1572803 1572811 1573041 1573046) (-970 "PRIMES.spad" 1571056 1571066 1572793 1572798) (-969 "PRIMELT.spad" 1569137 1569151 1571046 1571051) (-968 "PRIMCAT.spad" 1568764 1568772 1569127 1569132) (-967 "PRIMARR.spad" 1567769 1567779 1567947 1567974) (-966 "PRIMARR2.spad" 1566536 1566548 1567759 1567764) (-965 "PREASSOC.spad" 1565918 1565930 1566526 1566531) (-964 "PPCURVE.spad" 1565055 1565063 1565908 1565913) (-963 "PORTNUM.spad" 1564830 1564838 1565045 1565050) (-962 "POLYROOT.spad" 1563679 1563701 1564786 1564791) (-961 "POLY.spad" 1561014 1561024 1561529 1561656) (-960 "POLYLIFT.spad" 1560279 1560302 1561004 1561009) (-959 "POLYCATQ.spad" 1558397 1558419 1560269 1560274) (-958 "POLYCAT.spad" 1551867 1551888 1558265 1558392) (-957 "POLYCAT.spad" 1544675 1544698 1551075 1551080) (-956 "POLY2UP.spad" 1544127 1544141 1544665 1544670) (-955 "POLY2.spad" 1543724 1543736 1544117 1544122) (-954 "POLUTIL.spad" 1542665 1542694 1543680 1543685) (-953 "POLTOPOL.spad" 1541413 1541428 1542655 1542660) (-952 "POINT.spad" 1540251 1540261 1540338 1540365) (-951 "PNTHEORY.spad" 1536953 1536961 1540241 1540246) (-950 "PMTOOLS.spad" 1535728 1535742 1536943 1536948) (-949 "PMSYM.spad" 1535277 1535287 1535718 1535723) (-948 "PMQFCAT.spad" 1534868 1534882 1535267 1535272) (-947 "PMPRED.spad" 1534347 1534361 1534858 1534863) (-946 "PMPREDFS.spad" 1533801 1533823 1534337 1534342) (-945 "PMPLCAT.spad" 1532881 1532899 1533733 1533738) (-944 "PMLSAGG.spad" 1532466 1532480 1532871 1532876) (-943 "PMKERNEL.spad" 1532045 1532057 1532456 1532461) (-942 "PMINS.spad" 1531625 1531635 1532035 1532040) (-941 "PMFS.spad" 1531202 1531220 1531615 1531620) (-940 "PMDOWN.spad" 1530492 1530506 1531192 1531197) (-939 "PMASS.spad" 1529502 1529510 1530482 1530487) (-938 "PMASSFS.spad" 1528469 1528485 1529492 1529497) (-937 "PLOTTOOL.spad" 1528249 1528257 1528459 1528464) (-936 "PLOT.spad" 1523172 1523180 1528239 1528244) (-935 "PLOT3D.spad" 1519636 1519644 1523162 1523167) (-934 "PLOT1.spad" 1518793 1518803 1519626 1519631) (-933 "PLEQN.spad" 1506083 1506110 1518783 1518788) (-932 "PINTERP.spad" 1505705 1505724 1506073 1506078) (-931 "PINTERPA.spad" 1505489 1505505 1505695 1505700) (-930 "PI.spad" 1505098 1505106 1505463 1505484) (-929 "PID.spad" 1504068 1504076 1505024 1505093) (-928 "PICOERCE.spad" 1503725 1503735 1504058 1504063) (-927 "PGROEB.spad" 1502326 1502340 1503715 1503720) (-926 "PGE.spad" 1493943 1493951 1502316 1502321) (-925 "PGCD.spad" 1492833 1492850 1493933 1493938) (-924 "PFRPAC.spad" 1491982 1491992 1492823 1492828) (-923 "PFR.spad" 1488645 1488655 1491884 1491977) (-922 "PFOTOOLS.spad" 1487903 1487919 1488635 1488640) (-921 "PFOQ.spad" 1487273 1487291 1487893 1487898) (-920 "PFO.spad" 1486692 1486719 1487263 1487268) (-919 "PF.spad" 1486266 1486278 1486497 1486590) (-918 "PFECAT.spad" 1483948 1483956 1486192 1486261) (-917 "PFECAT.spad" 1481658 1481668 1483904 1483909) (-916 "PFBRU.spad" 1479546 1479558 1481648 1481653) (-915 "PFBR.spad" 1477106 1477129 1479536 1479541) (-914 "PERM.spad" 1472913 1472923 1476936 1476951) (-913 "PERMGRP.spad" 1467683 1467693 1472903 1472908) (-912 "PERMCAT.spad" 1466344 1466354 1467663 1467678) (-911 "PERMAN.spad" 1464876 1464890 1466334 1466339) (-910 "PENDTREE.spad" 1464217 1464227 1464505 1464510) (-909 "PDRING.spad" 1462768 1462778 1464197 1464212) (-908 "PDRING.spad" 1461327 1461339 1462758 1462763) (-907 "PDEPROB.spad" 1460342 1460350 1461317 1461322) (-906 "PDEPACK.spad" 1454382 1454390 1460332 1460337) (-905 "PDECOMP.spad" 1453852 1453869 1454372 1454377) (-904 "PDECAT.spad" 1452208 1452216 1453842 1453847) (-903 "PCOMP.spad" 1452061 1452074 1452198 1452203) (-902 "PBWLB.spad" 1450649 1450666 1452051 1452056) (-901 "PATTERN.spad" 1445188 1445198 1450639 1450644) (-900 "PATTERN2.spad" 1444926 1444938 1445178 1445183) (-899 "PATTERN1.spad" 1443262 1443278 1444916 1444921) (-898 "PATRES.spad" 1440837 1440849 1443252 1443257) (-897 "PATRES2.spad" 1440509 1440523 1440827 1440832) (-896 "PATMATCH.spad" 1438706 1438737 1440217 1440222) (-895 "PATMAB.spad" 1438135 1438145 1438696 1438701) (-894 "PATLRES.spad" 1437221 1437235 1438125 1438130) (-893 "PATAB.spad" 1436985 1436995 1437211 1437216) (-892 "PARTPERM.spad" 1434993 1435001 1436975 1436980) (-891 "PARSURF.spad" 1434427 1434455 1434983 1434988) (-890 "PARSU2.spad" 1434224 1434240 1434417 1434422) (-889 "script-parser.spad" 1433744 1433752 1434214 1434219) (-888 "PARSCURV.spad" 1433178 1433206 1433734 1433739) (-887 "PARSC2.spad" 1432969 1432985 1433168 1433173) (-886 "PARPCURV.spad" 1432431 1432459 1432959 1432964) (-885 "PARPC2.spad" 1432222 1432238 1432421 1432426) (-884 "PARAMAST.spad" 1431350 1431358 1432212 1432217) (-883 "PAN2EXPR.spad" 1430762 1430770 1431340 1431345) (-882 "PALETTE.spad" 1429732 1429740 1430752 1430757) (-881 "PAIR.spad" 1428719 1428732 1429320 1429325) (-880 "PADICRC.spad" 1426053 1426071 1427224 1427317) (-879 "PADICRAT.spad" 1424068 1424080 1424289 1424382) (-878 "PADIC.spad" 1423763 1423775 1423994 1424063) (-877 "PADICCT.spad" 1422312 1422324 1423689 1423758) (-876 "PADEPAC.spad" 1421001 1421020 1422302 1422307) (-875 "PADE.spad" 1419753 1419769 1420991 1420996) (-874 "OWP.spad" 1418993 1419023 1419611 1419678) (-873 "OVERSET.spad" 1418566 1418574 1418983 1418988) (-872 "OVAR.spad" 1418347 1418370 1418556 1418561) (-871 "OUT.spad" 1417433 1417441 1418337 1418342) (-870 "OUTFORM.spad" 1406825 1406833 1417423 1417428) (-869 "OUTBFILE.spad" 1406243 1406251 1406815 1406820) (-868 "OUTBCON.spad" 1405249 1405257 1406233 1406238) (-867 "OUTBCON.spad" 1404253 1404263 1405239 1405244) (-866 "OSI.spad" 1403728 1403736 1404243 1404248) (-865 "OSGROUP.spad" 1403646 1403654 1403718 1403723) (-864 "ORTHPOL.spad" 1402131 1402141 1403563 1403568) (-863 "OREUP.spad" 1401584 1401612 1401811 1401850) (-862 "ORESUP.spad" 1400885 1400909 1401264 1401303) (-861 "OREPCTO.spad" 1398742 1398754 1400805 1400810) (-860 "OREPCAT.spad" 1392889 1392899 1398698 1398737) (-859 "OREPCAT.spad" 1386926 1386938 1392737 1392742) (-858 "ORDSET.spad" 1386098 1386106 1386916 1386921) (-857 "ORDSET.spad" 1385268 1385278 1386088 1386093) (-856 "ORDRING.spad" 1384658 1384666 1385248 1385263) (-855 "ORDRING.spad" 1384056 1384066 1384648 1384653) (-854 "ORDMON.spad" 1383911 1383919 1384046 1384051) (-853 "ORDFUNS.spad" 1383043 1383059 1383901 1383906) (-852 "ORDFIN.spad" 1382863 1382871 1383033 1383038) (-851 "ORDCOMP.spad" 1381328 1381338 1382410 1382439) (-850 "ORDCOMP2.spad" 1380621 1380633 1381318 1381323) (-849 "OPTPROB.spad" 1379259 1379267 1380611 1380616) (-848 "OPTPACK.spad" 1371668 1371676 1379249 1379254) (-847 "OPTCAT.spad" 1369347 1369355 1371658 1371663) (-846 "OPSIG.spad" 1369001 1369009 1369337 1369342) (-845 "OPQUERY.spad" 1368550 1368558 1368991 1368996) (-844 "OP.spad" 1368292 1368302 1368372 1368439) (-843 "OPERCAT.spad" 1367758 1367768 1368282 1368287) (-842 "OPERCAT.spad" 1367222 1367234 1367748 1367753) (-841 "ONECOMP.spad" 1365967 1365977 1366769 1366798) (-840 "ONECOMP2.spad" 1365391 1365403 1365957 1365962) (-839 "OMSERVER.spad" 1364397 1364405 1365381 1365386) (-838 "OMSAGG.spad" 1364185 1364195 1364353 1364392) (-837 "OMPKG.spad" 1362801 1362809 1364175 1364180) (-836 "OM.spad" 1361774 1361782 1362791 1362796) (-835 "OMLO.spad" 1361175 1361187 1361636 1361675) (-834 "OMEXPR.spad" 1361009 1361019 1361165 1361170) (-833 "OMERR.spad" 1360554 1360562 1360999 1361004) (-832 "OMERRK.spad" 1359588 1359596 1360544 1360549) (-831 "OMENC.spad" 1358932 1358940 1359578 1359583) (-830 "OMDEV.spad" 1353241 1353249 1358922 1358927) (-829 "OMCONN.spad" 1352650 1352658 1353231 1353236) (-828 "OINTDOM.spad" 1352413 1352421 1352576 1352645) (-827 "OFMONOID.spad" 1350536 1350546 1352369 1352374) (-826 "ODVAR.spad" 1349797 1349807 1350526 1350531) (-825 "ODR.spad" 1349441 1349467 1349609 1349758) (-824 "ODPOL.spad" 1346823 1346833 1347163 1347290) (-823 "ODP.spad" 1336670 1336690 1337043 1337174) (-822 "ODETOOLS.spad" 1335319 1335338 1336660 1336665) (-821 "ODESYS.spad" 1333013 1333030 1335309 1335314) (-820 "ODERTRIC.spad" 1329022 1329039 1332970 1332975) (-819 "ODERED.spad" 1328421 1328445 1329012 1329017) (-818 "ODERAT.spad" 1326036 1326053 1328411 1328416) (-817 "ODEPRRIC.spad" 1323073 1323095 1326026 1326031) (-816 "ODEPROB.spad" 1322330 1322338 1323063 1323068) (-815 "ODEPRIM.spad" 1319664 1319686 1322320 1322325) (-814 "ODEPAL.spad" 1319050 1319074 1319654 1319659) (-813 "ODEPACK.spad" 1305716 1305724 1319040 1319045) (-812 "ODEINT.spad" 1305151 1305167 1305706 1305711) (-811 "ODEIFTBL.spad" 1302546 1302554 1305141 1305146) (-810 "ODEEF.spad" 1298037 1298053 1302536 1302541) (-809 "ODECONST.spad" 1297574 1297592 1298027 1298032) (-808 "ODECAT.spad" 1296172 1296180 1297564 1297569) (-807 "OCT.spad" 1294308 1294318 1295022 1295061) (-806 "OCTCT2.spad" 1293954 1293975 1294298 1294303) (-805 "OC.spad" 1291750 1291760 1293910 1293949) (-804 "OC.spad" 1289271 1289283 1291433 1291438) (-803 "OCAMON.spad" 1289119 1289127 1289261 1289266) (-802 "OASGP.spad" 1288934 1288942 1289109 1289114) (-801 "OAMONS.spad" 1288456 1288464 1288924 1288929) (-800 "OAMON.spad" 1288317 1288325 1288446 1288451) (-799 "OAGROUP.spad" 1288179 1288187 1288307 1288312) (-798 "NUMTUBE.spad" 1287770 1287786 1288169 1288174) (-797 "NUMQUAD.spad" 1275746 1275754 1287760 1287765) (-796 "NUMODE.spad" 1267100 1267108 1275736 1275741) (-795 "NUMINT.spad" 1264666 1264674 1267090 1267095) (-794 "NUMFMT.spad" 1263506 1263514 1264656 1264661) (-793 "NUMERIC.spad" 1255620 1255630 1263311 1263316) (-792 "NTSCAT.spad" 1254128 1254144 1255588 1255615) (-791 "NTPOLFN.spad" 1253679 1253689 1254045 1254050) (-790 "NSUP.spad" 1246725 1246735 1251265 1251418) (-789 "NSUP2.spad" 1246117 1246129 1246715 1246720) (-788 "NSMP.spad" 1242347 1242366 1242655 1242782) (-787 "NREP.spad" 1240725 1240739 1242337 1242342) (-786 "NPCOEF.spad" 1239971 1239991 1240715 1240720) (-785 "NORMRETR.spad" 1239569 1239608 1239961 1239966) (-784 "NORMPK.spad" 1237471 1237490 1239559 1239564) (-783 "NORMMA.spad" 1237159 1237185 1237461 1237466) (-782 "NONE.spad" 1236900 1236908 1237149 1237154) (-781 "NONE1.spad" 1236576 1236586 1236890 1236895) (-780 "NODE1.spad" 1236063 1236079 1236566 1236571) (-779 "NNI.spad" 1234958 1234966 1236037 1236058) (-778 "NLINSOL.spad" 1233584 1233594 1234948 1234953) (-777 "NIPROB.spad" 1232125 1232133 1233574 1233579) (-776 "NFINTBAS.spad" 1229685 1229702 1232115 1232120) (-775 "NETCLT.spad" 1229659 1229670 1229675 1229680) (-774 "NCODIV.spad" 1227875 1227891 1229649 1229654) (-773 "NCNTFRAC.spad" 1227517 1227531 1227865 1227870) (-772 "NCEP.spad" 1225683 1225697 1227507 1227512) (-771 "NASRING.spad" 1225279 1225287 1225673 1225678) (-770 "NASRING.spad" 1224873 1224883 1225269 1225274) (-769 "NARNG.spad" 1224225 1224233 1224863 1224868) (-768 "NARNG.spad" 1223575 1223585 1224215 1224220) (-767 "NAGSP.spad" 1222652 1222660 1223565 1223570) (-766 "NAGS.spad" 1212313 1212321 1222642 1222647) (-765 "NAGF07.spad" 1210744 1210752 1212303 1212308) (-764 "NAGF04.spad" 1205146 1205154 1210734 1210739) (-763 "NAGF02.spad" 1199215 1199223 1205136 1205141) (-762 "NAGF01.spad" 1194976 1194984 1199205 1199210) (-761 "NAGE04.spad" 1188676 1188684 1194966 1194971) (-760 "NAGE02.spad" 1179336 1179344 1188666 1188671) (-759 "NAGE01.spad" 1175338 1175346 1179326 1179331) (-758 "NAGD03.spad" 1173342 1173350 1175328 1175333) (-757 "NAGD02.spad" 1166089 1166097 1173332 1173337) (-756 "NAGD01.spad" 1160382 1160390 1166079 1166084) (-755 "NAGC06.spad" 1156257 1156265 1160372 1160377) (-754 "NAGC05.spad" 1154758 1154766 1156247 1156252) (-753 "NAGC02.spad" 1154025 1154033 1154748 1154753) (-752 "NAALG.spad" 1153566 1153576 1153993 1154020) (-751 "NAALG.spad" 1153127 1153139 1153556 1153561) (-750 "MULTSQFR.spad" 1150085 1150102 1153117 1153122) (-749 "MULTFACT.spad" 1149468 1149485 1150075 1150080) (-748 "MTSCAT.spad" 1147562 1147583 1149366 1149463) (-747 "MTHING.spad" 1147221 1147231 1147552 1147557) (-746 "MSYSCMD.spad" 1146655 1146663 1147211 1147216) (-745 "MSET.spad" 1144613 1144623 1146361 1146400) (-744 "MSETAGG.spad" 1144458 1144468 1144581 1144608) (-743 "MRING.spad" 1141435 1141447 1144166 1144233) (-742 "MRF2.spad" 1141005 1141019 1141425 1141430) (-741 "MRATFAC.spad" 1140551 1140568 1140995 1141000) (-740 "MPRFF.spad" 1138591 1138610 1140541 1140546) (-739 "MPOLY.spad" 1136062 1136077 1136421 1136548) (-738 "MPCPF.spad" 1135326 1135345 1136052 1136057) (-737 "MPC3.spad" 1135143 1135183 1135316 1135321) (-736 "MPC2.spad" 1134789 1134822 1135133 1135138) (-735 "MONOTOOL.spad" 1133140 1133157 1134779 1134784) (-734 "MONOID.spad" 1132459 1132467 1133130 1133135) (-733 "MONOID.spad" 1131776 1131786 1132449 1132454) (-732 "MONOGEN.spad" 1130524 1130537 1131636 1131771) (-731 "MONOGEN.spad" 1129294 1129309 1130408 1130413) (-730 "MONADWU.spad" 1127324 1127332 1129284 1129289) (-729 "MONADWU.spad" 1125352 1125362 1127314 1127319) (-728 "MONAD.spad" 1124512 1124520 1125342 1125347) (-727 "MONAD.spad" 1123670 1123680 1124502 1124507) (-726 "MOEBIUS.spad" 1122406 1122420 1123650 1123665) (-725 "MODULE.spad" 1122276 1122286 1122374 1122401) (-724 "MODULE.spad" 1122166 1122178 1122266 1122271) (-723 "MODRING.spad" 1121501 1121540 1122146 1122161) (-722 "MODOP.spad" 1120166 1120178 1121323 1121390) (-721 "MODMONOM.spad" 1119897 1119915 1120156 1120161) (-720 "MODMON.spad" 1116692 1116708 1117411 1117564) (-719 "MODFIELD.spad" 1116054 1116093 1116594 1116687) (-718 "MMLFORM.spad" 1114914 1114922 1116044 1116049) (-717 "MMAP.spad" 1114656 1114690 1114904 1114909) (-716 "MLO.spad" 1113115 1113125 1114612 1114651) (-715 "MLIFT.spad" 1111727 1111744 1113105 1113110) (-714 "MKUCFUNC.spad" 1111262 1111280 1111717 1111722) (-713 "MKRECORD.spad" 1110866 1110879 1111252 1111257) (-712 "MKFUNC.spad" 1110273 1110283 1110856 1110861) (-711 "MKFLCFN.spad" 1109241 1109251 1110263 1110268) (-710 "MKBCFUNC.spad" 1108736 1108754 1109231 1109236) (-709 "MINT.spad" 1108175 1108183 1108638 1108731) (-708 "MHROWRED.spad" 1106686 1106696 1108165 1108170) (-707 "MFLOAT.spad" 1105206 1105214 1106576 1106681) (-706 "MFINFACT.spad" 1104606 1104628 1105196 1105201) (-705 "MESH.spad" 1102388 1102396 1104596 1104601) (-704 "MDDFACT.spad" 1100599 1100609 1102378 1102383) (-703 "MDAGG.spad" 1099890 1099900 1100579 1100594) (-702 "MCMPLX.spad" 1095901 1095909 1096515 1096716) (-701 "MCDEN.spad" 1095111 1095123 1095891 1095896) (-700 "MCALCFN.spad" 1092233 1092259 1095101 1095106) (-699 "MAYBE.spad" 1091517 1091528 1092223 1092228) (-698 "MATSTOR.spad" 1088825 1088835 1091507 1091512) (-697 "MATRIX.spad" 1087529 1087539 1088013 1088040) (-696 "MATLIN.spad" 1084873 1084897 1087413 1087418) (-695 "MATCAT.spad" 1076602 1076624 1084841 1084868) (-694 "MATCAT.spad" 1068203 1068227 1076444 1076449) (-693 "MATCAT2.spad" 1067485 1067533 1068193 1068198) (-692 "MAPPKG3.spad" 1066400 1066414 1067475 1067480) (-691 "MAPPKG2.spad" 1065738 1065750 1066390 1066395) (-690 "MAPPKG1.spad" 1064566 1064576 1065728 1065733) (-689 "MAPPAST.spad" 1063881 1063889 1064556 1064561) (-688 "MAPHACK3.spad" 1063693 1063707 1063871 1063876) (-687 "MAPHACK2.spad" 1063462 1063474 1063683 1063688) (-686 "MAPHACK1.spad" 1063106 1063116 1063452 1063457) (-685 "MAGMA.spad" 1060896 1060913 1063096 1063101) (-684 "MACROAST.spad" 1060475 1060483 1060886 1060891) (-683 "M3D.spad" 1058195 1058205 1059853 1059858) (-682 "LZSTAGG.spad" 1055433 1055443 1058185 1058190) (-681 "LZSTAGG.spad" 1052669 1052681 1055423 1055428) (-680 "LWORD.spad" 1049374 1049391 1052659 1052664) (-679 "LSTAST.spad" 1049158 1049166 1049364 1049369) (-678 "LSQM.spad" 1047388 1047402 1047782 1047833) (-677 "LSPP.spad" 1046923 1046940 1047378 1047383) (-676 "LSMP.spad" 1045773 1045801 1046913 1046918) (-675 "LSMP1.spad" 1043591 1043605 1045763 1045768) (-674 "LSAGG.spad" 1043260 1043270 1043559 1043586) (-673 "LSAGG.spad" 1042949 1042961 1043250 1043255) (-672 "LPOLY.spad" 1041903 1041922 1042805 1042874) (-671 "LPEFRAC.spad" 1041174 1041184 1041893 1041898) (-670 "LO.spad" 1040575 1040589 1041108 1041135) (-669 "LOGIC.spad" 1040177 1040185 1040565 1040570) (-668 "LOGIC.spad" 1039777 1039787 1040167 1040172) (-667 "LODOOPS.spad" 1038707 1038719 1039767 1039772) (-666 "LODO.spad" 1038091 1038107 1038387 1038426) (-665 "LODOF.spad" 1037137 1037154 1038048 1038053) (-664 "LODOCAT.spad" 1035803 1035813 1037093 1037132) (-663 "LODOCAT.spad" 1034467 1034479 1035759 1035764) (-662 "LODO2.spad" 1033740 1033752 1034147 1034186) (-661 "LODO1.spad" 1033140 1033150 1033420 1033459) (-660 "LODEEF.spad" 1031942 1031960 1033130 1033135) (-659 "LNAGG.spad" 1028089 1028099 1031932 1031937) (-658 "LNAGG.spad" 1024200 1024212 1028045 1028050) (-657 "LMOPS.spad" 1020968 1020985 1024190 1024195) (-656 "LMODULE.spad" 1020736 1020746 1020958 1020963) (-655 "LMDICT.spad" 1020023 1020033 1020287 1020314) (-654 "LLINSET.spad" 1019420 1019430 1020013 1020018) (-653 "LITERAL.spad" 1019326 1019337 1019410 1019415) (-652 "LIST.spad" 1017061 1017071 1018473 1018500) (-651 "LIST3.spad" 1016372 1016386 1017051 1017056) (-650 "LIST2.spad" 1015074 1015086 1016362 1016367) (-649 "LIST2MAP.spad" 1011977 1011989 1015064 1015069) (-648 "LINSET.spad" 1011599 1011609 1011967 1011972) (-647 "LINEXP.spad" 1011033 1011043 1011579 1011594) (-646 "LINDEP.spad" 1009842 1009854 1010945 1010950) (-645 "LIMITRF.spad" 1007770 1007780 1009832 1009837) (-644 "LIMITPS.spad" 1006673 1006686 1007760 1007765) (-643 "LIE.spad" 1004689 1004701 1005963 1006108) (-642 "LIECAT.spad" 1004165 1004175 1004615 1004684) (-641 "LIECAT.spad" 1003669 1003681 1004121 1004126) (-640 "LIB.spad" 1001882 1001890 1002328 1002343) (-639 "LGROBP.spad" 999235 999254 1001872 1001877) (-638 "LF.spad" 998190 998206 999225 999230) (-637 "LFCAT.spad" 997249 997257 998180 998185) (-636 "LEXTRIPK.spad" 992752 992767 997239 997244) (-635 "LEXP.spad" 990755 990782 992732 992747) (-634 "LETAST.spad" 990454 990462 990745 990750) (-633 "LEADCDET.spad" 988852 988869 990444 990449) (-632 "LAZM3PK.spad" 987556 987578 988842 988847) (-631 "LAUPOL.spad" 986249 986262 987149 987218) (-630 "LAPLACE.spad" 985832 985848 986239 986244) (-629 "LA.spad" 985272 985286 985754 985793) (-628 "LALG.spad" 985048 985058 985252 985267) (-627 "LALG.spad" 984832 984844 985038 985043) (-626 "KVTFROM.spad" 984567 984577 984822 984827) (-625 "KTVLOGIC.spad" 984079 984087 984557 984562) (-624 "KRCFROM.spad" 983817 983827 984069 984074) (-623 "KOVACIC.spad" 982540 982557 983807 983812) (-622 "KONVERT.spad" 982262 982272 982530 982535) (-621 "KOERCE.spad" 981999 982009 982252 982257) (-620 "KERNEL.spad" 980654 980664 981783 981788) (-619 "KERNEL2.spad" 980357 980369 980644 980649) (-618 "KDAGG.spad" 979466 979488 980337 980352) (-617 "KDAGG.spad" 978583 978607 979456 979461) (-616 "KAFILE.spad" 977546 977562 977781 977808) (-615 "JORDAN.spad" 975375 975387 976836 976981) (-614 "JOINAST.spad" 975069 975077 975365 975370) (-613 "JAVACODE.spad" 974935 974943 975059 975064) (-612 "IXAGG.spad" 973068 973092 974925 974930) (-611 "IXAGG.spad" 971056 971082 972915 972920) (-610 "IVECTOR.spad" 969826 969841 969981 970008) (-609 "ITUPLE.spad" 968987 968997 969816 969821) (-608 "ITRIGMNP.spad" 967826 967845 968977 968982) (-607 "ITFUN3.spad" 967332 967346 967816 967821) (-606 "ITFUN2.spad" 967076 967088 967322 967327) (-605 "ITFORM.spad" 966431 966439 967066 967071) (-604 "ITAYLOR.spad" 964425 964440 966295 966392) (-603 "ISUPS.spad" 956862 956877 963399 963496) (-602 "ISUMP.spad" 956363 956379 956852 956857) (-601 "ISTRING.spad" 955451 955464 955532 955559) (-600 "ISAST.spad" 955170 955178 955441 955446) (-599 "IRURPK.spad" 953887 953906 955160 955165) (-598 "IRSN.spad" 951859 951867 953877 953882) (-597 "IRRF2F.spad" 950344 950354 951815 951820) (-596 "IRREDFFX.spad" 949945 949956 950334 950339) (-595 "IROOT.spad" 948284 948294 949935 949940) (-594 "IR.spad" 946085 946099 948139 948166) (-593 "IRFORM.spad" 945409 945417 946075 946080) (-592 "IR2.spad" 944437 944453 945399 945404) (-591 "IR2F.spad" 943643 943659 944427 944432) (-590 "IPRNTPK.spad" 943403 943411 943633 943638) (-589 "IPF.spad" 942968 942980 943208 943301) (-588 "IPADIC.spad" 942729 942755 942894 942963) (-587 "IP4ADDR.spad" 942286 942294 942719 942724) (-586 "IOMODE.spad" 941808 941816 942276 942281) (-585 "IOBFILE.spad" 941169 941177 941798 941803) (-584 "IOBCON.spad" 941034 941042 941159 941164) (-583 "INVLAPLA.spad" 940683 940699 941024 941029) (-582 "INTTR.spad" 934065 934082 940673 940678) (-581 "INTTOOLS.spad" 931820 931836 933639 933644) (-580 "INTSLPE.spad" 931140 931148 931810 931815) (-579 "INTRVL.spad" 930706 930716 931054 931135) (-578 "INTRF.spad" 929130 929144 930696 930701) (-577 "INTRET.spad" 928562 928572 929120 929125) (-576 "INTRAT.spad" 927289 927306 928552 928557) (-575 "INTPM.spad" 925674 925690 926932 926937) (-574 "INTPAF.spad" 923538 923556 925606 925611) (-573 "INTPACK.spad" 913912 913920 923528 923533) (-572 "INT.spad" 913360 913368 913766 913907) (-571 "INTHERTR.spad" 912634 912651 913350 913355) (-570 "INTHERAL.spad" 912304 912328 912624 912629) (-569 "INTHEORY.spad" 908743 908751 912294 912299) (-568 "INTG0.spad" 902476 902494 908675 908680) (-567 "INTFTBL.spad" 896505 896513 902466 902471) (-566 "INTFACT.spad" 895564 895574 896495 896500) (-565 "INTEF.spad" 893949 893965 895554 895559) (-564 "INTDOM.spad" 892572 892580 893875 893944) (-563 "INTDOM.spad" 891257 891267 892562 892567) (-562 "INTCAT.spad" 889516 889526 891171 891252) (-561 "INTBIT.spad" 889023 889031 889506 889511) (-560 "INTALG.spad" 888211 888238 889013 889018) (-559 "INTAF.spad" 887711 887727 888201 888206) (-558 "INTABL.spad" 886229 886260 886392 886419) (-557 "INT8.spad" 886109 886117 886219 886224) (-556 "INT64.spad" 885988 885996 886099 886104) (-555 "INT32.spad" 885867 885875 885978 885983) (-554 "INT16.spad" 885746 885754 885857 885862) (-553 "INS.spad" 883249 883257 885648 885741) (-552 "INS.spad" 880838 880848 883239 883244) (-551 "INPSIGN.spad" 880286 880299 880828 880833) (-550 "INPRODPF.spad" 879382 879401 880276 880281) (-549 "INPRODFF.spad" 878470 878494 879372 879377) (-548 "INNMFACT.spad" 877445 877462 878460 878465) (-547 "INMODGCD.spad" 876933 876963 877435 877440) (-546 "INFSP.spad" 875230 875252 876923 876928) (-545 "INFPROD0.spad" 874310 874329 875220 875225) (-544 "INFORM.spad" 871509 871517 874300 874305) (-543 "INFORM1.spad" 871134 871144 871499 871504) (-542 "INFINITY.spad" 870686 870694 871124 871129) (-541 "INETCLTS.spad" 870663 870671 870676 870681) (-540 "INEP.spad" 869201 869223 870653 870658) (-539 "INDE.spad" 868930 868947 869191 869196) (-538 "INCRMAPS.spad" 868351 868361 868920 868925) (-537 "INBFILE.spad" 867423 867431 868341 868346) (-536 "INBFF.spad" 863217 863228 867413 867418) (-535 "INBCON.spad" 861507 861515 863207 863212) (-534 "INBCON.spad" 859795 859805 861497 861502) (-533 "INAST.spad" 859456 859464 859785 859790) (-532 "IMPTAST.spad" 859164 859172 859446 859451) (-531 "IMATRIX.spad" 858109 858135 858621 858648) (-530 "IMATQF.spad" 857203 857247 858065 858070) (-529 "IMATLIN.spad" 855808 855832 857159 857164) (-528 "ILIST.spad" 854466 854481 854991 855018) (-527 "IIARRAY2.spad" 853854 853892 854073 854100) (-526 "IFF.spad" 853264 853280 853535 853628) (-525 "IFAST.spad" 852878 852886 853254 853259) (-524 "IFARRAY.spad" 850371 850386 852061 852088) (-523 "IFAMON.spad" 850233 850250 850327 850332) (-522 "IEVALAB.spad" 849638 849650 850223 850228) (-521 "IEVALAB.spad" 849041 849055 849628 849633) (-520 "IDPO.spad" 848839 848851 849031 849036) (-519 "IDPOAMS.spad" 848595 848607 848829 848834) (-518 "IDPOAM.spad" 848315 848327 848585 848590) (-517 "IDPC.spad" 847253 847265 848305 848310) (-516 "IDPAM.spad" 846998 847010 847243 847248) (-515 "IDPAG.spad" 846745 846757 846988 846993) (-514 "IDENT.spad" 846395 846403 846735 846740) (-513 "IDECOMP.spad" 843634 843652 846385 846390) (-512 "IDEAL.spad" 838583 838622 843569 843574) (-511 "ICDEN.spad" 837772 837788 838573 838578) (-510 "ICARD.spad" 836963 836971 837762 837767) (-509 "IBPTOOLS.spad" 835570 835587 836953 836958) (-508 "IBITS.spad" 834773 834786 835206 835233) (-507 "IBATOOL.spad" 831750 831769 834763 834768) (-506 "IBACHIN.spad" 830257 830272 831740 831745) (-505 "IARRAY2.spad" 829245 829271 829864 829891) (-504 "IARRAY1.spad" 828290 828305 828428 828455) (-503 "IAN.spad" 826513 826521 828106 828199) (-502 "IALGFACT.spad" 826116 826149 826503 826508) (-501 "HYPCAT.spad" 825540 825548 826106 826111) (-500 "HYPCAT.spad" 824962 824972 825530 825535) (-499 "HOSTNAME.spad" 824770 824778 824952 824957) (-498 "HOMOTOP.spad" 824513 824523 824760 824765) (-497 "HOAGG.spad" 821795 821805 824503 824508) (-496 "HOAGG.spad" 818852 818864 821562 821567) (-495 "HEXADEC.spad" 816954 816962 817319 817412) (-494 "HEUGCD.spad" 815989 816000 816944 816949) (-493 "HELLFDIV.spad" 815579 815603 815979 815984) (-492 "HEAP.spad" 814971 814981 815186 815213) (-491 "HEADAST.spad" 814504 814512 814961 814966) (-490 "HDP.spad" 804347 804363 804724 804855) (-489 "HDMP.spad" 801561 801576 802177 802304) (-488 "HB.spad" 799812 799820 801551 801556) (-487 "HASHTBL.spad" 798282 798313 798493 798520) (-486 "HASAST.spad" 797998 798006 798272 798277) (-485 "HACKPI.spad" 797489 797497 797900 797993) (-484 "GTSET.spad" 796428 796444 797135 797162) (-483 "GSTBL.spad" 794947 794982 795121 795136) (-482 "GSERIES.spad" 792118 792145 793079 793228) (-481 "GROUP.spad" 791391 791399 792098 792113) (-480 "GROUP.spad" 790672 790682 791381 791386) (-479 "GROEBSOL.spad" 789166 789187 790662 790667) (-478 "GRMOD.spad" 787737 787749 789156 789161) (-477 "GRMOD.spad" 786306 786320 787727 787732) (-476 "GRIMAGE.spad" 779195 779203 786296 786301) (-475 "GRDEF.spad" 777574 777582 779185 779190) (-474 "GRAY.spad" 776037 776045 777564 777569) (-473 "GRALG.spad" 775114 775126 776027 776032) (-472 "GRALG.spad" 774189 774203 775104 775109) (-471 "GPOLSET.spad" 773643 773666 773871 773898) (-470 "GOSPER.spad" 772912 772930 773633 773638) (-469 "GMODPOL.spad" 772060 772087 772880 772907) (-468 "GHENSEL.spad" 771143 771157 772050 772055) (-467 "GENUPS.spad" 767436 767449 771133 771138) (-466 "GENUFACT.spad" 767013 767023 767426 767431) (-465 "GENPGCD.spad" 766599 766616 767003 767008) (-464 "GENMFACT.spad" 766051 766070 766589 766594) (-463 "GENEEZ.spad" 764002 764015 766041 766046) (-462 "GDMP.spad" 761058 761075 761832 761959) (-461 "GCNAALG.spad" 754981 755008 760852 760919) (-460 "GCDDOM.spad" 754157 754165 754907 754976) (-459 "GCDDOM.spad" 753395 753405 754147 754152) (-458 "GB.spad" 750921 750959 753351 753356) (-457 "GBINTERN.spad" 746941 746979 750911 750916) (-456 "GBF.spad" 742708 742746 746931 746936) (-455 "GBEUCLID.spad" 740590 740628 742698 742703) (-454 "GAUSSFAC.spad" 739903 739911 740580 740585) (-453 "GALUTIL.spad" 738229 738239 739859 739864) (-452 "GALPOLYU.spad" 736683 736696 738219 738224) (-451 "GALFACTU.spad" 734856 734875 736673 736678) (-450 "GALFACT.spad" 725045 725056 734846 734851) (-449 "FVFUN.spad" 722068 722076 725035 725040) (-448 "FVC.spad" 721120 721128 722058 722063) (-447 "FUNDESC.spad" 720798 720806 721110 721115) (-446 "FUNCTION.spad" 720647 720659 720788 720793) (-445 "FT.spad" 718944 718952 720637 720642) (-444 "FTEM.spad" 718109 718117 718934 718939) (-443 "FSUPFACT.spad" 717009 717028 718045 718050) (-442 "FST.spad" 715095 715103 716999 717004) (-441 "FSRED.spad" 714575 714591 715085 715090) (-440 "FSPRMELT.spad" 713457 713473 714532 714537) (-439 "FSPECF.spad" 711548 711564 713447 713452) (-438 "FS.spad" 705816 705826 711323 711543) (-437 "FS.spad" 699862 699874 705371 705376) (-436 "FSINT.spad" 699522 699538 699852 699857) (-435 "FSERIES.spad" 698713 698725 699342 699441) (-434 "FSCINT.spad" 698030 698046 698703 698708) (-433 "FSAGG.spad" 697147 697157 697986 698025) (-432 "FSAGG.spad" 696226 696238 697067 697072) (-431 "FSAGG2.spad" 694969 694985 696216 696221) (-430 "FS2UPS.spad" 689460 689494 694959 694964) (-429 "FS2.spad" 689107 689123 689450 689455) (-428 "FS2EXPXP.spad" 688232 688255 689097 689102) (-427 "FRUTIL.spad" 687186 687196 688222 688227) (-426 "FR.spad" 680718 680728 686026 686095) (-425 "FRNAALG.spad" 675987 675997 680660 680713) (-424 "FRNAALG.spad" 671268 671280 675943 675948) (-423 "FRNAAF2.spad" 670724 670742 671258 671263) (-422 "FRMOD.spad" 670134 670164 670655 670660) (-421 "FRIDEAL.spad" 669359 669380 670114 670129) (-420 "FRIDEAL2.spad" 668963 668995 669349 669354) (-419 "FRETRCT.spad" 668474 668484 668953 668958) (-418 "FRETRCT.spad" 667851 667863 668332 668337) (-417 "FRAMALG.spad" 666199 666212 667807 667846) (-416 "FRAMALG.spad" 664579 664594 666189 666194) (-415 "FRAC.spad" 661678 661688 662081 662254) (-414 "FRAC2.spad" 661283 661295 661668 661673) (-413 "FR2.spad" 660619 660631 661273 661278) (-412 "FPS.spad" 657434 657442 660509 660614) (-411 "FPS.spad" 654277 654287 657354 657359) (-410 "FPC.spad" 653323 653331 654179 654272) (-409 "FPC.spad" 652455 652465 653313 653318) (-408 "FPATMAB.spad" 652217 652227 652445 652450) (-407 "FPARFRAC.spad" 650704 650721 652207 652212) (-406 "FORTRAN.spad" 649210 649253 650694 650699) (-405 "FORT.spad" 648159 648167 649200 649205) (-404 "FORTFN.spad" 645329 645337 648149 648154) (-403 "FORTCAT.spad" 645013 645021 645319 645324) (-402 "FORMULA.spad" 642487 642495 645003 645008) (-401 "FORMULA1.spad" 641966 641976 642477 642482) (-400 "FORDER.spad" 641657 641681 641956 641961) (-399 "FOP.spad" 640858 640866 641647 641652) (-398 "FNLA.spad" 640282 640304 640826 640853) (-397 "FNCAT.spad" 638877 638885 640272 640277) (-396 "FNAME.spad" 638769 638777 638867 638872) (-395 "FMTC.spad" 638567 638575 638695 638764) (-394 "FMONOID.spad" 638232 638242 638523 638528) (-393 "FMONCAT.spad" 635385 635395 638222 638227) (-392 "FM.spad" 635080 635092 635319 635346) (-391 "FMFUN.spad" 632110 632118 635070 635075) (-390 "FMC.spad" 631162 631170 632100 632105) (-389 "FMCAT.spad" 628830 628848 631130 631157) (-388 "FM1.spad" 628187 628199 628764 628791) (-387 "FLOATRP.spad" 625922 625936 628177 628182) (-386 "FLOAT.spad" 619236 619244 625788 625917) (-385 "FLOATCP.spad" 616667 616681 619226 619231) (-384 "FLINEXP.spad" 616379 616389 616647 616662) (-383 "FLINEXP.spad" 616045 616057 616315 616320) (-382 "FLASORT.spad" 615371 615383 616035 616040) (-381 "FLALG.spad" 613017 613036 615297 615366) (-380 "FLAGG.spad" 610059 610069 612997 613012) (-379 "FLAGG.spad" 607002 607014 609942 609947) (-378 "FLAGG2.spad" 605727 605743 606992 606997) (-377 "FINRALG.spad" 603788 603801 605683 605722) (-376 "FINRALG.spad" 601775 601790 603672 603677) (-375 "FINITE.spad" 600927 600935 601765 601770) (-374 "FINAALG.spad" 590048 590058 600869 600922) (-373 "FINAALG.spad" 579181 579193 590004 590009) (-372 "FILE.spad" 578764 578774 579171 579176) (-371 "FILECAT.spad" 577290 577307 578754 578759) (-370 "FIELD.spad" 576696 576704 577192 577285) (-369 "FIELD.spad" 576188 576198 576686 576691) (-368 "FGROUP.spad" 574835 574845 576168 576183) (-367 "FGLMICPK.spad" 573622 573637 574825 574830) (-366 "FFX.spad" 572997 573012 573338 573431) (-365 "FFSLPE.spad" 572500 572521 572987 572992) (-364 "FFPOLY.spad" 563762 563773 572490 572495) (-363 "FFPOLY2.spad" 562822 562839 563752 563757) (-362 "FFP.spad" 562219 562239 562538 562631) (-361 "FF.spad" 561667 561683 561900 561993) (-360 "FFNBX.spad" 560179 560199 561383 561476) (-359 "FFNBP.spad" 558692 558709 559895 559988) (-358 "FFNB.spad" 557157 557178 558373 558466) (-357 "FFINTBAS.spad" 554671 554690 557147 557152) (-356 "FFIELDC.spad" 552248 552256 554573 554666) (-355 "FFIELDC.spad" 549911 549921 552238 552243) (-354 "FFHOM.spad" 548659 548676 549901 549906) (-353 "FFF.spad" 546094 546105 548649 548654) (-352 "FFCGX.spad" 544941 544961 545810 545903) (-351 "FFCGP.spad" 543830 543850 544657 544750) (-350 "FFCG.spad" 542622 542643 543511 543604) (-349 "FFCAT.spad" 535795 535817 542461 542617) (-348 "FFCAT.spad" 529047 529071 535715 535720) (-347 "FFCAT2.spad" 528794 528834 529037 529042) (-346 "FEXPR.spad" 520511 520557 528550 528589) (-345 "FEVALAB.spad" 520219 520229 520501 520506) (-344 "FEVALAB.spad" 519712 519724 519996 520001) (-343 "FDIV.spad" 519154 519178 519702 519707) (-342 "FDIVCAT.spad" 517218 517242 519144 519149) (-341 "FDIVCAT.spad" 515280 515306 517208 517213) (-340 "FDIV2.spad" 514936 514976 515270 515275) (-339 "FCTRDATA.spad" 513944 513952 514926 514931) (-338 "FCPAK1.spad" 512511 512519 513934 513939) (-337 "FCOMP.spad" 511890 511900 512501 512506) (-336 "FC.spad" 501897 501905 511880 511885) (-335 "FAXF.spad" 494868 494882 501799 501892) (-334 "FAXF.spad" 487891 487907 494824 494829) (-333 "FARRAY.spad" 486041 486051 487074 487101) (-332 "FAMR.spad" 484177 484189 485939 486036) (-331 "FAMR.spad" 482297 482311 484061 484066) (-330 "FAMONOID.spad" 481965 481975 482251 482256) (-329 "FAMONC.spad" 480261 480273 481955 481960) (-328 "FAGROUP.spad" 479885 479895 480157 480184) (-327 "FACUTIL.spad" 478089 478106 479875 479880) (-326 "FACTFUNC.spad" 477283 477293 478079 478084) (-325 "EXPUPXS.spad" 474116 474139 475415 475564) (-324 "EXPRTUBE.spad" 471404 471412 474106 474111) (-323 "EXPRODE.spad" 468564 468580 471394 471399) (-322 "EXPR.spad" 463839 463849 464553 464960) (-321 "EXPR2UPS.spad" 459961 459974 463829 463834) (-320 "EXPR2.spad" 459666 459678 459951 459956) (-319 "EXPEXPAN.spad" 456606 456631 457238 457331) (-318 "EXIT.spad" 456277 456285 456596 456601) (-317 "EXITAST.spad" 456013 456021 456267 456272) (-316 "EVALCYC.spad" 455473 455487 456003 456008) (-315 "EVALAB.spad" 455045 455055 455463 455468) (-314 "EVALAB.spad" 454615 454627 455035 455040) (-313 "EUCDOM.spad" 452189 452197 454541 454610) (-312 "EUCDOM.spad" 449825 449835 452179 452184) (-311 "ESTOOLS.spad" 441671 441679 449815 449820) (-310 "ESTOOLS2.spad" 441274 441288 441661 441666) (-309 "ESTOOLS1.spad" 440959 440970 441264 441269) (-308 "ES.spad" 433774 433782 440949 440954) (-307 "ES.spad" 426495 426505 433672 433677) (-306 "ESCONT.spad" 423288 423296 426485 426490) (-305 "ESCONT1.spad" 423037 423049 423278 423283) (-304 "ES2.spad" 422542 422558 423027 423032) (-303 "ES1.spad" 422112 422128 422532 422537) (-302 "ERROR.spad" 419439 419447 422102 422107) (-301 "EQTBL.spad" 417911 417933 418120 418147) (-300 "EQ.spad" 412716 412726 415503 415615) (-299 "EQ2.spad" 412434 412446 412706 412711) (-298 "EP.spad" 408760 408770 412424 412429) (-297 "ENV.spad" 407438 407446 408750 408755) (-296 "ENTIRER.spad" 407106 407114 407382 407433) (-295 "EMR.spad" 406394 406435 407032 407101) (-294 "ELTAGG.spad" 404648 404667 406384 406389) (-293 "ELTAGG.spad" 402866 402887 404604 404609) (-292 "ELTAB.spad" 402341 402354 402856 402861) (-291 "ELFUTS.spad" 401728 401747 402331 402336) (-290 "ELEMFUN.spad" 401417 401425 401718 401723) (-289 "ELEMFUN.spad" 401104 401114 401407 401412) (-288 "ELAGG.spad" 399075 399085 401084 401099) (-287 "ELAGG.spad" 396983 396995 398994 398999) (-286 "ELABOR.spad" 396329 396337 396973 396978) (-285 "ELABEXPR.spad" 395261 395269 396319 396324) (-284 "EFUPXS.spad" 392037 392067 395217 395222) (-283 "EFULS.spad" 388873 388896 391993 391998) (-282 "EFSTRUC.spad" 386888 386904 388863 388868) (-281 "EF.spad" 381664 381680 386878 386883) (-280 "EAB.spad" 379940 379948 381654 381659) (-279 "E04UCFA.spad" 379476 379484 379930 379935) (-278 "E04NAFA.spad" 379053 379061 379466 379471) (-277 "E04MBFA.spad" 378633 378641 379043 379048) (-276 "E04JAFA.spad" 378169 378177 378623 378628) (-275 "E04GCFA.spad" 377705 377713 378159 378164) (-274 "E04FDFA.spad" 377241 377249 377695 377700) (-273 "E04DGFA.spad" 376777 376785 377231 377236) (-272 "E04AGNT.spad" 372627 372635 376767 376772) (-271 "DVARCAT.spad" 369316 369326 372617 372622) (-270 "DVARCAT.spad" 366003 366015 369306 369311) (-269 "DSMP.spad" 363470 363484 363775 363902) (-268 "DROPT.spad" 357429 357437 363460 363465) (-267 "DROPT1.spad" 357094 357104 357419 357424) (-266 "DROPT0.spad" 351951 351959 357084 357089) (-265 "DRAWPT.spad" 350124 350132 351941 351946) (-264 "DRAW.spad" 343000 343013 350114 350119) (-263 "DRAWHACK.spad" 342308 342318 342990 342995) (-262 "DRAWCX.spad" 339778 339786 342298 342303) (-261 "DRAWCURV.spad" 339325 339340 339768 339773) (-260 "DRAWCFUN.spad" 328857 328865 339315 339320) (-259 "DQAGG.spad" 327035 327045 328825 328852) (-258 "DPOLCAT.spad" 322384 322400 326903 327030) (-257 "DPOLCAT.spad" 317795 317813 322316 322321) (-256 "DPMO.spad" 310021 310037 310159 310460) (-255 "DPMM.spad" 302260 302278 302385 302686) (-254 "DOMTMPLT.spad" 302031 302039 302250 302255) (-253 "DOMCTOR.spad" 301786 301794 302021 302026) (-252 "DOMAIN.spad" 300873 300881 301776 301781) (-251 "DMP.spad" 298133 298148 298703 298830) (-250 "DLP.spad" 297485 297495 298123 298128) (-249 "DLIST.spad" 296064 296074 296668 296695) (-248 "DLAGG.spad" 294481 294491 296054 296059) (-247 "DIVRING.spad" 294023 294031 294425 294476) (-246 "DIVRING.spad" 293609 293619 294013 294018) (-245 "DISPLAY.spad" 291799 291807 293599 293604) (-244 "DIRPROD.spad" 281379 281395 282019 282150) (-243 "DIRPROD2.spad" 280197 280215 281369 281374) (-242 "DIRPCAT.spad" 279141 279157 280061 280192) (-241 "DIRPCAT.spad" 277814 277832 278736 278741) (-240 "DIOSP.spad" 276639 276647 277804 277809) (-239 "DIOPS.spad" 275635 275645 276619 276634) (-238 "DIOPS.spad" 274605 274617 275591 275596) (-237 "DIFRING.spad" 274211 274219 274585 274600) (-236 "DIFRING.spad" 273825 273835 274201 274206) (-235 "DIFFDOM.spad" 272990 273001 273815 273820) (-234 "DIFFDOM.spad" 272153 272166 272980 272985) (-233 "DIFEXT.spad" 271324 271334 272133 272148) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file |