* algebra/: Don't quote '!' at end of names.

author: dos-reis <gdr@axiomatics.org> 2009-06-11 23:00:40 +0000
committer: dos-reis <gdr@axiomatics.org> 2009-06-11 23:00:40 +0000
commit: 9e07dcd91c45bf8b22d932321f5c97e931ffe8ac (patch)
tree: 6d2174e90e5779b1b3ab4ae7df3ae6603b66c6c2 /src/share/algebra/browse.daase
parent: 7bd82b57975bbc1ff5b87fed0739815c620ecdcc (diff)
download: open-axiom-9e07dcd91c45bf8b22d932321f5c97e931ffe8ac.tar.gz
1 files changed, 321 insertions, 321 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 81b080e3..5c151794 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2285499 . 3453610657)       
+(2285497 . 3453749792)       
 (-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 
@@ -56,7 +56,7 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -2286) 
+(-32 R -2382) 
 ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) 
 NIL 
 ((|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) 
@@ -88,11 +88,11 @@ NIL
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -2286 UP UPUP -3750) 
+(-40 -2382 UP UPUP -4030) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2700 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2700 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2700 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2700 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) 
-(-41 R -2286) 
+((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) 
+(-41 R -2382) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) 
@@ -111,7 +111,7 @@ NIL
 (-45 |Key| |Entry|) 
 ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) 
 ((-4417 . T) (-4418 . T)) 
-((-2700 (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|))))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|))))))) 
+((-2805 (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|))))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -2286) 
+(-54 |Base| R -2382) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) 
 NIL 
 NIL 
@@ -167,64 +167,64 @@ NIL
 (-59 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
-(-61 -2520) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+(-61 -2628) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-62 -2520) 
+(-62 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-63 -2520) 
+(-63 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-64 -2520) 
+(-64 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-65 -2520) 
+(-65 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -2520) 
+(-66 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-67 -2520) 
+(-67 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-68 -2520) 
+(-68 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -2520) 
+(-69 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-70 -2520) 
+(-70 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-71 -2520) 
+(-71 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-72 -2520) 
+(-72 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-73 -2520) 
+(-73 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-74 -2520) 
+(-74 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
@@ -236,55 +236,55 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-77 -2520) 
+(-77 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-78 -2520) 
+(-78 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -2520) 
+(-79 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -2520) 
+(-80 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -2520) 
+(-81 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-82 -2520) 
+(-82 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -2520) 
+(-83 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -2520) 
+(-84 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -2520) 
+(-85 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -2520) 
+(-86 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -2520) 
+(-87 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-88 -2520) 
+(-88 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-89 -2520) 
+(-89 -2628) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -295,7 +295,7 @@ NIL
 (-91 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -343,7 +343,7 @@ NIL
 (-103 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-104 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
@@ -363,7 +363,7 @@ NIL
 (-108) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2700 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
+((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
 (-109) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -388,7 +388,7 @@ NIL
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
 NIL 
 NIL 
-(-115 -2286 UP) 
+(-115 -2382 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
@@ -399,7 +399,7 @@ NIL
 (-117 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-116 |#1|) (QUOTE (-909))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1022))) (|HasCategory| (-116 |#1|) (QUOTE (-820))) (-2700 (|HasCategory| (-116 |#1|) (QUOTE (-820))) (|HasCategory| (-116 |#1|) (QUOTE (-850)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-1150))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-308))) (|HasCategory| (-116 |#1|) (QUOTE (-547))) (|HasCategory| (-116 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) 
+((|HasCategory| (-116 |#1|) (QUOTE (-909))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1022))) (|HasCategory| (-116 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-116 |#1|) (QUOTE (-820))) (|HasCategory| (-116 |#1|) (QUOTE (-850)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-1150))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-308))) (|HasCategory| (-116 |#1|) (QUOTE (-547))) (|HasCategory| (-116 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) 
 (-118 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -415,7 +415,7 @@ NIL
 (-121 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-122 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
 NIL 
@@ -435,15 +435,15 @@ NIL
 (-126 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-128) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2700 (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099)))) (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) 
+((-2805 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2805 (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099)))) (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) 
 (-129) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) 
 NIL 
@@ -468,11 +468,11 @@ NIL
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) 
 (((-4419 "*") . T)) 
 NIL 
-(-135 |minix| -2201 S T$) 
+(-135 |minix| -2293 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-136 |minix| -2201 R) 
+(-136 |minix| -2293 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
@@ -495,7 +495,7 @@ NIL
 (-141) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
 ((-4417 . T) (-4407 . T) (-4418 . T)) 
-((-2700 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
+((-2805 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
 (-142 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -520,7 +520,7 @@ NIL
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
 ((-4414 . T)) 
 NIL 
-(-148 -2286 UP UPUP) 
+(-148 -2382 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) 
 NIL 
 NIL 
@@ -560,7 +560,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-158 R -2286) 
+(-158 R -2382) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -594,7 +594,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-1002))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasCategory| |#2| (QUOTE (-1059))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4413)) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558)))) 
 (-166 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})"))) 
-((-4410 -2700 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3611 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-4410 -2805 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3654 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-167 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."))) 
@@ -606,8 +606,8 @@ NIL
 NIL 
 (-169 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}."))) 
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(QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1022)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1199)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 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(|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-351))))) 
+((-4410 -2805 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3654 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1022)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1199)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1199)))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-1059))) (-12 (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-1199)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasAttribute| |#1| (QUOTE -4413)) (|HasAttribute| |#1| (QUOTE -4416)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-351))))) 
 (-170 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -680,7 +680,7 @@ NIL
 ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-188 R -2286) 
+(-188 R -2382) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -788,23 +788,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-215 -2286 UP UPUP R) 
+(-215 -2382 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-216 -2286 FP) 
+(-216 -2382 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
 (-217) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2700 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
+((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
 (-218) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-219 R -2286) 
+(-219 R -2382) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -819,18 +819,18 @@ NIL
 (-222 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-223 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
 ((-4414 . T)) 
 NIL 
-(-224 R -2286) 
+(-224 R -2382) 
 ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) 
 NIL 
 NIL 
 (-225) 
 ((|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}."))) 
-((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-226) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) 
@@ -839,7 +839,7 @@ NIL
 (-227 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-228 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
@@ -876,22 +876,22 @@ NIL
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-237 S -2201 R) 
+(-237 S -2293 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (QUOTE (-848))) (|HasAttribute| |#3| (QUOTE -4414)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-726))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (QUOTE (-1099)))) 
-(-238 -2201 R) 
+(-238 -2293 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 ((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) 
 NIL 
-(-239 -2201 A B) 
+(-239 -2293 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-240 -2201 R) 
+(-240 -2293 R) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) 
 ((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-726))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (-2700 (-12 (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-365))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1049)))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-793))) (-2700 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-726))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1049)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1049)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1049)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1049)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (|HasCategory| |#2| (QUOTE (-233))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE 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(LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-726))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) 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 (-241) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
@@ -911,7 +911,7 @@ NIL
 (-245 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
 ((-4418 . T) (-4417 . T)) 
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 (-246 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
@@ -919,7 +919,7 @@ NIL
 (-247 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 
 NIL 
@@ -934,12 +934,12 @@ NIL
 NIL 
 (-251 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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 (-253 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 
@@ -991,7 +991,7 @@ NIL
 (-265 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
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 (-266 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -1036,11 +1036,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-277 R -2286) 
+(-277 R -2382) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-278 R -2286) 
+(-278 R -2382) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
@@ -1088,7 +1088,7 @@ 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 
-(-290 S R |Mod| -1467 -2806 |exactQuo|) 
+(-290 S R |Mod| -3550 -3132 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
@@ -1110,21 +1110,21 @@ NIL
 NIL 
 (-295 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-4414 -2700 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4411 |has| |#1| (-1049)) (-4412 |has| |#1| (-1049))) 
-((|HasCategory| |#1| (QUOTE (-365))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726)))) (|HasCategory| |#1| (QUOTE (-475))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-303))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-475)))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726)))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-726)))) 
+((-4414 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4411 |has| |#1| (-1049)) (-4412 |has| |#1| (-1049))) 
+((|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726)))) (|HasCategory| |#1| (QUOTE (-475))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-303))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-475)))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-726)))) 
 (-296 |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."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-297) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
 NIL 
-(-298 -2286 S) 
+(-298 -2382 S) 
 ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) 
 NIL 
 NIL 
-(-299 E -2286) 
+(-299 E -2382) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) 
 NIL 
 NIL 
@@ -1172,7 +1172,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-311 -2286) 
+(-311 -2382) 
 ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) 
 NIL 
 NIL 
@@ -1187,7 +1187,7 @@ NIL
 (-314 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
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+((|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))))) 
 (-315 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1198,9 +1198,9 @@ NIL
 NIL 
 (-317 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-4414 -2700 (-2336 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2700 (-2336 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) 
-((-2700 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2700 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2700 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2700 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) 
-(-318 R -2286) 
+((-4414 -2805 (-2438 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2805 (-2438 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) 
+((-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) 
+(-318 R -2382) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) 
 NIL 
 NIL 
@@ -1211,7 +1211,7 @@ NIL
 (-320 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."))) 
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 (-321 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 
@@ -1243,12 +1243,12 @@ NIL
 (-328 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
 ((-4418 . T) (-4417 . T)) 
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-(-329 S -2286) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+(-329 S -2382) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-370)))) 
-(-330 -2286) 
+(-330 -2382) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
@@ -1272,15 +1272,15 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-336 S -2286 UP UPUP R) 
+(-336 S -2382 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-337 -2286 UP UPUP R) 
+(-337 -2382 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-338 -2286 UP UPUP R) 
+(-338 -2382 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
@@ -1300,26 +1300,26 @@ NIL
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-343 S -2286 UP UPUP) 
+(-343 S -2382 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-365)))) 
-(-344 -2286 UP UPUP) 
+(-344 -2382 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-345 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
+((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
 (-346 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-347 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-348 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1336,31 +1336,31 @@ NIL
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
-(-352 R UP -2286) 
+(-352 R UP -2382) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-353 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
+((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
 (-354 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-355 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-356 |p| |n|) 
 ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
+((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) 
 (-357 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
-(-358 -2286 GF) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+(-358 -2382 GF) 
 ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
@@ -1368,14 +1368,14 @@ NIL
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-360 -2286 FP FPP) 
+(-360 -2382 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
 (-361 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) 
 (-362 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) 
 NIL 
@@ -1454,7 +1454,7 @@ NIL
 NIL 
 (-381) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4400 . T) (-4408 . T) (-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-4400 . T) (-4408 . T) (-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-382 |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}."))) 
@@ -1504,7 +1504,7 @@ NIL
 ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) 
 NIL 
 NIL 
-(-394 -2286 UP UPUP R) 
+(-394 -2382 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1528,11 +1528,11 @@ NIL
 ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-400 -2520 |returnType| -2143 |symbols|) 
+(-400 -2628 |returnType| -2763 |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-401 -2286 UP) 
+(-401 -2382 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1554,7 +1554,7 @@ NIL
 ((|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4408))) 
 (-406) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) 
-((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-407 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."))) 
@@ -1567,7 +1567,7 @@ NIL
 (-409 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
 ((-4404 -12 (|has| |#1| (-6 -4415)) (|has| |#1| (-454)) (|has| |#1| (-6 -4404))) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2700 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2805 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
 (-410 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
@@ -1588,11 +1588,11 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-415 R -2286 UP A) 
+(-415 R -2382 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) 
 ((-4414 . T)) 
 NIL 
-(-416 R -2286 UP A |ibasis|) 
+(-416 R -2382 UP A |ibasis|) 
 ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) 
 NIL 
 ((|HasCategory| |#4| (LIST (QUOTE -1038) (|devaluate| |#2|)))) 
@@ -1611,7 +1611,7 @@ NIL
 (-420 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."))) 
 ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1218))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1218)))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-454)))) 
+((|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1218))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1218)))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-454)))) 
 (-421 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 
@@ -1640,7 +1640,7 @@ NIL
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 ((-4417 . T) (-4407 . T) (-4418 . T)) 
 NIL 
-(-428 R -2286) 
+(-428 R -2382) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
@@ -1648,7 +1648,7 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) 
 ((-4404 -12 (|has| |#1| (-6 -4404)) (|has| |#2| (-6 -4404))) (-4411 . T) (-4412 . T) (-4414 . T)) 
 ((-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4404)))) 
-(-430 R -2286) 
+(-430 R -2382) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) 
 NIL 
 NIL 
@@ -1658,17 +1658,17 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) 
 (-432 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-4414 -2700 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) 
+((-4414 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) 
 NIL 
-(-433 R -2286) 
+(-433 R -2382) 
 ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) 
 NIL 
 NIL 
-(-434 R -2286) 
+(-434 R -2382) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-435 R -2286) 
+(-435 R -2382) 
 ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1676,7 +1676,7 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-437 R -2286 UP) 
+(-437 R -2382 UP) 
 ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) 
 NIL 
 ((|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-48))))) 
@@ -1708,7 +1708,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-445 R UP -2286) 
+(-445 R UP -2382) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
@@ -1755,7 +1755,7 @@ NIL
 (-456 |vl| R E) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
 (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
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 (-457 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) 
 NIL 
@@ -1820,7 +1820,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-473 |lv| -2286 R) 
+(-473 |lv| -2382 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1835,11 +1835,11 @@ NIL
 (-476 |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."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) 
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 (-477 |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."))) 
 ((-4418 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099)))) 
 (-478 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)}"))) 
 ((-4418 . T) (-4417 . T)) 
@@ -1855,7 +1855,7 @@ NIL
 (-481 |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."))) 
 ((-4417 . T) (-4418 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-482) 
 ((|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 
@@ -1863,11 +1863,11 @@ NIL
 (-483 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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-(-484 -2201 S) 
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+(-484 -2293 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) 
 NIL 
@@ -1875,8 +1875,8 @@ NIL
 (-486 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
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-(-487 -2286 UP UPUP R) 
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 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
@@ -1887,7 +1887,7 @@ NIL
 (-489) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
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+((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
 (-490 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1912,7 +1912,7 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-496 -2286 UP |AlExt| |AlPol|) 
+(-496 -2382 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
@@ -1923,16 +1923,16 @@ NIL
 (-498 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-499 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-500 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) 
 NIL 
 NIL 
-(-501 R UP -2286) 
+(-501 R UP -2382) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
@@ -1952,7 +1952,7 @@ NIL
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
 NIL 
-(-506 -2286 |Expon| |VarSet| |DPoly|) 
+(-506 -2382 |Expon| |VarSet| |DPoly|) 
 ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-1175))))) 
@@ -2003,7 +2003,7 @@ NIL
 (-518 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-519) 
 ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) 
 NIL 
@@ -2011,15 +2011,15 @@ NIL
 (-520 |p| |n|) 
 ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((-2700 (|HasCategory| (-583 |#1|) (QUOTE (-145))) (|HasCategory| (-583 |#1|) (QUOTE (-370)))) (|HasCategory| (-583 |#1|) (QUOTE (-147))) (|HasCategory| (-583 |#1|) (QUOTE (-370))) (|HasCategory| (-583 |#1|) (QUOTE (-145)))) 
+((-2805 (|HasCategory| (-583 |#1|) (QUOTE (-145))) (|HasCategory| (-583 |#1|) (QUOTE (-370)))) (|HasCategory| (-583 |#1|) (QUOTE (-147))) (|HasCategory| (-583 |#1|) (QUOTE (-370))) (|HasCategory| (-583 |#1|) (QUOTE (-145)))) 
 (-521 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-522 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-523 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
@@ -2031,7 +2031,7 @@ NIL
 (-525 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-526) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
@@ -2064,7 +2064,7 @@ NIL
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
 NIL 
-(-534 K -2286 |Par|) 
+(-534 K -2382 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
@@ -2088,7 +2088,7 @@ NIL
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-540 K -2286 |Par|) 
+(-540 K -2382 |Par|) 
 ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) 
 NIL 
 NIL 
@@ -2139,12 +2139,12 @@ NIL
 (-552 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
-(-553 R -2286) 
+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
+(-553 R -2382) 
 ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) 
 NIL 
 NIL 
-(-554 R0 -2286 UP UPUP R) 
+(-554 R0 -2382 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) 
 NIL 
 NIL 
@@ -2154,7 +2154,7 @@ NIL
 NIL 
 (-556 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."))) 
-((-3601 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-557 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."))) 
@@ -2164,7 +2164,7 @@ NIL
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
 ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
-(-559 R -2286) 
+(-559 R -2382) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
@@ -2176,7 +2176,7 @@ NIL
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-562 R -2286 L) 
+(-562 R -2382 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -656) (|devaluate| |#2|)))) 
@@ -2184,11 +2184,11 @@ NIL
 ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) 
 NIL 
 NIL 
-(-564 -2286 UP UPUP R) 
+(-564 -2382 UP UPUP R) 
 ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) 
 NIL 
 NIL 
-(-565 -2286 UP) 
+(-565 -2382 UP) 
 ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) 
 NIL 
 NIL 
@@ -2200,15 +2200,15 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) 
 NIL 
 NIL 
-(-568 R -2286 L) 
+(-568 R -2382 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -656) (|devaluate| |#2|)))) 
-(-569 R -2286) 
+(-569 R -2382) 
 ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1138)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-629))))) 
-(-570 -2286 UP) 
+(-570 -2382 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
@@ -2216,27 +2216,27 @@ NIL
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-572 -2286) 
+(-572 -2382) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
 (-573 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."))) 
-((-3601 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-574) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-575 R -2286) 
+(-575 R -2382) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-629))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-558)))) 
-(-576 -2286 UP) 
+(-576 -2382 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-577 R -2286) 
+(-577 R -2382) 
 ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) 
 NIL 
 NIL 
@@ -2268,15 +2268,15 @@ NIL
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-585 R -2286) 
+(-585 R -2382) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-586 E -2286) 
+(-586 E -2382) 
 ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) 
 NIL 
 NIL 
-(-587 -2286) 
+(-587 -2382) 
 ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) 
 ((-4412 . T) (-4411 . T)) 
 ((|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175))))) 
@@ -2307,7 +2307,7 @@ NIL
 (-594 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2700 (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
+((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2805 (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
 (-595 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
@@ -2315,7 +2315,7 @@ NIL
 (-596 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) 
 (-597 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
 ((-4412 |has| |#1| (-558)) (-4411 |has| |#1| (-558)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4414 . T)) 
@@ -2328,7 +2328,7 @@ NIL
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) 
 NIL 
 NIL 
-(-600 R -2286 FG) 
+(-600 R -2382 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
@@ -2339,7 +2339,7 @@ NIL
 (-602 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-603 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
@@ -2358,12 +2358,12 @@ NIL
 NIL 
 (-607 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-4414 -2700 (-2336 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) 
-((-2700 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) 
+((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) 
+((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) 
 (-608 |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."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-609 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 
@@ -2388,7 +2388,7 @@ NIL
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-615 -2286 UP) 
+(-615 -2382 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
@@ -2416,7 +2416,7 @@ NIL
 ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 ((|HasCategory| |#1| (QUOTE (-848)))) 
-(-622 R -2286) 
+(-622 R -2382) 
 ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) 
 NIL 
 NIL 
@@ -2448,18 +2448,18 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-630 R -2286) 
+(-630 R -2382) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
-(-631 |lv| -2286) 
+(-631 |lv| -2382) 
 ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) 
 NIL 
 NIL 
 (-632) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099)))) 
+((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099)))) 
 (-633 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2470,8 +2470,8 @@ NIL
 NIL 
 (-635 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) 
-((-4414 -2700 (-2336 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) 
-((-2700 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) 
+((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) 
+((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) 
 (-636 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) 
 NIL 
@@ -2483,7 +2483,7 @@ NIL
 (-638 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 
-((-2326 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) 
+((-2426 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) 
 (-639 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) 
 ((-4414 . T)) 
@@ -2507,7 +2507,7 @@ NIL
 (-644 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-645 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
@@ -2519,7 +2519,7 @@ NIL
 (-647 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-648 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
@@ -2536,7 +2536,7 @@ NIL
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-652 R -2286 L) 
+(-652 R -2382 L) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
@@ -2556,11 +2556,11 @@ NIL
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
-(-657 -2286 UP) 
+(-657 -2382 UP) 
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-658 A -2887) 
+(-658 A -2614) 
 ((|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}}"))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) 
@@ -2596,11 +2596,11 @@ NIL
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
 ((-4418 . T) (-4417 . T)) 
 NIL 
-(-667 -2286) 
+(-667 -2382) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-668 -2286 |Row| |Col| M) 
+(-668 -2382 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
@@ -2611,7 +2611,7 @@ NIL
 (-670 |n| R) 
 ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) 
 ((-4414 . T) (-4417 . T) (-4411 . T) (-4412 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2700 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
+((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2805 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
 (-671) 
 ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) 
 NIL 
@@ -2631,7 +2631,7 @@ NIL
 (-675 R) 
 ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) 
 NIL 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-676) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -2687,7 +2687,7 @@ NIL
 (-689 R) 
 ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) 
 ((-4417 . T) (-4418 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-690 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
@@ -2696,7 +2696,7 @@ NIL
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) 
 NIL 
 NIL 
-(-692 S -2286 FLAF FLAS) 
+(-692 S -2382 FLAF FLAS) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 
 NIL 
 NIL 
@@ -2706,8 +2706,8 @@ NIL
 NIL 
 (-694) 
 ((|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"))) 
-((-4410 . T) (-4415 |has| (-699) (-365)) (-4409 |has| (-699) (-365)) (-3611 . T) (-4416 |has| (-699) (-6 -4416)) (-4413 |has| (-699) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2700 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2700 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2700 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4416)) (|HasAttribute| (-699) (QUOTE -4413)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) 
+((-4410 . T) (-4415 |has| (-699) (-365)) (-4409 |has| (-699) (-365)) (-3654 . T) (-4416 |has| (-699) (-6 -4416)) (-4413 |has| (-699) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2805 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2805 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4416)) (|HasAttribute| (-699) (QUOTE -4413)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) 
 (-695 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}."))) 
 ((-4418 . T)) 
@@ -2720,13 +2720,13 @@ NIL
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) 
 NIL 
 NIL 
-(-698 OV E -2286 PG) 
+(-698 OV E -2382 PG) 
 ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) 
 NIL 
 NIL 
 (-699) 
 ((|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}"))) 
-((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
+((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-700 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."))) 
@@ -2752,7 +2752,7 @@ 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 
-(-706 S -2739 I) 
+(-706 S -2840 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 
@@ -2772,14 +2772,14 @@ NIL
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-711 R |Mod| -1467 -2806 |exactQuo|) 
+(-711 R |Mod| -3550 -3132 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-712 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
 (-713 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
@@ -2788,7 +2788,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) 
-(-715 R |Mod| -1467 -2806 |exactQuo|) 
+(-715 R |Mod| -3550 -3132 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
 ((-4414 . T)) 
 NIL 
@@ -2800,7 +2800,7 @@ NIL
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 ((-4412 . T) (-4411 . T)) 
 NIL 
-(-718 -2286) 
+(-718 -2382) 
 ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) 
 ((-4414 . T)) 
 NIL 
@@ -2836,7 +2836,7 @@ NIL
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-727 -2286 UP) 
+(-727 -2382 UP) 
 ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
@@ -2855,7 +2855,7 @@ NIL
 (-731 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) 
 (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#2| (QUOTE (-909))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
 (-732 E OV R PRF) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
@@ -2988,11 +2988,11 @@ NIL
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-765 -2286) 
+(-765 -2382) 
 ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) 
 NIL 
 NIL 
-(-766 P -2286) 
+(-766 P -2382) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) 
 NIL 
 NIL 
@@ -3000,7 +3000,7 @@ NIL
 NIL 
 NIL 
 NIL 
-(-768 UP -2286) 
+(-768 UP -2382) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
@@ -3016,7 +3016,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) 
 (((-4419 "*") . T)) 
 NIL 
-(-772 R -2286) 
+(-772 R -2382) 
 ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) 
 NIL 
 NIL 
@@ -3036,7 +3036,7 @@ NIL
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-777 -2286 |ExtF| |SUEx| |ExtP| |n|) 
+(-777 -2382 |ExtF| |SUEx| |ExtP| |n|) 
 ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3051,7 +3051,7 @@ NIL
 (-780 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."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
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 (-781 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 
@@ -3059,7 +3059,7 @@ NIL
 (-782 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
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 (-783 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) 
 NIL 
@@ -3120,23 +3120,23 @@ NIL
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
-(-798 -2700 R OS S) 
+(-798 -2805 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
 (-799 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
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 (-800) 
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-801 R -2286 L) 
+(-801 R -2382 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-802 R -2286) 
+(-802 R -2382) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
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@@ -3144,7 +3144,7 @@ NIL
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) 
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-(-804 R -2286) 
+(-804 R -2382) 
 ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) 
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@@ -3152,11 +3152,11 @@ NIL
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
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-(-806 -2286 UP UPUP R) 
+(-806 -2382 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
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-(-807 -2286 UP L LQ) 
+(-807 -2382 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
 NIL 
 NIL 
@@ -3164,38 +3164,38 @@ NIL
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-809 -2286 UP L LQ) 
+(-809 -2382 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-810 -2286 UP) 
+(-810 -2382 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-811 -2286 L UP A LO) 
+(-811 -2382 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
 NIL 
 NIL 
-(-812 -2286 UP) 
+(-812 -2382 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-813 -2286 LO) 
+(-813 -2382 LO) 
 ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) 
 NIL 
 NIL 
-(-814 -2286 LODO) 
+(-814 -2382 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-815 -2201 S |f|) 
+(-815 -2293 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
 ((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) 
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(|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (|HasCategory| |#2| (QUOTE (-1049))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4414)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) 
 (-816 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
 (-817 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
 (((-4419 "*") |has| |#2| (-365)) (-4410 |has| |#2| (-365)) (-4415 |has| |#2| (-365)) (-4409 |has| |#2| (-365)) (-4414 . T) (-4412 . T) (-4411 . T)) 
@@ -3263,7 +3263,7 @@ NIL
 (-833 R) 
 ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) 
 ((-4414 |has| |#1| (-848))) 
-((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) 
+((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) 
 (-834 A S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,{}n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
@@ -3303,12 +3303,12 @@ NIL
 (-843 R) 
 ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) 
 ((-4414 |has| |#1| (-848))) 
-((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) 
+((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) 
 (-844) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-845 -2201 S) 
+(-845 -2293 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
@@ -3344,11 +3344,11 @@ NIL
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) 
-(-854 R |sigma| -1674) 
+(-854 R |sigma| -2916) 
 ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) 
-(-855 |x| R |sigma| -1674) 
+(-855 |x| R |sigma| -2916) 
 ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) 
 ((-4411 . T) (-4412 . T) (-4414 . T)) 
 ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-365)))) 
@@ -3415,15 +3415,15 @@ NIL
 (-871 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-870 |#1|) (QUOTE (-909))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-147))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-870 |#1|) (QUOTE (-1022))) (|HasCategory| (-870 |#1|) (QUOTE (-820))) (-2700 (|HasCategory| (-870 |#1|) (QUOTE (-820))) (|HasCategory| (-870 |#1|) (QUOTE (-850)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-1150))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-233))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-308))) (|HasCategory| (-870 |#1|) (QUOTE (-547))) (|HasCategory| (-870 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))))) 
+((|HasCategory| (-870 |#1|) (QUOTE (-909))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-147))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-870 |#1|) (QUOTE (-1022))) (|HasCategory| (-870 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-870 |#1|) (QUOTE (-820))) (|HasCategory| (-870 |#1|) (QUOTE (-850)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-1150))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-233))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-308))) (|HasCategory| (-870 |#1|) (QUOTE (-547))) (|HasCategory| (-870 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))))) 
 (-872 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (-2700 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (-2805 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
 (-873 S T$) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) 
 (-874) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) 
 NIL 
@@ -3479,7 +3479,7 @@ NIL
 (-887 |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 (-2326 (|HasCategory| |#2| (QUOTE (-1049)))) (-2326 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2326 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) 
+((-12 (-2426 (|HasCategory| |#2| (QUOTE (-1049)))) (-2426 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2426 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) 
 (-888 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 
@@ -3488,7 +3488,7 @@ 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 
-(-890 R -2739) 
+(-890 R -2840) 
 ((|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 
@@ -3512,7 +3512,7 @@ NIL
 ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-896 UP -2286) 
+(-896 UP -2382) 
 ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3535,7 +3535,7 @@ NIL
 (-901 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-902 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
@@ -3551,7 +3551,7 @@ NIL
 (-905 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
 ((-4414 . T)) 
-((-2700 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) 
+((-2805 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) 
 (-906 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
@@ -3572,7 +3572,7 @@ NIL
 ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) 
-(-911 R0 -2286 UP UPUP R) 
+(-911 R0 -2382 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3600,7 +3600,7 @@ NIL
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) 
 NIL 
 NIL 
-(-918 -2286) 
+(-918 -2382) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
@@ -3616,11 +3616,11 @@ NIL
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
 (((-4419 "*") . T)) 
 NIL 
-(-922 -2286 P) 
+(-922 -2382 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-923 |xx| -2286) 
+(-923 |xx| -2382) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) 
 NIL 
 NIL 
@@ -3644,7 +3644,7 @@ NIL
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-929 R -2286) 
+(-929 R -2382) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
@@ -3656,7 +3656,7 @@ NIL
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-932 S R -2286) 
+(-932 S R -2382) 
 ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
@@ -3676,11 +3676,11 @@ 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 -886) (|devaluate| |#1|)))) 
-(-937 R -2286 -2739) 
+(-937 R -2382 -2840) 
 ((|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 
-(-938 -2739) 
+(-938 -2840) 
 ((|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 
@@ -3703,7 +3703,7 @@ NIL
 (-943 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-944 |lv| R) 
 ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) 
 NIL 
@@ -3728,7 +3728,7 @@ NIL
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
 NIL 
-(-950 E V R P -2286) 
+(-950 E V R P -2382) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
@@ -3739,8 +3739,8 @@ NIL
 (-952 R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
-(-953 E V R P -2286) 
+((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) 
+(-953 E V R P -2382) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-454)))) 
@@ -3763,12 +3763,12 @@ NIL
 (-958 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-959) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) 
 NIL 
 NIL 
-(-960 -2286) 
+(-960 -2382) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
@@ -3783,11 +3783,11 @@ NIL
 (-963 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4415))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4415))) 
 (-964 A B) 
 ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) 
 ((-4414 -12 (|has| |#2| (-475)) (|has| |#1| (-475)))) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) 
 (-965) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
@@ -3868,7 +3868,7 @@ NIL
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-985 K R UP -2286) 
+(-985 K R UP -2382) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
@@ -3927,11 +3927,11 @@ NIL
 (-999 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.}"))) 
 ((-4410 |has| |#1| (-291)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547)))) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547)))) 
 (-1000 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}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1001 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
@@ -3940,14 +3940,14 @@ NIL
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1003 -2286 UP UPUP |radicnd| |n|) 
+(-1003 -2382 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
 ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2700 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2700 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2700 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2700 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) 
+((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) 
 (-1004 |bb|) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2700 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
+((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) 
 (-1005) 
 ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) 
 NIL 
@@ -3980,19 +3980,19 @@ NIL
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 ((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) 
 NIL 
-(-1013 R -2286) 
+(-1013 R -2382) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) 
 NIL 
 NIL 
-(-1014 R -2286) 
+(-1014 R -2382) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) 
 NIL 
 NIL 
-(-1015 -2286 UP) 
+(-1015 -2382 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-1016 -2286 UP) 
+(-1016 -2382 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
@@ -4027,8 +4027,8 @@ NIL
 (-1024 |TheField|) 
 ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) 
 ((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) 
-((-2700 (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566))))) 
-(-1025 -2286 L) 
+((-2805 (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566))))) 
+(-1025 -2382 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
@@ -4064,14 +4064,14 @@ NIL
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-1034 -2286 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1034 -2382 |Expon| |VarSet| |FPol| |LFPol|) 
 ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) 
 (((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
 (-1035) 
 ((|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.}"))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1036) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4128,7 +4128,7 @@ NIL
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 ((-4414 . T)) 
 NIL 
-(-1050 |xx| -2286) 
+(-1050 |xx| -2382) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
@@ -4147,7 +4147,7 @@ NIL
 (-1054 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
 ((-4417 . T) (-4412 . T) (-4411 . T)) 
-((|HasCategory| |#3| (QUOTE (-172))) (-2700 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-558))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((|HasCategory| |#3| (QUOTE (-172))) (-2805 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-558))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1055 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
@@ -4179,7 +4179,7 @@ NIL
 (-1062) 
 ((|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}"))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1063 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 
@@ -4228,11 +4228,11 @@ NIL
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1075 |Base| R -2286) 
+(-1075 |Base| R -2382) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-1076 |Base| R -2286) 
+(-1076 |Base| R -2382) 
 ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) 
 NIL 
 NIL 
@@ -4247,7 +4247,7 @@ NIL
 (-1079 R UP M) 
 ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) 
 ((-4410 |has| |#1| (-365)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) 
 (-1080 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
@@ -4275,7 +4275,7 @@ NIL
 (-1086 R) 
 ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) 
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 (-1087 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) 
 NIL 
@@ -4335,7 +4335,7 @@ NIL
 (-1101 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) 
 ((-4417 . T) (-4407 . T) (-4418 . T)) 
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 (-1102 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
@@ -4379,7 +4379,7 @@ NIL
 (-1112 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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 (-1113 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
@@ -4388,7 +4388,7 @@ NIL
 ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) 
 NIL 
 NIL 
-(-1115 R -2286) 
+(-1115 R -2382) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
@@ -4427,16 +4427,16 @@ NIL
 (-1124 R |VarSet|) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) 
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 (-1125 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) 
 (-1126 R E V P) 
 ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) 
 ((-4418 . T) (-4417 . T)) 
 NIL 
-(-1127 UP -2286) 
+(-1127 UP -2382) 
 ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) 
 NIL 
 NIL 
@@ -4491,11 +4491,11 @@ NIL
 (-1140 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2700 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2805 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1141 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) 
 ((-4414 . T) (-4406 |has| |#2| (-6 (-4419 "*"))) (-4417 . T) (-4411 . T) (-4412 . T)) 
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+((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (-2805 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) 
 (-1142 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
@@ -4515,7 +4515,7 @@ NIL
 (-1146 S) 
 ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1147 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
@@ -4527,7 +4527,7 @@ NIL
 (-1149 |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."))) 
 ((-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099)))) 
+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099)))) 
 (-1150) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
@@ -4551,7 +4551,7 @@ NIL
 (-1155 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
 ((-4418 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1156) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
 ((-4418 . T) (-4417 . T)) 
@@ -4559,11 +4559,11 @@ NIL
 (-1157) 
 NIL 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
+((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) 
 (-1158 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#1|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1159 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) 
 NIL 
@@ -4594,9 +4594,9 @@ NIL
 NIL 
 (-1166 |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."))) 
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+(-1167 R -2382) 
 ((|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 
 NIL 
@@ -4615,15 +4615,15 @@ NIL
 (-1171 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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 (-1172 |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}."))) 
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-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
 (-1173 |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}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
 (-1174) 
 ((|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 
@@ -4639,7 +4639,7 @@ NIL
 (-1177 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| (-971) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasAttribute| |#1| (QUOTE -4415))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| (-971) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasAttribute| |#1| (QUOTE -4415))) 
 (-1178) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
@@ -4679,7 +4679,7 @@ NIL
 (-1187 |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}"))) 
 ((-4417 . T) (-4418 . T)) 
-((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1188 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) 
 NIL 
@@ -4731,7 +4731,7 @@ NIL
 (-1200 S) 
 ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
 ((-4418 . T) (-4417 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
 (-1201 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
@@ -4740,7 +4740,7 @@ NIL
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1203 R -2286) 
+(-1203 R -2382) 
 ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -4748,7 +4748,7 @@ NIL
 ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) 
 NIL 
 NIL 
-(-1205 R -2286) 
+(-1205 R -2382) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -886) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -886) (|devaluate| |#1|))))) 
@@ -4763,7 +4763,7 @@ NIL
 (-1208 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) 
 (-1209 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) 
 NIL 
@@ -4776,7 +4776,7 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) 
-(-1212 -2286) 
+(-1212 -2382) 
 ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) 
 NIL 
 NIL 
@@ -4839,11 +4839,11 @@ NIL
 (-1227 |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)}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) 
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 (-1229 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 
@@ -4879,7 +4879,7 @@ NIL
 (-1237 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
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-((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
+((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) 
 (-1238 R PR S PS) 
 ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) 
 NIL 
@@ -4895,7 +4895,7 @@ NIL
 (-1241 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2409) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) 
+((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2512) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) 
 (-1242 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
@@ -4923,21 +4923,21 @@ NIL
 (-1248 |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)}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) 
+((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) 
 (-1249 |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}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
 (-1250 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))}."))) 
 (((-4419 "*") |has| (-1249 |#2| |#3| |#4|) (-172)) (-4410 |has| (-1249 |#2| |#3| |#4|) (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-172))) (-2700 (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-558)))) 
+((|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-172))) (-2805 (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-558)))) 
 (-1251 A S) 
-((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
+((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 ((|HasAttribute| |#1| (QUOTE -4418))) 
 (-1252 S) 
-((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
+((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
 (-1253 |Coef1| |Coef2| UTS1 UTS2) 
@@ -4947,7 +4947,7 @@ NIL
 (-1254 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3450) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4117) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) 
 (-1255 |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."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
@@ -4955,12 +4955,12 @@ NIL
 (-1256 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
 (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) 
 (-1257 |Coef| UTS) 
 ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) 
 NIL 
 NIL 
-(-1258 -2286 UP L UTS) 
+(-1258 -2382 UP L UTS) 
 ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-558)))) 
@@ -4987,7 +4987,7 @@ NIL
 (-1264 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
 ((-4418 . T) (-4417 . T)) 
-((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
+((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) 
 (-1265) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
@@ -5020,7 +5020,7 @@ NIL
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1273 K R UP -2286) 
+(-1273 K R UP -2382) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
@@ -5056,11 +5056,11 @@ NIL
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
 ((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) 
 NIL 
-(-1282 S -2286) 
+(-1282 S -2382) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) 
-(-1283 -2286) 
+(-1283 -2382) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) 
 NIL 
@@ -5116,4 +5116,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2285479 2285484 2285489 2285494) (-2 NIL 2285459 2285464 2285469 2285474) (-1 NIL 2285439 2285444 2285449 2285454) (0 NIL 2285419 2285424 2285429 2285434) (-1292 "ZMOD.spad" 2285228 2285241 2285357 2285414) (-1291 "ZLINDEP.spad" 2284272 2284283 2285218 2285223) (-1290 "ZDSOLVE.spad" 2274121 2274143 2284262 2284267) (-1289 "YSTREAM.spad" 2273614 2273625 2274111 2274116) (-1288 "XRPOLY.spad" 2272834 2272854 2273470 2273539) (-1287 "XPR.spad" 2270625 2270638 2272552 2272651) (-1286 "XPOLY.spad" 2270180 2270191 2270481 2270550) (-1285 "XPOLYC.spad" 2269497 2269513 2270106 2270175) (-1284 "XPBWPOLY.spad" 2267934 2267954 2269277 2269346) (-1283 "XF.spad" 2266395 2266410 2267836 2267929) (-1282 "XF.spad" 2264836 2264853 2266279 2266284) (-1281 "XFALG.spad" 2261860 2261876 2264762 2264831) (-1280 "XEXPPKG.spad" 2261111 2261137 2261850 2261855) (-1279 "XDPOLY.spad" 2260725 2260741 2260967 2261036) (-1278 "XALG.spad" 2260385 2260396 2260681 2260720) (-1277 "WUTSET.spad" 2256224 2256241 2260031 2260058) (-1276 "WP.spad" 2255423 2255467 2256082 2256149) (-1275 "WHILEAST.spad" 2255221 2255230 2255413 2255418) (-1274 "WHEREAST.spad" 2254892 2254901 2255211 2255216) (-1273 "WFFINTBS.spad" 2252455 2252477 2254882 2254887) (-1272 "WEIER.spad" 2250669 2250680 2252445 2252450) (-1271 "VSPACE.spad" 2250342 2250353 2250637 2250664) (-1270 "VSPACE.spad" 2250035 2250048 2250332 2250337) (-1269 "VOID.spad" 2249712 2249721 2250025 2250030) (-1268 "VIEW.spad" 2247334 2247343 2249702 2249707) (-1267 "VIEWDEF.spad" 2242531 2242540 2247324 2247329) (-1266 "VIEW3D.spad" 2226366 2226375 2242521 2242526) (-1265 "VIEW2D.spad" 2214103 2214112 2226356 2226361) (-1264 "VECTOR.spad" 2212777 2212788 2213028 2213055) (-1263 "VECTOR2.spad" 2211404 2211417 2212767 2212772) (-1262 "VECTCAT.spad" 2209304 2209315 2211372 2211399) (-1261 "VECTCAT.spad" 2207011 2207024 2209081 2209086) (-1260 "VARIABLE.spad" 2206791 2206806 2207001 2207006) (-1259 "UTYPE.spad" 2206435 2206444 2206781 2206786) (-1258 "UTSODETL.spad" 2205728 2205752 2206391 2206396) (-1257 "UTSODE.spad" 2203916 2203936 2205718 2205723) (-1256 "UTS.spad" 2198705 2198733 2202383 2202480) (-1255 "UTSCAT.spad" 2196156 2196172 2198603 2198700) (-1254 "UTSCAT.spad" 2193251 2193269 2195700 2195705) (-1253 "UTS2.spad" 2192844 2192879 2193241 2193246) (-1252 "URAGG.spad" 2187476 2187487 2192834 2192839) (-1251 "URAGG.spad" 2182072 2182085 2187432 2187437) (-1250 "UPXSSING.spad" 2179715 2179741 2181153 2181286) (-1249 "UPXS.spad" 2176863 2176891 2177847 2177996) (-1248 "UPXSCONS.spad" 2174620 2174640 2174995 2175144) (-1247 "UPXSCCA.spad" 2173185 2173205 2174466 2174615) (-1246 "UPXSCCA.spad" 2171892 2171914 2173175 2173180) (-1245 "UPXSCAT.spad" 2170473 2170489 2171738 2171887) (-1244 "UPXS2.spad" 2170014 2170067 2170463 2170468) (-1243 "UPSQFREE.spad" 2168426 2168440 2170004 2170009) (-1242 "UPSCAT.spad" 2166019 2166043 2168324 2168421) (-1241 "UPSCAT.spad" 2163318 2163344 2165625 2165630) (-1240 "UPOLYC.spad" 2158296 2158307 2163160 2163313) (-1239 "UPOLYC.spad" 2153166 2153179 2158032 2158037) (-1238 "UPOLYC2.spad" 2152635 2152654 2153156 2153161) (-1237 "UP.spad" 2149828 2149843 2150221 2150374) (-1236 "UPMP.spad" 2148718 2148731 2149818 2149823) (-1235 "UPDIVP.spad" 2148281 2148295 2148708 2148713) (-1234 "UPDECOMP.spad" 2146518 2146532 2148271 2148276) (-1233 "UPCDEN.spad" 2145725 2145741 2146508 2146513) (-1232 "UP2.spad" 2145087 2145108 2145715 2145720) (-1231 "UNISEG.spad" 2144440 2144451 2145006 2145011) (-1230 "UNISEG2.spad" 2143933 2143946 2144396 2144401) (-1229 "UNIFACT.spad" 2143034 2143046 2143923 2143928) (-1228 "ULS.spad" 2133586 2133614 2134679 2135108) (-1227 "ULSCONS.spad" 2125980 2126000 2126352 2126501) (-1226 "ULSCCAT.spad" 2123709 2123729 2125826 2125975) (-1225 "ULSCCAT.spad" 2121546 2121568 2123665 2123670) (-1224 "ULSCAT.spad" 2119762 2119778 2121392 2121541) (-1223 "ULS2.spad" 2119274 2119327 2119752 2119757) (-1222 "UINT8.spad" 2119151 2119160 2119264 2119269) (-1221 "UINT64.spad" 2119027 2119036 2119141 2119146) (-1220 "UINT32.spad" 2118903 2118912 2119017 2119022) (-1219 "UINT16.spad" 2118779 2118788 2118893 2118898) (-1218 "UFD.spad" 2117844 2117853 2118705 2118774) (-1217 "UFD.spad" 2116971 2116982 2117834 2117839) (-1216 "UDVO.spad" 2115818 2115827 2116961 2116966) (-1215 "UDPO.spad" 2113245 2113256 2115774 2115779) (-1214 "TYPE.spad" 2113177 2113186 2113235 2113240) (-1213 "TYPEAST.spad" 2113096 2113105 2113167 2113172) (-1212 "TWOFACT.spad" 2111746 2111761 2113086 2113091) (-1211 "TUPLE.spad" 2111230 2111241 2111645 2111650) (-1210 "TUBETOOL.spad" 2108067 2108076 2111220 2111225) (-1209 "TUBE.spad" 2106708 2106725 2108057 2108062) (-1208 "TS.spad" 2105297 2105313 2106273 2106370) (-1207 "TSETCAT.spad" 2092424 2092441 2105265 2105292) (-1206 "TSETCAT.spad" 2079537 2079556 2092380 2092385) (-1205 "TRMANIP.spad" 2073903 2073920 2079243 2079248) (-1204 "TRIMAT.spad" 2072862 2072887 2073893 2073898) (-1203 "TRIGMNIP.spad" 2071379 2071396 2072852 2072857) (-1202 "TRIGCAT.spad" 2070891 2070900 2071369 2071374) (-1201 "TRIGCAT.spad" 2070401 2070412 2070881 2070886) (-1200 "TREE.spad" 2068972 2068983 2070008 2070035) (-1199 "TRANFUN.spad" 2068803 2068812 2068962 2068967) (-1198 "TRANFUN.spad" 2068632 2068643 2068793 2068798) (-1197 "TOPSP.spad" 2068306 2068315 2068622 2068627) (-1196 "TOOLSIGN.spad" 2067969 2067980 2068296 2068301) (-1195 "TEXTFILE.spad" 2066526 2066535 2067959 2067964) (-1194 "TEX.spad" 2063658 2063667 2066516 2066521) (-1193 "TEX1.spad" 2063214 2063225 2063648 2063653) (-1192 "TEMUTL.spad" 2062769 2062778 2063204 2063209) (-1191 "TBCMPPK.spad" 2060862 2060885 2062759 2062764) (-1190 "TBAGG.spad" 2059898 2059921 2060842 2060857) (-1189 "TBAGG.spad" 2058942 2058967 2059888 2059893) (-1188 "TANEXP.spad" 2058318 2058329 2058932 2058937) (-1187 "TABLE.spad" 2056729 2056752 2056999 2057026) (-1186 "TABLEAU.spad" 2056210 2056221 2056719 2056724) (-1185 "TABLBUMP.spad" 2052993 2053004 2056200 2056205) (-1184 "SYSTEM.spad" 2052221 2052230 2052983 2052988) (-1183 "SYSSOLP.spad" 2049694 2049705 2052211 2052216) (-1182 "SYSNNI.spad" 2048874 2048885 2049684 2049689) (-1181 "SYSINT.spad" 2048278 2048289 2048864 2048869) (-1180 "SYNTAX.spad" 2044472 2044481 2048268 2048273) (-1179 "SYMTAB.spad" 2042528 2042537 2044462 2044467) (-1178 "SYMS.spad" 2038513 2038522 2042518 2042523) (-1177 "SYMPOLY.spad" 2037520 2037531 2037602 2037729) (-1176 "SYMFUNC.spad" 2036995 2037006 2037510 2037515) (-1175 "SYMBOL.spad" 2034422 2034431 2036985 2036990) (-1174 "SWITCH.spad" 2031179 2031188 2034412 2034417) (-1173 "SUTS.spad" 2028078 2028106 2029646 2029743) (-1172 "SUPXS.spad" 2025213 2025241 2026210 2026359) (-1171 "SUP.spad" 2022018 2022029 2022799 2022952) (-1170 "SUPFRACF.spad" 2021123 2021141 2022008 2022013) (-1169 "SUP2.spad" 2020513 2020526 2021113 2021118) (-1168 "SUMRF.spad" 2019479 2019490 2020503 2020508) (-1167 "SUMFS.spad" 2019112 2019129 2019469 2019474) (-1166 "SULS.spad" 2009651 2009679 2010757 2011186) (-1165 "SUCHTAST.spad" 2009420 2009429 2009641 2009646) (-1164 "SUCH.spad" 2009100 2009115 2009410 2009415) (-1163 "SUBSPACE.spad" 2001107 2001122 2009090 2009095) (-1162 "SUBRESP.spad" 2000267 2000281 2001063 2001068) (-1161 "STTF.spad" 1996366 1996382 2000257 2000262) (-1160 "STTFNC.spad" 1992834 1992850 1996356 1996361) (-1159 "STTAYLOR.spad" 1985232 1985243 1992715 1992720) (-1158 "STRTBL.spad" 1983737 1983754 1983886 1983913) (-1157 "STRING.spad" 1983146 1983155 1983160 1983187) (-1156 "STRICAT.spad" 1982934 1982943 1983114 1983141) (-1155 "STREAM.spad" 1979792 1979803 1982459 1982474) (-1154 "STREAM3.spad" 1979337 1979352 1979782 1979787) (-1153 "STREAM2.spad" 1978405 1978418 1979327 1979332) (-1152 "STREAM1.spad" 1978109 1978120 1978395 1978400) (-1151 "STINPROD.spad" 1977015 1977031 1978099 1978104) (-1150 "STEP.spad" 1976216 1976225 1977005 1977010) (-1149 "STBL.spad" 1974742 1974770 1974909 1974924) (-1148 "STAGG.spad" 1973817 1973828 1974732 1974737) (-1147 "STAGG.spad" 1972890 1972903 1973807 1973812) (-1146 "STACK.spad" 1972241 1972252 1972497 1972524) (-1145 "SREGSET.spad" 1969945 1969962 1971887 1971914) (-1144 "SRDCMPK.spad" 1968490 1968510 1969935 1969940) (-1143 "SRAGG.spad" 1963587 1963596 1968458 1968485) (-1142 "SRAGG.spad" 1958704 1958715 1963577 1963582) (-1141 "SQMATRIX.spad" 1956320 1956338 1957236 1957323) (-1140 "SPLTREE.spad" 1950872 1950885 1955756 1955783) (-1139 "SPLNODE.spad" 1947460 1947473 1950862 1950867) (-1138 "SPFCAT.spad" 1946237 1946246 1947450 1947455) (-1137 "SPECOUT.spad" 1944787 1944796 1946227 1946232) (-1136 "SPADXPT.spad" 1936926 1936935 1944777 1944782) (-1135 "spad-parser.spad" 1936391 1936400 1936916 1936921) (-1134 "SPADAST.spad" 1936092 1936101 1936381 1936386) (-1133 "SPACEC.spad" 1920105 1920116 1936082 1936087) (-1132 "SPACE3.spad" 1919881 1919892 1920095 1920100) (-1131 "SORTPAK.spad" 1919426 1919439 1919837 1919842) (-1130 "SOLVETRA.spad" 1917183 1917194 1919416 1919421) (-1129 "SOLVESER.spad" 1915703 1915714 1917173 1917178) (-1128 "SOLVERAD.spad" 1911713 1911724 1915693 1915698) (-1127 "SOLVEFOR.spad" 1910133 1910151 1911703 1911708) (-1126 "SNTSCAT.spad" 1909733 1909750 1910101 1910128) (-1125 "SMTS.spad" 1907993 1908019 1909298 1909395) (-1124 "SMP.spad" 1905468 1905488 1905858 1905985) (-1123 "SMITH.spad" 1904311 1904336 1905458 1905463) (-1122 "SMATCAT.spad" 1902421 1902451 1904255 1904306) (-1121 "SMATCAT.spad" 1900463 1900495 1902299 1902304) (-1120 "SKAGG.spad" 1899424 1899435 1900431 1900458) (-1119 "SINT.spad" 1898250 1898259 1899290 1899419) (-1118 "SIMPAN.spad" 1897978 1897987 1898240 1898245) (-1117 "SIG.spad" 1897306 1897315 1897968 1897973) (-1116 "SIGNRF.spad" 1896414 1896425 1897296 1897301) (-1115 "SIGNEF.spad" 1895683 1895700 1896404 1896409) (-1114 "SIGAST.spad" 1895064 1895073 1895673 1895678) (-1113 "SHP.spad" 1892982 1892997 1895020 1895025) (-1112 "SHDP.spad" 1882693 1882720 1883202 1883333) (-1111 "SGROUP.spad" 1882301 1882310 1882683 1882688) (-1110 "SGROUP.spad" 1881907 1881918 1882291 1882296) (-1109 "SGCF.spad" 1874788 1874797 1881897 1881902) (-1108 "SFRTCAT.spad" 1873716 1873733 1874756 1874783) (-1107 "SFRGCD.spad" 1872779 1872799 1873706 1873711) (-1106 "SFQCMPK.spad" 1867416 1867436 1872769 1872774) (-1105 "SFORT.spad" 1866851 1866865 1867406 1867411) (-1104 "SEXOF.spad" 1866694 1866734 1866841 1866846) (-1103 "SEX.spad" 1866586 1866595 1866684 1866689) (-1102 "SEXCAT.spad" 1864137 1864177 1866576 1866581) (-1101 "SET.spad" 1862437 1862448 1863558 1863597) (-1100 "SETMN.spad" 1860871 1860888 1862427 1862432) (-1099 "SETCAT.spad" 1860193 1860202 1860861 1860866) (-1098 "SETCAT.spad" 1859513 1859524 1860183 1860188) (-1097 "SETAGG.spad" 1856034 1856045 1859493 1859508) (-1096 "SETAGG.spad" 1852563 1852576 1856024 1856029) (-1095 "SEQAST.spad" 1852266 1852275 1852553 1852558) (-1094 "SEGXCAT.spad" 1851388 1851401 1852256 1852261) (-1093 "SEG.spad" 1851201 1851212 1851307 1851312) (-1092 "SEGCAT.spad" 1850108 1850119 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1300457) (-792 "OAMON.spad" 1299843 1299851 1299972 1299977) (-791 "OAGROUP.spad" 1299705 1299713 1299833 1299838) (-790 "NUMTUBE.spad" 1299292 1299308 1299695 1299700) (-789 "NUMQUAD.spad" 1287154 1287162 1299282 1299287) (-788 "NUMODE.spad" 1278290 1278298 1287144 1287149) (-787 "NUMINT.spad" 1275848 1275856 1278280 1278285) (-786 "NUMFMT.spad" 1274688 1274696 1275838 1275843) (-785 "NUMERIC.spad" 1266760 1266770 1274493 1274498) (-784 "NTSCAT.spad" 1265262 1265278 1266728 1266755) (-783 "NTPOLFN.spad" 1264807 1264817 1265179 1265184) (-782 "NSUP.spad" 1257853 1257863 1262393 1262546) (-781 "NSUP2.spad" 1257245 1257257 1257843 1257848) (-780 "NSMP.spad" 1253476 1253495 1253784 1253911) (-779 "NREP.spad" 1251848 1251862 1253466 1253471) (-778 "NPCOEF.spad" 1251094 1251114 1251838 1251843) (-777 "NORMRETR.spad" 1250692 1250731 1251084 1251089) (-776 "NORMPK.spad" 1248594 1248613 1250682 1250687) (-775 "NORMMA.spad" 1248282 1248308 1248584 1248589) (-774 "NONE.spad" 1248023 1248031 1248272 1248277) (-773 "NONE1.spad" 1247699 1247709 1248013 1248018) (-772 "NODE1.spad" 1247168 1247184 1247689 1247694) (-771 "NNI.spad" 1246055 1246063 1247142 1247163) (-770 "NLINSOL.spad" 1244677 1244687 1246045 1246050) (-769 "NIPROB.spad" 1243218 1243226 1244667 1244672) (-768 "NFINTBAS.spad" 1240678 1240695 1243208 1243213) (-767 "NETCLT.spad" 1240652 1240663 1240668 1240673) (-766 "NCODIV.spad" 1238850 1238866 1240642 1240647) (-765 "NCNTFRAC.spad" 1238492 1238506 1238840 1238845) (-764 "NCEP.spad" 1236652 1236666 1238482 1238487) (-763 "NASRING.spad" 1236248 1236256 1236642 1236647) (-762 "NASRING.spad" 1235842 1235852 1236238 1236243) (-761 "NARNG.spad" 1235186 1235194 1235832 1235837) (-760 "NARNG.spad" 1234528 1234538 1235176 1235181) (-759 "NAGSP.spad" 1233601 1233609 1234518 1234523) (-758 "NAGS.spad" 1223126 1223134 1233591 1233596) (-757 "NAGF07.spad" 1221519 1221527 1223116 1223121) (-756 "NAGF04.spad" 1215751 1215759 1221509 1221514) (-755 "NAGF02.spad" 1209560 1209568 1215741 1215746) (-754 "NAGF01.spad" 1205163 1205171 1209550 1209555) (-753 "NAGE04.spad" 1198623 1198631 1205153 1205158) (-752 "NAGE02.spad" 1188965 1188973 1198613 1198618) (-751 "NAGE01.spad" 1184849 1184857 1188955 1188960) (-750 "NAGD03.spad" 1182769 1182777 1184839 1184844) (-749 "NAGD02.spad" 1175300 1175308 1182759 1182764) (-748 "NAGD01.spad" 1169413 1169421 1175290 1175295) (-747 "NAGC06.spad" 1165200 1165208 1169403 1169408) (-746 "NAGC05.spad" 1163669 1163677 1165190 1165195) (-745 "NAGC02.spad" 1162924 1162932 1163659 1163664) (-744 "NAALG.spad" 1162459 1162469 1162892 1162919) (-743 "NAALG.spad" 1162014 1162026 1162449 1162454) (-742 "MULTSQFR.spad" 1158972 1158989 1162004 1162009) (-741 "MULTFACT.spad" 1158355 1158372 1158962 1158967) (-740 "MTSCAT.spad" 1156389 1156410 1158253 1158350) (-739 "MTHING.spad" 1156046 1156056 1156379 1156384) (-738 "MSYSCMD.spad" 1155480 1155488 1156036 1156041) (-737 "MSET.spad" 1153422 1153432 1155186 1155225) (-736 "MSETAGG.spad" 1153267 1153277 1153390 1153417) (-735 "MRING.spad" 1150238 1150250 1152975 1153042) (-734 "MRF2.spad" 1149806 1149820 1150228 1150233) (-733 "MRATFAC.spad" 1149352 1149369 1149796 1149801) (-732 "MPRFF.spad" 1147382 1147401 1149342 1149347) (-731 "MPOLY.spad" 1144853 1144868 1145212 1145339) (-730 "MPCPF.spad" 1144117 1144136 1144843 1144848) (-729 "MPC3.spad" 1143932 1143972 1144107 1144112) (-728 "MPC2.spad" 1143574 1143607 1143922 1143927) (-727 "MONOTOOL.spad" 1141909 1141926 1143564 1143569) (-726 "MONOID.spad" 1141228 1141236 1141899 1141904) (-725 "MONOID.spad" 1140545 1140555 1141218 1141223) (-724 "MONOGEN.spad" 1139291 1139304 1140405 1140540) (-723 "MONOGEN.spad" 1138059 1138074 1139175 1139180) (-722 "MONADWU.spad" 1136073 1136081 1138049 1138054) (-721 "MONADWU.spad" 1134085 1134095 1136063 1136068) (-720 "MONAD.spad" 1133229 1133237 1134075 1134080) (-719 "MONAD.spad" 1132371 1132381 1133219 1133224) (-718 "MOEBIUS.spad" 1131057 1131071 1132351 1132366) (-717 "MODULE.spad" 1130927 1130937 1131025 1131052) (-716 "MODULE.spad" 1130817 1130829 1130917 1130922) (-715 "MODRING.spad" 1130148 1130187 1130797 1130812) (-714 "MODOP.spad" 1128807 1128819 1129970 1130037) (-713 "MODMONOM.spad" 1128536 1128554 1128797 1128802) (-712 "MODMON.spad" 1125331 1125347 1126050 1126203) (-711 "MODFIELD.spad" 1124689 1124728 1125233 1125326) (-710 "MMLFORM.spad" 1123549 1123557 1124679 1124684) (-709 "MMAP.spad" 1123289 1123323 1123539 1123544) (-708 "MLO.spad" 1121716 1121726 1123245 1123284) (-707 "MLIFT.spad" 1120288 1120305 1121706 1121711) (-706 "MKUCFUNC.spad" 1119821 1119839 1120278 1120283) (-705 "MKRECORD.spad" 1119423 1119436 1119811 1119816) (-704 "MKFUNC.spad" 1118804 1118814 1119413 1119418) (-703 "MKFLCFN.spad" 1117760 1117770 1118794 1118799) (-702 "MKBCFUNC.spad" 1117245 1117263 1117750 1117755) (-701 "MINT.spad" 1116684 1116692 1117147 1117240) (-700 "MHROWRED.spad" 1115185 1115195 1116674 1116679) (-699 "MFLOAT.spad" 1113701 1113709 1115075 1115180) (-698 "MFINFACT.spad" 1113101 1113123 1113691 1113696) (-697 "MESH.spad" 1110833 1110841 1113091 1113096) (-696 "MDDFACT.spad" 1109026 1109036 1110823 1110828) (-695 "MDAGG.spad" 1108313 1108323 1109006 1109021) (-694 "MCMPLX.spad" 1104324 1104332 1104938 1105139) (-693 "MCDEN.spad" 1103532 1103544 1104314 1104319) (-692 "MCALCFN.spad" 1100634 1100660 1103522 1103527) (-691 "MAYBE.spad" 1099918 1099929 1100624 1100629) (-690 "MATSTOR.spad" 1097194 1097204 1099908 1099913) (-689 "MATRIX.spad" 1095898 1095908 1096382 1096409) (-688 "MATLIN.spad" 1093224 1093248 1095782 1095787) (-687 "MATCAT.spad" 1084809 1084831 1093192 1093219) (-686 "MATCAT.spad" 1076266 1076290 1084651 1084656) (-685 "MATCAT2.spad" 1075534 1075582 1076256 1076261) (-684 "MAPPKG3.spad" 1074433 1074447 1075524 1075529) (-683 "MAPPKG2.spad" 1073767 1073779 1074423 1074428) (-682 "MAPPKG1.spad" 1072585 1072595 1073757 1073762) (-681 "MAPPAST.spad" 1071898 1071906 1072575 1072580) (-680 "MAPHACK3.spad" 1071706 1071720 1071888 1071893) (-679 "MAPHACK2.spad" 1071471 1071483 1071696 1071701) (-678 "MAPHACK1.spad" 1071101 1071111 1071461 1071466) (-677 "MAGMA.spad" 1068891 1068908 1071091 1071096) (-676 "MACROAST.spad" 1068470 1068478 1068881 1068886) (-675 "M3D.spad" 1066166 1066176 1067848 1067853) (-674 "LZSTAGG.spad" 1063394 1063404 1066156 1066161) (-673 "LZSTAGG.spad" 1060620 1060632 1063384 1063389) (-672 "LWORD.spad" 1057325 1057342 1060610 1060615) (-671 "LSTAST.spad" 1057109 1057117 1057315 1057320) (-670 "LSQM.spad" 1055335 1055349 1055733 1055784) (-669 "LSPP.spad" 1054868 1054885 1055325 1055330) (-668 "LSMP.spad" 1053708 1053736 1054858 1054863) (-667 "LSMP1.spad" 1051512 1051526 1053698 1053703) (-666 "LSAGG.spad" 1051181 1051191 1051480 1051507) (-665 "LSAGG.spad" 1050870 1050882 1051171 1051176) (-664 "LPOLY.spad" 1049824 1049843 1050726 1050795) (-663 "LPEFRAC.spad" 1049081 1049091 1049814 1049819) (-662 "LO.spad" 1048482 1048496 1049015 1049042) (-661 "LOGIC.spad" 1048084 1048092 1048472 1048477) (-660 "LOGIC.spad" 1047684 1047694 1048074 1048079) (-659 "LODOOPS.spad" 1046602 1046614 1047674 1047679) (-658 "LODO.spad" 1045986 1046002 1046282 1046321) (-657 "LODOF.spad" 1045030 1045047 1045943 1045948) (-656 "LODOCAT.spad" 1043688 1043698 1044986 1045025) (-655 "LODOCAT.spad" 1042344 1042356 1043644 1043649) (-654 "LODO2.spad" 1041617 1041629 1042024 1042063) (-653 "LODO1.spad" 1041017 1041027 1041297 1041336) (-652 "LODEEF.spad" 1039789 1039807 1041007 1041012) (-651 "LNAGG.spad" 1035591 1035601 1039779 1039784) (-650 "LNAGG.spad" 1031357 1031369 1035547 1035552) (-649 "LMOPS.spad" 1028093 1028110 1031347 1031352) (-648 "LMODULE.spad" 1027861 1027871 1028083 1028088) (-647 "LMDICT.spad" 1027144 1027154 1027412 1027439) (-646 "LLINSET.spad" 1026541 1026551 1027134 1027139) (-645 "LITERAL.spad" 1026447 1026458 1026531 1026536) (-644 "LIST.spad" 1024165 1024175 1025594 1025621) (-643 "LIST3.spad" 1023456 1023470 1024155 1024160) (-642 "LIST2.spad" 1022096 1022108 1023446 1023451) (-641 "LIST2MAP.spad" 1018973 1018985 1022086 1022091) (-640 "LINSET.spad" 1018595 1018605 1018963 1018968) (-639 "LINEXP.spad" 1018027 1018037 1018575 1018590) (-638 "LINDEP.spad" 1016804 1016816 1017939 1017944) (-637 "LIMITRF.spad" 1014718 1014728 1016794 1016799) (-636 "LIMITPS.spad" 1013601 1013614 1014708 1014713) (-635 "LIE.spad" 1011615 1011627 1012891 1013036) (-634 "LIECAT.spad" 1011091 1011101 1011541 1011610) (-633 "LIECAT.spad" 1010595 1010607 1011047 1011052) (-632 "LIB.spad" 1008643 1008651 1009254 1009269) (-631 "LGROBP.spad" 1005996 1006015 1008633 1008638) (-630 "LF.spad" 1004915 1004931 1005986 1005991) (-629 "LFCAT.spad" 1003934 1003942 1004905 1004910) (-628 "LEXTRIPK.spad" 999437 999452 1003924 1003929) (-627 "LEXP.spad" 997440 997467 999417 999432) (-626 "LETAST.spad" 997139 997147 997430 997435) (-625 "LEADCDET.spad" 995523 995540 997129 997134) (-624 "LAZM3PK.spad" 994227 994249 995513 995518) (-623 "LAUPOL.spad" 992916 992929 993820 993889) (-622 "LAPLACE.spad" 992489 992505 992906 992911) (-621 "LA.spad" 991929 991943 992411 992450) (-620 "LALG.spad" 991705 991715 991909 991924) (-619 "LALG.spad" 991489 991501 991695 991700) (-618 "KVTFROM.spad" 991224 991234 991479 991484) (-617 "KTVLOGIC.spad" 990736 990744 991214 991219) (-616 "KRCFROM.spad" 990474 990484 990726 990731) (-615 "KOVACIC.spad" 989187 989204 990464 990469) (-614 "KONVERT.spad" 988909 988919 989177 989182) (-613 "KOERCE.spad" 988646 988656 988899 988904) (-612 "KERNEL.spad" 987265 987275 988430 988435) (-611 "KERNEL2.spad" 986968 986980 987255 987260) (-610 "KDAGG.spad" 986071 986093 986948 986963) (-609 "KDAGG.spad" 985182 985206 986061 986066) (-608 "KAFILE.spad" 984145 984161 984380 984407) (-607 "JORDAN.spad" 981972 981984 983435 983580) (-606 "JOINAST.spad" 981666 981674 981962 981967) (-605 "JAVACODE.spad" 981532 981540 981656 981661) (-604 "IXAGG.spad" 979655 979679 981522 981527) (-603 "IXAGG.spad" 977633 977659 979502 979507) (-602 "IVECTOR.spad" 976403 976418 976558 976585) (-601 "ITUPLE.spad" 975548 975558 976393 976398) (-600 "ITRIGMNP.spad" 974359 974378 975538 975543) (-599 "ITFUN3.spad" 973853 973867 974349 974354) (-598 "ITFUN2.spad" 973583 973595 973843 973848) (-597 "ITAYLOR.spad" 971375 971390 973419 973544) (-596 "ISUPS.spad" 963786 963801 970349 970446) (-595 "ISUMP.spad" 963283 963299 963776 963781) (-594 "ISTRING.spad" 962286 962299 962452 962479) (-593 "ISAST.spad" 962005 962013 962276 962281) (-592 "IRURPK.spad" 960718 960737 961995 962000) (-591 "IRSN.spad" 958678 958686 960708 960713) (-590 "IRRF2F.spad" 957153 957163 958634 958639) (-589 "IRREDFFX.spad" 956754 956765 957143 957148) (-588 "IROOT.spad" 955085 955095 956744 956749) (-587 "IR.spad" 952874 952888 954940 954967) (-586 "IR2.spad" 951894 951910 952864 952869) (-585 "IR2F.spad" 951094 951110 951884 951889) (-584 "IPRNTPK.spad" 950854 950862 951084 951089) (-583 "IPF.spad" 950419 950431 950659 950752) (-582 "IPADIC.spad" 950180 950206 950345 950414) (-581 "IP4ADDR.spad" 949737 949745 950170 950175) (-580 "IOMODE.spad" 949358 949366 949727 949732) (-579 "IOBFILE.spad" 948719 948727 949348 949353) (-578 "IOBCON.spad" 948584 948592 948709 948714) (-577 "INVLAPLA.spad" 948229 948245 948574 948579) (-576 "INTTR.spad" 941475 941492 948219 948224) (-575 "INTTOOLS.spad" 939186 939202 941049 941054) (-574 "INTSLPE.spad" 938492 938500 939176 939181) (-573 "INTRVL.spad" 938058 938068 938406 938487) (-572 "INTRF.spad" 936422 936436 938048 938053) (-571 "INTRET.spad" 935854 935864 936412 936417) (-570 "INTRAT.spad" 934529 934546 935844 935849) (-569 "INTPM.spad" 932892 932908 934172 934177) (-568 "INTPAF.spad" 930660 930678 932824 932829) (-567 "INTPACK.spad" 920970 920978 930650 930655) (-566 "INT.spad" 920331 920339 920824 920965) (-565 "INTHERTR.spad" 919597 919614 920321 920326) (-564 "INTHERAL.spad" 919263 919287 919587 919592) (-563 "INTHEORY.spad" 915676 915684 919253 919258) (-562 "INTG0.spad" 909139 909157 915608 915613) (-561 "INTFTBL.spad" 903168 903176 909129 909134) (-560 "INTFACT.spad" 902227 902237 903158 903163) (-559 "INTEF.spad" 900542 900558 902217 902222) (-558 "INTDOM.spad" 899157 899165 900468 900537) (-557 "INTDOM.spad" 897834 897844 899147 899152) (-556 "INTCAT.spad" 896087 896097 897748 897829) (-555 "INTBIT.spad" 895590 895598 896077 896082) (-554 "INTALG.spad" 894772 894799 895580 895585) (-553 "INTAF.spad" 894264 894280 894762 894767) (-552 "INTABL.spad" 892782 892813 892945 892972) (-551 "INT8.spad" 892662 892670 892772 892777) (-550 "INT64.spad" 892541 892549 892652 892657) (-549 "INT32.spad" 892420 892428 892531 892536) (-548 "INT16.spad" 892299 892307 892410 892415) (-547 "INS.spad" 889766 889774 892201 892294) (-546 "INS.spad" 887319 887329 889756 889761) (-545 "INPSIGN.spad" 886753 886766 887309 887314) (-544 "INPRODPF.spad" 885819 885838 886743 886748) (-543 "INPRODFF.spad" 884877 884901 885809 885814) (-542 "INNMFACT.spad" 883848 883865 884867 884872) (-541 "INMODGCD.spad" 883332 883362 883838 883843) (-540 "INFSP.spad" 881617 881639 883322 883327) (-539 "INFPROD0.spad" 880667 880686 881607 881612) (-538 "INFORM.spad" 877828 877836 880657 880662) (-537 "INFORM1.spad" 877453 877463 877818 877823) (-536 "INFINITY.spad" 877005 877013 877443 877448) (-535 "INETCLTS.spad" 876982 876990 876995 877000) (-534 "INEP.spad" 875514 875536 876972 876977) (-533 "INDE.spad" 875243 875260 875504 875509) (-532 "INCRMAPS.spad" 874664 874674 875233 875238) (-531 "INBFILE.spad" 873736 873744 874654 874659) (-530 "INBFF.spad" 869506 869517 873726 873731) (-529 "INBCON.spad" 867794 867802 869496 869501) (-528 "INBCON.spad" 866080 866090 867784 867789) (-527 "INAST.spad" 865741 865749 866070 866075) (-526 "IMPTAST.spad" 865449 865457 865731 865736) (-525 "IMATRIX.spad" 864394 864420 864906 864933) (-524 "IMATQF.spad" 863488 863532 864350 864355) (-523 "IMATLIN.spad" 862093 862117 863444 863449) (-522 "ILIST.spad" 860749 860764 861276 861303) (-521 "IIARRAY2.spad" 860137 860175 860356 860383) (-520 "IFF.spad" 859547 859563 859818 859911) (-519 "IFAST.spad" 859161 859169 859537 859542) (-518 "IFARRAY.spad" 856648 856663 858344 858371) (-517 "IFAMON.spad" 856510 856527 856604 856609) (-516 "IEVALAB.spad" 855899 855911 856500 856505) (-515 "IEVALAB.spad" 855286 855300 855889 855894) (-514 "IDPO.spad" 855084 855096 855276 855281) (-513 "IDPOAMS.spad" 854840 854852 855074 855079) (-512 "IDPOAM.spad" 854560 854572 854830 854835) (-511 "IDPC.spad" 853494 853506 854550 854555) (-510 "IDPAM.spad" 853239 853251 853484 853489) (-509 "IDPAG.spad" 852986 852998 853229 853234) (-508 "IDENT.spad" 852636 852644 852976 852981) (-507 "IDECOMP.spad" 849873 849891 852626 852631) (-506 "IDEAL.spad" 844796 844835 849808 849813) (-505 "ICDEN.spad" 843947 843963 844786 844791) (-504 "ICARD.spad" 843136 843144 843937 843942) (-503 "IBPTOOLS.spad" 841729 841746 843126 843131) (-502 "IBITS.spad" 840928 840941 841365 841392) (-501 "IBATOOL.spad" 837803 837822 840918 840923) (-500 "IBACHIN.spad" 836290 836305 837793 837798) (-499 "IARRAY2.spad" 835278 835304 835897 835924) (-498 "IARRAY1.spad" 834323 834338 834461 834488) (-497 "IAN.spad" 832536 832544 834139 834232) (-496 "IALGFACT.spad" 832137 832170 832526 832531) (-495 "HYPCAT.spad" 831561 831569 832127 832132) (-494 "HYPCAT.spad" 830983 830993 831551 831556) (-493 "HOSTNAME.spad" 830791 830799 830973 830978) (-492 "HOMOTOP.spad" 830534 830544 830781 830786) (-491 "HOAGG.spad" 827802 827812 830524 830529) (-490 "HOAGG.spad" 824845 824857 827569 827574) (-489 "HEXADEC.spad" 822947 822955 823312 823405) (-488 "HEUGCD.spad" 821962 821973 822937 822942) (-487 "HELLFDIV.spad" 821552 821576 821952 821957) (-486 "HEAP.spad" 820944 820954 821159 821186) (-485 "HEADAST.spad" 820475 820483 820934 820939) (-484 "HDP.spad" 810318 810334 810695 810826) (-483 "HDMP.spad" 807530 807545 808148 808275) (-482 "HB.spad" 805767 805775 807520 807525) (-481 "HASHTBL.spad" 804237 804268 804448 804475) 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(-398 "FORTFN.spad" 649600 649608 652420 652425) (-397 "FORTCAT.spad" 649284 649292 649590 649595) (-396 "FORMULA.spad" 646748 646756 649274 649279) (-395 "FORMULA1.spad" 646227 646237 646738 646743) (-394 "FORDER.spad" 645918 645942 646217 646222) (-393 "FOP.spad" 645119 645127 645908 645913) (-392 "FNLA.spad" 644543 644565 645087 645114) (-391 "FNCAT.spad" 643130 643138 644533 644538) (-390 "FNAME.spad" 643022 643030 643120 643125) (-389 "FMTC.spad" 642820 642828 642948 643017) (-388 "FMONOID.spad" 639875 639885 642776 642781) (-387 "FM.spad" 639570 639582 639809 639836) (-386 "FMFUN.spad" 636600 636608 639560 639565) (-385 "FMC.spad" 635652 635660 636590 636595) (-384 "FMCAT.spad" 633306 633324 635620 635647) (-383 "FM1.spad" 632663 632675 633240 633267) (-382 "FLOATRP.spad" 630384 630398 632653 632658) (-381 "FLOAT.spad" 623672 623680 630250 630379) (-380 "FLOATCP.spad" 621089 621103 623662 623667) (-379 "FLINEXP.spad" 620801 620811 621069 621084) (-378 "FLINEXP.spad" 620467 620479 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522649) (-336 "FDIVCAT.spad" 518736 518762 520686 520691) (-335 "FDIV2.spad" 518390 518430 518726 518731) (-334 "FCTRDATA.spad" 517422 517430 518380 518385) (-333 "FCPAK1.spad" 515975 515983 517412 517417) (-332 "FCOMP.spad" 515354 515364 515965 515970) (-331 "FC.spad" 505269 505277 515344 515349) (-330 "FAXF.spad" 498204 498218 505171 505264) (-329 "FAXF.spad" 491191 491207 498160 498165) (-328 "FARRAY.spad" 489337 489347 490374 490401) (-327 "FAMR.spad" 487457 487469 489235 489332) (-326 "FAMR.spad" 485561 485575 487341 487346) (-325 "FAMONOID.spad" 485211 485221 485515 485520) (-324 "FAMONC.spad" 483433 483445 485201 485206) (-323 "FAGROUP.spad" 483039 483049 483329 483356) (-322 "FACUTIL.spad" 481235 481252 483029 483034) (-321 "FACTFUNC.spad" 480411 480421 481225 481230) (-320 "EXPUPXS.spad" 477244 477267 478543 478692) (-319 "EXPRTUBE.spad" 474472 474480 477234 477239) (-318 "EXPRODE.spad" 471344 471360 474462 474467) (-317 "EXPR.spad" 466619 466629 467333 467740) (-316 "EXPR2UPS.spad" 462711 462724 466609 466614) (-315 "EXPR2.spad" 462414 462426 462701 462706) (-314 "EXPEXPAN.spad" 459352 459377 459986 460079) (-313 "EXIT.spad" 459023 459031 459342 459347) (-312 "EXITAST.spad" 458759 458767 459013 459018) (-311 "EVALCYC.spad" 458217 458231 458749 458754) (-310 "EVALAB.spad" 457781 457791 458207 458212) (-309 "EVALAB.spad" 457343 457355 457771 457776) (-308 "EUCDOM.spad" 454885 454893 457269 457338) (-307 "EUCDOM.spad" 452489 452499 454875 454880) (-306 "ESTOOLS.spad" 444329 444337 452479 452484) (-305 "ESTOOLS2.spad" 443930 443944 444319 444324) (-304 "ESTOOLS1.spad" 443615 443626 443920 443925) (-303 "ES.spad" 436162 436170 443605 443610) (-302 "ES.spad" 428615 428625 436060 436065) (-301 "ESCONT.spad" 425388 425396 428605 428610) (-300 "ESCONT1.spad" 425137 425149 425378 425383) (-299 "ES2.spad" 424632 424648 425127 425132) (-298 "ES1.spad" 424198 424214 424622 424627) (-297 "ERROR.spad" 421519 421527 424188 424193) (-296 "EQTBL.spad" 419991 420013 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"D01AKFA.spad" 229906 229914 230370 230375) (-193 "D01AJFA.spad" 229429 229437 229896 229901) (-192 "D01AGNT.spad" 225488 225496 229419 229424) (-191 "CYCLOTOM.spad" 224994 225002 225478 225483) (-190 "CYCLES.spad" 221826 221834 224984 224989) (-189 "CVMP.spad" 221243 221253 221816 221821) (-188 "CTRIGMNP.spad" 219733 219749 221233 221238) (-187 "CTOR.spad" 219424 219432 219723 219728) (-186 "CTORKIND.spad" 219027 219035 219414 219419) (-185 "CTORCAT.spad" 218276 218284 219017 219022) (-184 "CTORCAT.spad" 217523 217533 218266 218271) (-183 "CTORCALL.spad" 217103 217111 217513 217518) (-182 "CSTTOOLS.spad" 216346 216359 217093 217098) (-181 "CRFP.spad" 210050 210063 216336 216341) (-180 "CRCEAST.spad" 209770 209778 210040 210045) (-179 "CRAPACK.spad" 208813 208823 209760 209765) (-178 "CPMATCH.spad" 208313 208328 208738 208743) (-177 "CPIMA.spad" 208018 208037 208303 208308) (-176 "COORDSYS.spad" 202911 202921 208008 208013) (-175 "CONTOUR.spad" 202318 202326 202901 202906) (-174 "CONTFRAC.spad" 197930 197940 202220 202313) (-173 "CONDUIT.spad" 197688 197696 197920 197925) (-172 "COMRING.spad" 197362 197370 197626 197683) (-171 "COMPPROP.spad" 196876 196884 197352 197357) (-170 "COMPLPAT.spad" 196643 196658 196866 196871) (-169 "COMPLEX.spad" 190780 190790 191024 191285) (-168 "COMPLEX2.spad" 190493 190505 190770 190775) (-167 "COMPFACT.spad" 190095 190109 190483 190488) (-166 "COMPCAT.spad" 188163 188173 189829 190090) (-165 "COMPCAT.spad" 185959 185971 187627 187632) (-164 "COMMUPC.spad" 185705 185723 185949 185954) (-163 "COMMONOP.spad" 185238 185246 185695 185700) (-162 "COMM.spad" 185047 185055 185228 185233) (-161 "COMMAAST.spad" 184810 184818 185037 185042) (-160 "COMBOPC.spad" 183715 183723 184800 184805) (-159 "COMBINAT.spad" 182460 182470 183705 183710) (-158 "COMBF.spad" 179828 179844 182450 182455) (-157 "COLOR.spad" 178665 178673 179818 179823) (-156 "COLONAST.spad" 178331 178339 178655 178660) (-155 "CMPLXRT.spad" 178040 178057 178321 178326) (-154 "CLLCTAST.spad" 177702 177710 178030 178035) (-153 "CLIP.spad" 173794 173802 177692 177697) (-152 "CLIF.spad" 172433 172449 173750 173789) (-151 "CLAGG.spad" 168918 168928 172423 172428) (-150 "CLAGG.spad" 165274 165286 168781 168786) (-149 "CINTSLPE.spad" 164599 164612 165264 165269) (-148 "CHVAR.spad" 162677 162699 164589 164594) (-147 "CHARZ.spad" 162592 162600 162657 162672) (-146 "CHARPOL.spad" 162100 162110 162582 162587) (-145 "CHARNZ.spad" 161853 161861 162080 162095) (-144 "CHAR.spad" 159721 159729 161843 161848) (-143 "CFCAT.spad" 159037 159045 159711 159716) (-142 "CDEN.spad" 158195 158209 159027 159032) (-141 "CCLASS.spad" 156344 156352 157606 157645) (-140 "CATEGORY.spad" 155434 155442 156334 156339) (-139 "CATCTOR.spad" 155325 155333 155424 155429) (-138 "CATAST.spad" 154943 154951 155315 155320) (-137 "CASEAST.spad" 154657 154665 154933 154938) (-136 "CARTEN.spad" 149760 149784 154647 154652) (-135 "CARTEN2.spad" 149146 149173 149750 149755) (-134 "CARD.spad" 146435 146443 149120 149141) (-133 "CAPSLAST.spad" 146209 146217 146425 146430) (-132 "CACHSET.spad" 145831 145839 146199 146204) (-131 "CABMON.spad" 145384 145392 145821 145826) (-130 "BYTEORD.spad" 145059 145067 145374 145379) (-129 "BYTE.spad" 144484 144492 145049 145054) (-128 "BYTEBUF.spad" 142341 142349 143653 143680) (-127 "BTREE.spad" 141410 141420 141948 141975) (-126 "BTOURN.spad" 140413 140423 141017 141044) (-125 "BTCAT.spad" 139801 139811 140381 140408) (-124 "BTCAT.spad" 139209 139221 139791 139796) (-123 "BTAGG.spad" 138331 138339 139177 139204) (-122 "BTAGG.spad" 137473 137483 138321 138326) (-121 "BSTREE.spad" 136208 136218 137080 137107) (-120 "BRILL.spad" 134403 134414 136198 136203) (-119 "BRAGG.spad" 133327 133337 134393 134398) (-118 "BRAGG.spad" 132215 132227 133283 133288) (-117 "BPADICRT.spad" 130196 130208 130451 130544) (-116 "BPADIC.spad" 129860 129872 130122 130191) (-115 "BOUNDZRO.spad" 129516 129533 129850 129855) (-114 "BOP.spad" 124640 124648 129506 129511) (-113 "BOP1.spad" 122060 122070 124630 124635) (-112 "BOOLEAN.spad" 121492 121500 122050 122055) (-111 "BMODULE.spad" 121204 121216 121460 121487) (-110 "BITS.spad" 120623 120631 120840 120867) (-109 "BINDING.spad" 120034 120042 120613 120618) (-108 "BINARY.spad" 118145 118153 118501 118594) (-107 "BGAGG.spad" 117342 117352 118125 118140) (-106 "BGAGG.spad" 116547 116559 117332 117337) (-105 "BFUNCT.spad" 116111 116119 116527 116542) (-104 "BEZOUT.spad" 115245 115272 116061 116066) (-103 "BBTREE.spad" 112064 112074 114852 114879) (-102 "BASTYPE.spad" 111736 111744 112054 112059) (-101 "BASTYPE.spad" 111406 111416 111726 111731) (-100 "BALFACT.spad" 110845 110858 111396 111401) (-99 "AUTOMOR.spad" 110292 110301 110825 110840) (-98 "ATTREG.spad" 107011 107018 110044 110287) (-97 "ATTRBUT.spad" 103034 103041 106991 107006) (-96 "ATTRAST.spad" 102751 102758 103024 103029) (-95 "ATRIG.spad" 102221 102228 102741 102746) (-94 "ATRIG.spad" 101689 101698 102211 102216) (-93 "ASTCAT.spad" 101593 101600 101679 101684) (-92 "ASTCAT.spad" 101495 101504 101583 101588) (-91 "ASTACK.spad" 100828 100837 101102 101129) (-90 "ASSOCEQ.spad" 99628 99639 100784 100789) (-89 "ASP9.spad" 98709 98722 99618 99623) (-88 "ASP8.spad" 97752 97765 98699 98704) (-87 "ASP80.spad" 97074 97087 97742 97747) (-86 "ASP7.spad" 96234 96247 97064 97069) (-85 "ASP78.spad" 95685 95698 96224 96229) (-84 "ASP77.spad" 95054 95067 95675 95680) (-83 "ASP74.spad" 94146 94159 95044 95049) (-82 "ASP73.spad" 93417 93430 94136 94141) (-81 "ASP6.spad" 92284 92297 93407 93412) (-80 "ASP55.spad" 90793 90806 92274 92279) (-79 "ASP50.spad" 88610 88623 90783 90788) (-78 "ASP4.spad" 87905 87918 88600 88605) (-77 "ASP49.spad" 86904 86917 87895 87900) (-76 "ASP42.spad" 85311 85350 86894 86899) (-75 "ASP41.spad" 83890 83929 85301 85306) (-74 "ASP35.spad" 82878 82891 83880 83885) (-73 "ASP34.spad" 82179 82192 82868 82873) (-72 "ASP33.spad" 81739 81752 82169 82174) (-71 "ASP31.spad" 80879 80892 81729 81734) (-70 "ASP30.spad" 79771 79784 80869 80874) (-69 "ASP29.spad" 79237 79250 79761 79766) (-68 "ASP28.spad" 70510 70523 79227 79232) (-67 "ASP27.spad" 69407 69420 70500 70505) (-66 "ASP24.spad" 68494 68507 69397 69402) (-65 "ASP20.spad" 67958 67971 68484 68489) (-64 "ASP1.spad" 67339 67352 67948 67953) (-63 "ASP19.spad" 62025 62038 67329 67334) (-62 "ASP12.spad" 61439 61452 62015 62020) (-61 "ASP10.spad" 60710 60723 61429 61434) (-60 "ARRAY2.spad" 60070 60079 60317 60344) (-59 "ARRAY1.spad" 58905 58914 59253 59280) (-58 "ARRAY12.spad" 57574 57585 58895 58900) (-57 "ARR2CAT.spad" 53236 53257 57542 57569) (-56 "ARR2CAT.spad" 48918 48941 53226 53231) (-55 "ARITY.spad" 48290 48297 48908 48913) (-54 "APPRULE.spad" 47534 47556 48280 48285) (-53 "APPLYORE.spad" 47149 47162 47524 47529) (-52 "ANY.spad" 45491 45498 47139 47144) (-51 "ANY1.spad" 44562 44571 45481 45486) (-50 "ANTISYM.spad" 43001 43017 44542 44557) (-49 "ANON.spad" 42694 42701 42991 42996) (-48 "AN.spad" 40995 41002 42510 42603) (-47 "AMR.spad" 39174 39185 40893 40990) (-46 "AMR.spad" 37190 37203 38911 38916) (-45 "ALIST.spad" 34602 34623 34952 34979) (-44 "ALGSC.spad" 33725 33751 34474 34527) (-43 "ALGPKG.spad" 29434 29445 33681 33686) (-42 "ALGMFACT.spad" 28623 28637 29424 29429) (-41 "ALGMANIP.spad" 26079 26094 28456 28461) (-40 "ALGFF.spad" 24394 24421 24611 24767) (-39 "ALGFACT.spad" 23515 23525 24384 24389) (-38 "ALGEBRA.spad" 23348 23357 23471 23510) (-37 "ALGEBRA.spad" 23213 23224 23338 23343) (-36 "ALAGG.spad" 22723 22744 23181 23208) (-35 "AHYP.spad" 22104 22111 22713 22718) (-34 "AGG.spad" 20413 20420 22094 22099) (-33 "AGG.spad" 18686 18695 20369 20374) (-32 "AF.spad" 17111 17126 18621 18626) (-31 "ADDAST.spad" 16789 16796 17101 17106) (-30 "ACPLOT.spad" 15360 15367 16779 16784) (-29 "ACFS.spad" 13111 13120 15262 15355) (-28 "ACFS.spad" 10948 10959 13101 13106) (-27 "ACF.spad" 7550 7557 10850 10943) (-26 "ACF.spad" 4238 4247 7540 7545) (-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 2285477 2285482 2285487 2285492) (-2 NIL 2285457 2285462 2285467 2285472) (-1 NIL 2285437 2285442 2285447 2285452) (0 NIL 2285417 2285422 2285427 2285432) (-1292 "ZMOD.spad" 2285226 2285239 2285355 2285412) (-1291 "ZLINDEP.spad" 2284270 2284281 2285216 2285221) (-1290 "ZDSOLVE.spad" 2274119 2274141 2284260 2284265) (-1289 "YSTREAM.spad" 2273612 2273623 2274109 2274114) (-1288 "XRPOLY.spad" 2272832 2272852 2273468 2273537) (-1287 "XPR.spad" 2270623 2270636 2272550 2272649) (-1286 "XPOLY.spad" 2270178 2270189 2270479 2270548) (-1285 "XPOLYC.spad" 2269495 2269511 2270104 2270173) (-1284 "XPBWPOLY.spad" 2267932 2267952 2269275 2269344) (-1283 "XF.spad" 2266393 2266408 2267834 2267927) (-1282 "XF.spad" 2264834 2264851 2266277 2266282) (-1281 "XFALG.spad" 2261858 2261874 2264760 2264829) (-1280 "XEXPPKG.spad" 2261109 2261135 2261848 2261853) (-1279 "XDPOLY.spad" 2260723 2260739 2260965 2261034) (-1278 "XALG.spad" 2260383 2260394 2260679 2260718) (-1277 "WUTSET.spad" 2256222 2256239 2260029 2260056) (-1276 "WP.spad" 2255421 2255465 2256080 2256147) (-1275 "WHILEAST.spad" 2255219 2255228 2255411 2255416) (-1274 "WHEREAST.spad" 2254890 2254899 2255209 2255214) (-1273 "WFFINTBS.spad" 2252453 2252475 2254880 2254885) (-1272 "WEIER.spad" 2250667 2250678 2252443 2252448) (-1271 "VSPACE.spad" 2250340 2250351 2250635 2250662) (-1270 "VSPACE.spad" 2250033 2250046 2250330 2250335) (-1269 "VOID.spad" 2249710 2249719 2250023 2250028) (-1268 "VIEW.spad" 2247332 2247341 2249700 2249705) (-1267 "VIEWDEF.spad" 2242529 2242538 2247322 2247327) (-1266 "VIEW3D.spad" 2226364 2226373 2242519 2242524) (-1265 "VIEW2D.spad" 2214101 2214110 2226354 2226359) (-1264 "VECTOR.spad" 2212775 2212786 2213026 2213053) (-1263 "VECTOR2.spad" 2211402 2211415 2212765 2212770) (-1262 "VECTCAT.spad" 2209302 2209313 2211370 2211397) (-1261 "VECTCAT.spad" 2207009 2207022 2209079 2209084) (-1260 "VARIABLE.spad" 2206789 2206804 2206999 2207004) (-1259 "UTYPE.spad" 2206433 2206442 2206779 2206784) (-1258 "UTSODETL.spad" 2205726 2205750 2206389 2206394) (-1257 "UTSODE.spad" 2203914 2203934 2205716 2205721) (-1256 "UTS.spad" 2198703 2198731 2202381 2202478) (-1255 "UTSCAT.spad" 2196154 2196170 2198601 2198698) (-1254 "UTSCAT.spad" 2193249 2193267 2195698 2195703) (-1253 "UTS2.spad" 2192842 2192877 2193239 2193244) (-1252 "URAGG.spad" 2187475 2187486 2192832 2192837) (-1251 "URAGG.spad" 2182072 2182085 2187431 2187436) (-1250 "UPXSSING.spad" 2179715 2179741 2181153 2181286) (-1249 "UPXS.spad" 2176863 2176891 2177847 2177996) (-1248 "UPXSCONS.spad" 2174620 2174640 2174995 2175144) (-1247 "UPXSCCA.spad" 2173185 2173205 2174466 2174615) (-1246 "UPXSCCA.spad" 2171892 2171914 2173175 2173180) (-1245 "UPXSCAT.spad" 2170473 2170489 2171738 2171887) (-1244 "UPXS2.spad" 2170014 2170067 2170463 2170468) (-1243 "UPSQFREE.spad" 2168426 2168440 2170004 2170009) (-1242 "UPSCAT.spad" 2166019 2166043 2168324 2168421) (-1241 "UPSCAT.spad" 2163318 2163344 2165625 2165630) (-1240 "UPOLYC.spad" 2158296 2158307 2163160 2163313) (-1239 "UPOLYC.spad" 2153166 2153179 2158032 2158037) (-1238 "UPOLYC2.spad" 2152635 2152654 2153156 2153161) (-1237 "UP.spad" 2149828 2149843 2150221 2150374) (-1236 "UPMP.spad" 2148718 2148731 2149818 2149823) (-1235 "UPDIVP.spad" 2148281 2148295 2148708 2148713) (-1234 "UPDECOMP.spad" 2146518 2146532 2148271 2148276) (-1233 "UPCDEN.spad" 2145725 2145741 2146508 2146513) (-1232 "UP2.spad" 2145087 2145108 2145715 2145720) (-1231 "UNISEG.spad" 2144440 2144451 2145006 2145011) (-1230 "UNISEG2.spad" 2143933 2143946 2144396 2144401) (-1229 "UNIFACT.spad" 2143034 2143046 2143923 2143928) (-1228 "ULS.spad" 2133586 2133614 2134679 2135108) (-1227 "ULSCONS.spad" 2125980 2126000 2126352 2126501) (-1226 "ULSCCAT.spad" 2123709 2123729 2125826 2125975) (-1225 "ULSCCAT.spad" 2121546 2121568 2123665 2123670) (-1224 "ULSCAT.spad" 2119762 2119778 2121392 2121541) (-1223 "ULS2.spad" 2119274 2119327 2119752 2119757) (-1222 "UINT8.spad" 2119151 2119160 2119264 2119269) (-1221 "UINT64.spad" 2119027 2119036 2119141 2119146) (-1220 "UINT32.spad" 2118903 2118912 2119017 2119022) (-1219 "UINT16.spad" 2118779 2118788 2118893 2118898) (-1218 "UFD.spad" 2117844 2117853 2118705 2118774) (-1217 "UFD.spad" 2116971 2116982 2117834 2117839) (-1216 "UDVO.spad" 2115818 2115827 2116961 2116966) (-1215 "UDPO.spad" 2113245 2113256 2115774 2115779) (-1214 "TYPE.spad" 2113177 2113186 2113235 2113240) (-1213 "TYPEAST.spad" 2113096 2113105 2113167 2113172) (-1212 "TWOFACT.spad" 2111746 2111761 2113086 2113091) (-1211 "TUPLE.spad" 2111230 2111241 2111645 2111650) (-1210 "TUBETOOL.spad" 2108067 2108076 2111220 2111225) (-1209 "TUBE.spad" 2106708 2106725 2108057 2108062) (-1208 "TS.spad" 2105297 2105313 2106273 2106370) (-1207 "TSETCAT.spad" 2092424 2092441 2105265 2105292) (-1206 "TSETCAT.spad" 2079537 2079556 2092380 2092385) (-1205 "TRMANIP.spad" 2073903 2073920 2079243 2079248) (-1204 "TRIMAT.spad" 2072862 2072887 2073893 2073898) (-1203 "TRIGMNIP.spad" 2071379 2071396 2072852 2072857) (-1202 "TRIGCAT.spad" 2070891 2070900 2071369 2071374) (-1201 "TRIGCAT.spad" 2070401 2070412 2070881 2070886) (-1200 "TREE.spad" 2068972 2068983 2070008 2070035) (-1199 "TRANFUN.spad" 2068803 2068812 2068962 2068967) (-1198 "TRANFUN.spad" 2068632 2068643 2068793 2068798) (-1197 "TOPSP.spad" 2068306 2068315 2068622 2068627) (-1196 "TOOLSIGN.spad" 2067969 2067980 2068296 2068301) (-1195 "TEXTFILE.spad" 2066526 2066535 2067959 2067964) (-1194 "TEX.spad" 2063658 2063667 2066516 2066521) (-1193 "TEX1.spad" 2063214 2063225 2063648 2063653) (-1192 "TEMUTL.spad" 2062769 2062778 2063204 2063209) (-1191 "TBCMPPK.spad" 2060862 2060885 2062759 2062764) (-1190 "TBAGG.spad" 2059898 2059921 2060842 2060857) (-1189 "TBAGG.spad" 2058942 2058967 2059888 2059893) (-1188 "TANEXP.spad" 2058318 2058329 2058932 2058937) (-1187 "TABLE.spad" 2056729 2056752 2056999 2057026) (-1186 "TABLEAU.spad" 2056210 2056221 2056719 2056724) (-1185 "TABLBUMP.spad" 2052993 2053004 2056200 2056205) (-1184 "SYSTEM.spad" 2052221 2052230 2052983 2052988) (-1183 "SYSSOLP.spad" 2049694 2049705 2052211 2052216) (-1182 "SYSNNI.spad" 2048874 2048885 2049684 2049689) (-1181 "SYSINT.spad" 2048278 2048289 2048864 2048869) (-1180 "SYNTAX.spad" 2044472 2044481 2048268 2048273) (-1179 "SYMTAB.spad" 2042528 2042537 2044462 2044467) (-1178 "SYMS.spad" 2038513 2038522 2042518 2042523) (-1177 "SYMPOLY.spad" 2037520 2037531 2037602 2037729) (-1176 "SYMFUNC.spad" 2036995 2037006 2037510 2037515) (-1175 "SYMBOL.spad" 2034422 2034431 2036985 2036990) (-1174 "SWITCH.spad" 2031179 2031188 2034412 2034417) (-1173 "SUTS.spad" 2028078 2028106 2029646 2029743) (-1172 "SUPXS.spad" 2025213 2025241 2026210 2026359) (-1171 "SUP.spad" 2022018 2022029 2022799 2022952) (-1170 "SUPFRACF.spad" 2021123 2021141 2022008 2022013) (-1169 "SUP2.spad" 2020513 2020526 2021113 2021118) (-1168 "SUMRF.spad" 2019479 2019490 2020503 2020508) (-1167 "SUMFS.spad" 2019112 2019129 2019469 2019474) (-1166 "SULS.spad" 2009651 2009679 2010757 2011186) (-1165 "SUCHTAST.spad" 2009420 2009429 2009641 2009646) (-1164 "SUCH.spad" 2009100 2009115 2009410 2009415) (-1163 "SUBSPACE.spad" 2001107 2001122 2009090 2009095) (-1162 "SUBRESP.spad" 2000267 2000281 2001063 2001068) (-1161 "STTF.spad" 1996366 1996382 2000257 2000262) (-1160 "STTFNC.spad" 1992834 1992850 1996356 1996361) (-1159 "STTAYLOR.spad" 1985232 1985243 1992715 1992720) (-1158 "STRTBL.spad" 1983737 1983754 1983886 1983913) (-1157 "STRING.spad" 1983146 1983155 1983160 1983187) (-1156 "STRICAT.spad" 1982934 1982943 1983114 1983141) (-1155 "STREAM.spad" 1979792 1979803 1982459 1982474) (-1154 "STREAM3.spad" 1979337 1979352 1979782 1979787) (-1153 "STREAM2.spad" 1978405 1978418 1979327 1979332) (-1152 "STREAM1.spad" 1978109 1978120 1978395 1978400) (-1151 "STINPROD.spad" 1977015 1977031 1978099 1978104) (-1150 "STEP.spad" 1976216 1976225 1977005 1977010) (-1149 "STBL.spad" 1974742 1974770 1974909 1974924) (-1148 "STAGG.spad" 1973817 1973828 1974732 1974737) (-1147 "STAGG.spad" 1972890 1972903 1973807 1973812) (-1146 "STACK.spad" 1972241 1972252 1972497 1972524) (-1145 "SREGSET.spad" 1969945 1969962 1971887 1971914) (-1144 "SRDCMPK.spad" 1968490 1968510 1969935 1969940) (-1143 "SRAGG.spad" 1963587 1963596 1968458 1968485) (-1142 "SRAGG.spad" 1958704 1958715 1963577 1963582) (-1141 "SQMATRIX.spad" 1956320 1956338 1957236 1957323) (-1140 "SPLTREE.spad" 1950872 1950885 1955756 1955783) (-1139 "SPLNODE.spad" 1947460 1947473 1950862 1950867) (-1138 "SPFCAT.spad" 1946237 1946246 1947450 1947455) (-1137 "SPECOUT.spad" 1944787 1944796 1946227 1946232) (-1136 "SPADXPT.spad" 1936926 1936935 1944777 1944782) (-1135 "spad-parser.spad" 1936391 1936400 1936916 1936921) (-1134 "SPADAST.spad" 1936092 1936101 1936381 1936386) (-1133 "SPACEC.spad" 1920105 1920116 1936082 1936087) (-1132 "SPACE3.spad" 1919881 1919892 1920095 1920100) (-1131 "SORTPAK.spad" 1919426 1919439 1919837 1919842) (-1130 "SOLVETRA.spad" 1917183 1917194 1919416 1919421) (-1129 "SOLVESER.spad" 1915703 1915714 1917173 1917178) (-1128 "SOLVERAD.spad" 1911713 1911724 1915693 1915698) (-1127 "SOLVEFOR.spad" 1910133 1910151 1911703 1911708) (-1126 "SNTSCAT.spad" 1909733 1909750 1910101 1910128) (-1125 "SMTS.spad" 1907993 1908019 1909298 1909395) (-1124 "SMP.spad" 1905468 1905488 1905858 1905985) (-1123 "SMITH.spad" 1904311 1904336 1905458 1905463) (-1122 "SMATCAT.spad" 1902421 1902451 1904255 1904306) (-1121 "SMATCAT.spad" 1900463 1900495 1902299 1902304) (-1120 "SKAGG.spad" 1899424 1899435 1900431 1900458) (-1119 "SINT.spad" 1898250 1898259 1899290 1899419) (-1118 "SIMPAN.spad" 1897978 1897987 1898240 1898245) (-1117 "SIG.spad" 1897306 1897315 1897968 1897973) (-1116 "SIGNRF.spad" 1896414 1896425 1897296 1897301) (-1115 "SIGNEF.spad" 1895683 1895700 1896404 1896409) (-1114 "SIGAST.spad" 1895064 1895073 1895673 1895678) (-1113 "SHP.spad" 1892982 1892997 1895020 1895025) (-1112 "SHDP.spad" 1882693 1882720 1883202 1883333) (-1111 "SGROUP.spad" 1882301 1882310 1882683 1882688) (-1110 "SGROUP.spad" 1881907 1881918 1882291 1882296) (-1109 "SGCF.spad" 1874788 1874797 1881897 1881902) (-1108 "SFRTCAT.spad" 1873716 1873733 1874756 1874783) (-1107 "SFRGCD.spad" 1872779 1872799 1873706 1873711) (-1106 "SFQCMPK.spad" 1867416 1867436 1872769 1872774) (-1105 "SFORT.spad" 1866851 1866865 1867406 1867411) (-1104 "SEXOF.spad" 1866694 1866734 1866841 1866846) (-1103 "SEX.spad" 1866586 1866595 1866684 1866689) (-1102 "SEXCAT.spad" 1864137 1864177 1866576 1866581) (-1101 "SET.spad" 1862437 1862448 1863558 1863597) (-1100 "SETMN.spad" 1860871 1860888 1862427 1862432) (-1099 "SETCAT.spad" 1860193 1860202 1860861 1860866) (-1098 "SETCAT.spad" 1859513 1859524 1860183 1860188) (-1097 "SETAGG.spad" 1856034 1856045 1859493 1859508) (-1096 "SETAGG.spad" 1852563 1852576 1856024 1856029) (-1095 "SEQAST.spad" 1852266 1852275 1852553 1852558) (-1094 "SEGXCAT.spad" 1851388 1851401 1852256 1852261) (-1093 "SEG.spad" 1851201 1851212 1851307 1851312) (-1092 "SEGCAT.spad" 1850108 1850119 1851191 1851196) (-1091 "SEGBIND.spad" 1849180 1849191 1850063 1850068) (-1090 "SEGBIND2.spad" 1848876 1848889 1849170 1849175) (-1089 "SEGAST.spad" 1848590 1848599 1848866 1848871) (-1088 "SEG2.spad" 1848015 1848028 1848546 1848551) (-1087 "SDVAR.spad" 1847291 1847302 1848005 1848010) (-1086 "SDPOL.spad" 1844717 1844728 1845008 1845135) (-1085 "SCPKG.spad" 1842796 1842807 1844707 1844712) (-1084 "SCOPE.spad" 1841945 1841954 1842786 1842791) (-1083 "SCACHE.spad" 1840627 1840638 1841935 1841940) (-1082 "SASTCAT.spad" 1840536 1840545 1840617 1840622) (-1081 "SAOS.spad" 1840408 1840417 1840526 1840531) (-1080 "SAERFFC.spad" 1840121 1840141 1840398 1840403) (-1079 "SAE.spad" 1838296 1838312 1838907 1839042) (-1078 "SAEFACT.spad" 1837997 1838017 1838286 1838291) (-1077 "RURPK.spad" 1835638 1835654 1837987 1837992) (-1076 "RULESET.spad" 1835079 1835103 1835628 1835633) (-1075 "RULE.spad" 1833283 1833307 1835069 1835074) (-1074 "RULECOLD.spad" 1833135 1833148 1833273 1833278) (-1073 "RTVALUE.spad" 1832868 1832877 1833125 1833130) (-1072 "RSTRCAST.spad" 1832585 1832594 1832858 1832863) (-1071 "RSETGCD.spad" 1828963 1828983 1832575 1832580) (-1070 "RSETCAT.spad" 1818747 1818764 1828931 1828958) (-1069 "RSETCAT.spad" 1808551 1808570 1818737 1818742) (-1068 "RSDCMPK.spad" 1807003 1807023 1808541 1808546) (-1067 "RRCC.spad" 1805387 1805417 1806993 1806998) (-1066 "RRCC.spad" 1803769 1803801 1805377 1805382) (-1065 "RPTAST.spad" 1803471 1803480 1803759 1803764) (-1064 "RPOLCAT.spad" 1782831 1782846 1803339 1803466) (-1063 "RPOLCAT.spad" 1761905 1761922 1782415 1782420) (-1062 "ROUTINE.spad" 1757768 1757777 1760552 1760579) (-1061 "ROMAN.spad" 1757096 1757105 1757634 1757763) (-1060 "ROIRC.spad" 1756176 1756208 1757086 1757091) (-1059 "RNS.spad" 1755079 1755088 1756078 1756171) (-1058 "RNS.spad" 1754068 1754079 1755069 1755074) (-1057 "RNG.spad" 1753803 1753812 1754058 1754063) (-1056 "RMODULE.spad" 1753568 1753579 1753793 1753798) (-1055 "RMCAT2.spad" 1752976 1753033 1753558 1753563) (-1054 "RMATRIX.spad" 1751800 1751819 1752143 1752182) (-1053 "RMATCAT.spad" 1747333 1747364 1751756 1751795) (-1052 "RMATCAT.spad" 1742756 1742789 1747181 1747186) (-1051 "RLINSET.spad" 1742150 1742161 1742746 1742751) (-1050 "RINTERP.spad" 1742038 1742058 1742140 1742145) (-1049 "RING.spad" 1741508 1741517 1742018 1742033) (-1048 "RING.spad" 1740986 1740997 1741498 1741503) (-1047 "RIDIST.spad" 1740370 1740379 1740976 1740981) (-1046 "RGCHAIN.spad" 1738949 1738965 1739855 1739882) (-1045 "RGBCSPC.spad" 1738730 1738742 1738939 1738944) (-1044 "RGBCMDL.spad" 1738260 1738272 1738720 1738725) (-1043 "RF.spad" 1735874 1735885 1738250 1738255) (-1042 "RFFACTOR.spad" 1735336 1735347 1735864 1735869) (-1041 "RFFACT.spad" 1735071 1735083 1735326 1735331) (-1040 "RFDIST.spad" 1734059 1734068 1735061 1735066) (-1039 "RETSOL.spad" 1733476 1733489 1734049 1734054) (-1038 "RETRACT.spad" 1732904 1732915 1733466 1733471) (-1037 "RETRACT.spad" 1732330 1732343 1732894 1732899) (-1036 "RETAST.spad" 1732142 1732151 1732320 1732325) (-1035 "RESULT.spad" 1730202 1730211 1730789 1730816) (-1034 "RESRING.spad" 1729549 1729596 1730140 1730197) (-1033 "RESLATC.spad" 1728873 1728884 1729539 1729544) (-1032 "REPSQ.spad" 1728602 1728613 1728863 1728868) (-1031 "REP.spad" 1726154 1726163 1728592 1728597) (-1030 "REPDB.spad" 1725859 1725870 1726144 1726149) (-1029 "REP2.spad" 1715431 1715442 1725701 1725706) (-1028 "REP1.spad" 1709421 1709432 1715381 1715386) (-1027 "REGSET.spad" 1707218 1707235 1709067 1709094) (-1026 "REF.spad" 1706547 1706558 1707173 1707178) (-1025 "REDORDER.spad" 1705723 1705740 1706537 1706542) (-1024 "RECLOS.spad" 1704506 1704526 1705210 1705303) (-1023 "REALSOLV.spad" 1703638 1703647 1704496 1704501) (-1022 "REAL.spad" 1703510 1703519 1703628 1703633) (-1021 "REAL0Q.spad" 1700792 1700807 1703500 1703505) (-1020 "REAL0.spad" 1697620 1697635 1700782 1700787) (-1019 "RDUCEAST.spad" 1697341 1697350 1697610 1697615) (-1018 "RDIV.spad" 1696992 1697017 1697331 1697336) (-1017 "RDIST.spad" 1696555 1696566 1696982 1696987) (-1016 "RDETRS.spad" 1695351 1695369 1696545 1696550) (-1015 "RDETR.spad" 1693458 1693476 1695341 1695346) (-1014 "RDEEFS.spad" 1692531 1692548 1693448 1693453) (-1013 "RDEEF.spad" 1691527 1691544 1692521 1692526) (-1012 "RCFIELD.spad" 1688713 1688722 1691429 1691522) (-1011 "RCFIELD.spad" 1685985 1685996 1688703 1688708) (-1010 "RCAGG.spad" 1683897 1683908 1685975 1685980) (-1009 "RCAGG.spad" 1681736 1681749 1683816 1683821) (-1008 "RATRET.spad" 1681096 1681107 1681726 1681731) (-1007 "RATFACT.spad" 1680788 1680800 1681086 1681091) (-1006 "RANDSRC.spad" 1680107 1680116 1680778 1680783) (-1005 "RADUTIL.spad" 1679861 1679870 1680097 1680102) (-1004 "RADIX.spad" 1676762 1676776 1678328 1678421) (-1003 "RADFF.spad" 1675175 1675212 1675294 1675450) (-1002 "RADCAT.spad" 1674768 1674777 1675165 1675170) (-1001 "RADCAT.spad" 1674359 1674370 1674758 1674763) (-1000 "QUEUE.spad" 1673701 1673712 1673966 1673993) (-999 "QUAT.spad" 1672283 1672293 1672625 1672690) (-998 "QUATCT2.spad" 1671902 1671920 1672273 1672278) (-997 "QUATCAT.spad" 1670067 1670077 1671832 1671897) (-996 "QUATCAT.spad" 1667983 1667995 1669750 1669755) (-995 "QUAGG.spad" 1666809 1666819 1667951 1667978) (-994 "QQUTAST.spad" 1666578 1666586 1666799 1666804) (-993 "QFORM.spad" 1666041 1666055 1666568 1666573) (-992 "QFCAT.spad" 1664744 1664754 1665943 1666036) (-991 "QFCAT.spad" 1663038 1663050 1664239 1664244) (-990 "QFCAT2.spad" 1662729 1662745 1663028 1663033) (-989 "QEQUAT.spad" 1662286 1662294 1662719 1662724) (-988 "QCMPACK.spad" 1657033 1657052 1662276 1662281) (-987 "QALGSET.spad" 1653108 1653140 1656947 1656952) (-986 "QALGSET2.spad" 1651104 1651122 1653098 1653103) (-985 "PWFFINTB.spad" 1648414 1648435 1651094 1651099) (-984 "PUSHVAR.spad" 1647743 1647762 1648404 1648409) (-983 "PTRANFN.spad" 1643869 1643879 1647733 1647738) (-982 "PTPACK.spad" 1640957 1640967 1643859 1643864) (-981 "PTFUNC2.spad" 1640778 1640792 1640947 1640952) (-980 "PTCAT.spad" 1640027 1640037 1640746 1640773) (-979 "PSQFR.spad" 1639334 1639358 1640017 1640022) (-978 "PSEUDLIN.spad" 1638192 1638202 1639324 1639329) (-977 "PSETPK.spad" 1623625 1623641 1638070 1638075) (-976 "PSETCAT.spad" 1617545 1617568 1623605 1623620) (-975 "PSETCAT.spad" 1611439 1611464 1617501 1617506) (-974 "PSCURVE.spad" 1610422 1610430 1611429 1611434) (-973 "PSCAT.spad" 1609189 1609218 1610320 1610417) (-972 "PSCAT.spad" 1608046 1608077 1609179 1609184) (-971 "PRTITION.spad" 1606991 1606999 1608036 1608041) (-970 "PRTDAST.spad" 1606710 1606718 1606981 1606986) (-969 "PRS.spad" 1596272 1596289 1606666 1606671) (-968 "PRQAGG.spad" 1595703 1595713 1596240 1596267) (-967 "PROPLOG.spad" 1594998 1595006 1595693 1595698) (-966 "PROPFRML.spad" 1593806 1593817 1594988 1594993) (-965 "PROPERTY.spad" 1593292 1593300 1593796 1593801) (-964 "PRODUCT.spad" 1590972 1590984 1591258 1591313) (-963 "PR.spad" 1589358 1589370 1590063 1590190) (-962 "PRINT.spad" 1589110 1589118 1589348 1589353) (-961 "PRIMES.spad" 1587361 1587371 1589100 1589105) (-960 "PRIMELT.spad" 1585342 1585356 1587351 1587356) (-959 "PRIMCAT.spad" 1584965 1584973 1585332 1585337) (-958 "PRIMARR.spad" 1583970 1583980 1584148 1584175) (-957 "PRIMARR2.spad" 1582693 1582705 1583960 1583965) (-956 "PREASSOC.spad" 1582065 1582077 1582683 1582688) (-955 "PPCURVE.spad" 1581202 1581210 1582055 1582060) (-954 "PORTNUM.spad" 1580977 1580985 1581192 1581197) (-953 "POLYROOT.spad" 1579806 1579828 1580933 1580938) (-952 "POLY.spad" 1577139 1577149 1577656 1577783) (-951 "POLYLIFT.spad" 1576400 1576423 1577129 1577134) (-950 "POLYCATQ.spad" 1574502 1574524 1576390 1576395) (-949 "POLYCAT.spad" 1567908 1567929 1574370 1574497) (-948 "POLYCAT.spad" 1560652 1560675 1567116 1567121) (-947 "POLY2UP.spad" 1560100 1560114 1560642 1560647) (-946 "POLY2.spad" 1559695 1559707 1560090 1560095) (-945 "POLUTIL.spad" 1558636 1558665 1559651 1559656) (-944 "POLTOPOL.spad" 1557384 1557399 1558626 1558631) (-943 "POINT.spad" 1556222 1556232 1556309 1556336) (-942 "PNTHEORY.spad" 1552888 1552896 1556212 1556217) (-941 "PMTOOLS.spad" 1551645 1551659 1552878 1552883) (-940 "PMSYM.spad" 1551190 1551200 1551635 1551640) (-939 "PMQFCAT.spad" 1550777 1550791 1551180 1551185) (-938 "PMPRED.spad" 1550246 1550260 1550767 1550772) (-937 "PMPREDFS.spad" 1549690 1549712 1550236 1550241) (-936 "PMPLCAT.spad" 1548760 1548778 1549622 1549627) (-935 "PMLSAGG.spad" 1548341 1548355 1548750 1548755) (-934 "PMKERNEL.spad" 1547908 1547920 1548331 1548336) (-933 "PMINS.spad" 1547484 1547494 1547898 1547903) (-932 "PMFS.spad" 1547057 1547075 1547474 1547479) (-931 "PMDOWN.spad" 1546343 1546357 1547047 1547052) (-930 "PMASS.spad" 1545351 1545359 1546333 1546338) (-929 "PMASSFS.spad" 1544316 1544332 1545341 1545346) (-928 "PLOTTOOL.spad" 1544096 1544104 1544306 1544311) (-927 "PLOT.spad" 1538927 1538935 1544086 1544091) (-926 "PLOT3D.spad" 1535347 1535355 1538917 1538922) (-925 "PLOT1.spad" 1534488 1534498 1535337 1535342) (-924 "PLEQN.spad" 1521704 1521731 1534478 1534483) (-923 "PINTERP.spad" 1521320 1521339 1521694 1521699) (-922 "PINTERPA.spad" 1521102 1521118 1521310 1521315) (-921 "PI.spad" 1520709 1520717 1521076 1521097) (-920 "PID.spad" 1519665 1519673 1520635 1520704) (-919 "PICOERCE.spad" 1519322 1519332 1519655 1519660) (-918 "PGROEB.spad" 1517919 1517933 1519312 1519317) (-917 "PGE.spad" 1509172 1509180 1517909 1517914) (-916 "PGCD.spad" 1508054 1508071 1509162 1509167) (-915 "PFRPAC.spad" 1507197 1507207 1508044 1508049) (-914 "PFR.spad" 1503854 1503864 1507099 1507192) (-913 "PFOTOOLS.spad" 1503112 1503128 1503844 1503849) (-912 "PFOQ.spad" 1502482 1502500 1503102 1503107) (-911 "PFO.spad" 1501901 1501928 1502472 1502477) (-910 "PF.spad" 1501475 1501487 1501706 1501799) (-909 "PFECAT.spad" 1499141 1499149 1501401 1501470) (-908 "PFECAT.spad" 1496835 1496845 1499097 1499102) (-907 "PFBRU.spad" 1494705 1494717 1496825 1496830) (-906 "PFBR.spad" 1492243 1492266 1494695 1494700) (-905 "PERM.spad" 1487924 1487934 1492073 1492088) (-904 "PERMGRP.spad" 1482660 1482670 1487914 1487919) (-903 "PERMCAT.spad" 1481212 1481222 1482640 1482655) (-902 "PERMAN.spad" 1479744 1479758 1481202 1481207) (-901 "PENDTREE.spad" 1479083 1479093 1479373 1479378) (-900 "PDRING.spad" 1477574 1477584 1479063 1479078) (-899 "PDRING.spad" 1476073 1476085 1477564 1477569) (-898 "PDEPROB.spad" 1475088 1475096 1476063 1476068) (-897 "PDEPACK.spad" 1469090 1469098 1475078 1475083) (-896 "PDECOMP.spad" 1468552 1468569 1469080 1469085) (-895 "PDECAT.spad" 1466906 1466914 1468542 1468547) (-894 "PCOMP.spad" 1466757 1466770 1466896 1466901) (-893 "PBWLB.spad" 1465339 1465356 1466747 1466752) (-892 "PATTERN.spad" 1459770 1459780 1465329 1465334) (-891 "PATTERN2.spad" 1459506 1459518 1459760 1459765) (-890 "PATTERN1.spad" 1457808 1457824 1459496 1459501) (-889 "PATRES.spad" 1455355 1455367 1457798 1457803) (-888 "PATRES2.spad" 1455017 1455031 1455345 1455350) (-887 "PATMATCH.spad" 1453174 1453205 1454725 1454730) (-886 "PATMAB.spad" 1452599 1452609 1453164 1453169) (-885 "PATLRES.spad" 1451683 1451697 1452589 1452594) (-884 "PATAB.spad" 1451447 1451457 1451673 1451678) (-883 "PARTPERM.spad" 1448809 1448817 1451437 1451442) (-882 "PARSURF.spad" 1448237 1448265 1448799 1448804) (-881 "PARSU2.spad" 1448032 1448048 1448227 1448232) (-880 "script-parser.spad" 1447552 1447560 1448022 1448027) (-879 "PARSCURV.spad" 1446980 1447008 1447542 1447547) (-878 "PARSC2.spad" 1446769 1446785 1446970 1446975) (-877 "PARPCURV.spad" 1446227 1446255 1446759 1446764) (-876 "PARPC2.spad" 1446016 1446032 1446217 1446222) (-875 "PAN2EXPR.spad" 1445428 1445436 1446006 1446011) (-874 "PALETTE.spad" 1444398 1444406 1445418 1445423) (-873 "PAIR.spad" 1443381 1443394 1443986 1443991) (-872 "PADICRC.spad" 1440711 1440729 1441886 1441979) (-871 "PADICRAT.spad" 1438726 1438738 1438947 1439040) (-870 "PADIC.spad" 1438421 1438433 1438652 1438721) (-869 "PADICCT.spad" 1436962 1436974 1438347 1438416) (-868 "PADEPAC.spad" 1435641 1435660 1436952 1436957) (-867 "PADE.spad" 1434381 1434397 1435631 1435636) (-866 "OWP.spad" 1433621 1433651 1434239 1434306) (-865 "OVERSET.spad" 1433194 1433202 1433611 1433616) (-864 "OVAR.spad" 1432975 1432998 1433184 1433189) (-863 "OUT.spad" 1432059 1432067 1432965 1432970) (-862 "OUTFORM.spad" 1421355 1421363 1432049 1432054) (-861 "OUTBFILE.spad" 1420773 1420781 1421345 1421350) (-860 "OUTBCON.spad" 1419771 1419779 1420763 1420768) (-859 "OUTBCON.spad" 1418767 1418777 1419761 1419766) (-858 "OSI.spad" 1418242 1418250 1418757 1418762) (-857 "OSGROUP.spad" 1418160 1418168 1418232 1418237) (-856 "ORTHPOL.spad" 1416621 1416631 1418077 1418082) (-855 "OREUP.spad" 1416074 1416102 1416301 1416340) (-854 "ORESUP.spad" 1415373 1415397 1415754 1415793) (-853 "OREPCTO.spad" 1413192 1413204 1415293 1415298) (-852 "OREPCAT.spad" 1407249 1407259 1413148 1413187) (-851 "OREPCAT.spad" 1401196 1401208 1407097 1407102) (-850 "ORDSET.spad" 1400362 1400370 1401186 1401191) (-849 "ORDSET.spad" 1399526 1399536 1400352 1400357) (-848 "ORDRING.spad" 1398916 1398924 1399506 1399521) (-847 "ORDRING.spad" 1398314 1398324 1398906 1398911) (-846 "ORDMON.spad" 1398169 1398177 1398304 1398309) (-845 "ORDFUNS.spad" 1397295 1397311 1398159 1398164) (-844 "ORDFIN.spad" 1397115 1397123 1397285 1397290) (-843 "ORDCOMP.spad" 1395580 1395590 1396662 1396691) (-842 "ORDCOMP2.spad" 1394865 1394877 1395570 1395575) (-841 "OPTPROB.spad" 1393503 1393511 1394855 1394860) (-840 "OPTPACK.spad" 1385888 1385896 1393493 1393498) (-839 "OPTCAT.spad" 1383563 1383571 1385878 1385883) (-838 "OPSIG.spad" 1383215 1383223 1383553 1383558) (-837 "OPQUERY.spad" 1382764 1382772 1383205 1383210) (-836 "OP.spad" 1382506 1382516 1382586 1382653) (-835 "OPERCAT.spad" 1381970 1381980 1382496 1382501) (-834 "OPERCAT.spad" 1381432 1381444 1381960 1381965) (-833 "ONECOMP.spad" 1380177 1380187 1380979 1381008) (-832 "ONECOMP2.spad" 1379595 1379607 1380167 1380172) (-831 "OMSERVER.spad" 1378597 1378605 1379585 1379590) (-830 "OMSAGG.spad" 1378385 1378395 1378553 1378592) (-829 "OMPKG.spad" 1376997 1377005 1378375 1378380) (-828 "OM.spad" 1375962 1375970 1376987 1376992) (-827 "OMLO.spad" 1375387 1375399 1375848 1375887) (-826 "OMEXPR.spad" 1375221 1375231 1375377 1375382) (-825 "OMERR.spad" 1374764 1374772 1375211 1375216) (-824 "OMERRK.spad" 1373798 1373806 1374754 1374759) (-823 "OMENC.spad" 1373142 1373150 1373788 1373793) (-822 "OMDEV.spad" 1367431 1367439 1373132 1373137) (-821 "OMCONN.spad" 1366840 1366848 1367421 1367426) (-820 "OINTDOM.spad" 1366603 1366611 1366766 1366835) (-819 "OFMONOID.spad" 1362790 1362800 1366593 1366598) (-818 "ODVAR.spad" 1362051 1362061 1362780 1362785) (-817 "ODR.spad" 1361695 1361721 1361863 1362012) (-816 "ODPOL.spad" 1359077 1359087 1359417 1359544) (-815 "ODP.spad" 1348924 1348944 1349297 1349428) (-814 "ODETOOLS.spad" 1347507 1347526 1348914 1348919) (-813 "ODESYS.spad" 1345157 1345174 1347497 1347502) (-812 "ODERTRIC.spad" 1341098 1341115 1345114 1345119) 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1248272 1248277) (-773 "NONE1.spad" 1247699 1247709 1248013 1248018) (-772 "NODE1.spad" 1247168 1247184 1247689 1247694) (-771 "NNI.spad" 1246055 1246063 1247142 1247163) (-770 "NLINSOL.spad" 1244677 1244687 1246045 1246050) (-769 "NIPROB.spad" 1243218 1243226 1244667 1244672) (-768 "NFINTBAS.spad" 1240678 1240695 1243208 1243213) (-767 "NETCLT.spad" 1240652 1240663 1240668 1240673) (-766 "NCODIV.spad" 1238850 1238866 1240642 1240647) (-765 "NCNTFRAC.spad" 1238492 1238506 1238840 1238845) (-764 "NCEP.spad" 1236652 1236666 1238482 1238487) (-763 "NASRING.spad" 1236248 1236256 1236642 1236647) (-762 "NASRING.spad" 1235842 1235852 1236238 1236243) (-761 "NARNG.spad" 1235186 1235194 1235832 1235837) (-760 "NARNG.spad" 1234528 1234538 1235176 1235181) (-759 "NAGSP.spad" 1233601 1233609 1234518 1234523) (-758 "NAGS.spad" 1223126 1223134 1233591 1233596) (-757 "NAGF07.spad" 1221519 1221527 1223116 1223121) (-756 "NAGF04.spad" 1215751 1215759 1221509 1221514) (-755 "NAGF02.spad" 1209560 1209568 1215741 1215746) (-754 "NAGF01.spad" 1205163 1205171 1209550 1209555) (-753 "NAGE04.spad" 1198623 1198631 1205153 1205158) (-752 "NAGE02.spad" 1188965 1188973 1198613 1198618) (-751 "NAGE01.spad" 1184849 1184857 1188955 1188960) (-750 "NAGD03.spad" 1182769 1182777 1184839 1184844) (-749 "NAGD02.spad" 1175300 1175308 1182759 1182764) (-748 "NAGD01.spad" 1169413 1169421 1175290 1175295) (-747 "NAGC06.spad" 1165200 1165208 1169403 1169408) (-746 "NAGC05.spad" 1163669 1163677 1165190 1165195) (-745 "NAGC02.spad" 1162924 1162932 1163659 1163664) (-744 "NAALG.spad" 1162459 1162469 1162892 1162919) (-743 "NAALG.spad" 1162014 1162026 1162449 1162454) (-742 "MULTSQFR.spad" 1158972 1158989 1162004 1162009) (-741 "MULTFACT.spad" 1158355 1158372 1158962 1158967) (-740 "MTSCAT.spad" 1156389 1156410 1158253 1158350) (-739 "MTHING.spad" 1156046 1156056 1156379 1156384) (-738 "MSYSCMD.spad" 1155480 1155488 1156036 1156041) (-737 "MSET.spad" 1153422 1153432 1155186 1155225) (-736 "MSETAGG.spad" 1153267 1153277 1153390 1153417) (-735 "MRING.spad" 1150238 1150250 1152975 1153042) (-734 "MRF2.spad" 1149806 1149820 1150228 1150233) (-733 "MRATFAC.spad" 1149352 1149369 1149796 1149801) (-732 "MPRFF.spad" 1147382 1147401 1149342 1149347) (-731 "MPOLY.spad" 1144853 1144868 1145212 1145339) (-730 "MPCPF.spad" 1144117 1144136 1144843 1144848) (-729 "MPC3.spad" 1143932 1143972 1144107 1144112) (-728 "MPC2.spad" 1143574 1143607 1143922 1143927) (-727 "MONOTOOL.spad" 1141909 1141926 1143564 1143569) (-726 "MONOID.spad" 1141228 1141236 1141899 1141904) (-725 "MONOID.spad" 1140545 1140555 1141218 1141223) (-724 "MONOGEN.spad" 1139291 1139304 1140405 1140540) (-723 "MONOGEN.spad" 1138059 1138074 1139175 1139180) (-722 "MONADWU.spad" 1136073 1136081 1138049 1138054) (-721 "MONADWU.spad" 1134085 1134095 1136063 1136068) (-720 "MONAD.spad" 1133229 1133237 1134075 1134080) (-719 "MONAD.spad" 1132371 1132381 1133219 1133224) (-718 "MOEBIUS.spad" 1131057 1131071 1132351 1132366) (-717 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1115180) (-698 "MFINFACT.spad" 1113101 1113123 1113691 1113696) (-697 "MESH.spad" 1110833 1110841 1113091 1113096) (-696 "MDDFACT.spad" 1109026 1109036 1110823 1110828) (-695 "MDAGG.spad" 1108313 1108323 1109006 1109021) (-694 "MCMPLX.spad" 1104324 1104332 1104938 1105139) (-693 "MCDEN.spad" 1103532 1103544 1104314 1104319) (-692 "MCALCFN.spad" 1100634 1100660 1103522 1103527) (-691 "MAYBE.spad" 1099918 1099929 1100624 1100629) (-690 "MATSTOR.spad" 1097194 1097204 1099908 1099913) (-689 "MATRIX.spad" 1095898 1095908 1096382 1096409) (-688 "MATLIN.spad" 1093224 1093248 1095782 1095787) (-687 "MATCAT.spad" 1084809 1084831 1093192 1093219) (-686 "MATCAT.spad" 1076266 1076290 1084651 1084656) (-685 "MATCAT2.spad" 1075534 1075582 1076256 1076261) (-684 "MAPPKG3.spad" 1074433 1074447 1075524 1075529) (-683 "MAPPKG2.spad" 1073767 1073779 1074423 1074428) (-682 "MAPPKG1.spad" 1072585 1072595 1073757 1073762) (-681 "MAPPAST.spad" 1071898 1071906 1072575 1072580) (-680 "MAPHACK3.spad" 1071706 1071720 1071888 1071893) (-679 "MAPHACK2.spad" 1071471 1071483 1071696 1071701) (-678 "MAPHACK1.spad" 1071101 1071111 1071461 1071466) (-677 "MAGMA.spad" 1068891 1068908 1071091 1071096) (-676 "MACROAST.spad" 1068470 1068478 1068881 1068886) (-675 "M3D.spad" 1066166 1066176 1067848 1067853) (-674 "LZSTAGG.spad" 1063394 1063404 1066156 1066161) (-673 "LZSTAGG.spad" 1060620 1060632 1063384 1063389) (-672 "LWORD.spad" 1057325 1057342 1060610 1060615) (-671 "LSTAST.spad" 1057109 1057117 1057315 1057320) (-670 "LSQM.spad" 1055335 1055349 1055733 1055784) (-669 "LSPP.spad" 1054868 1054885 1055325 1055330) (-668 "LSMP.spad" 1053708 1053736 1054858 1054863) (-667 "LSMP1.spad" 1051512 1051526 1053698 1053703) (-666 "LSAGG.spad" 1051181 1051191 1051480 1051507) (-665 "LSAGG.spad" 1050870 1050882 1051171 1051176) (-664 "LPOLY.spad" 1049824 1049843 1050726 1050795) (-663 "LPEFRAC.spad" 1049081 1049091 1049814 1049819) (-662 "LO.spad" 1048482 1048496 1049015 1049042) (-661 "LOGIC.spad" 1048084 1048092 1048472 1048477) (-660 "LOGIC.spad" 1047684 1047694 1048074 1048079) (-659 "LODOOPS.spad" 1046602 1046614 1047674 1047679) (-658 "LODO.spad" 1045986 1046002 1046282 1046321) (-657 "LODOF.spad" 1045030 1045047 1045943 1045948) (-656 "LODOCAT.spad" 1043688 1043698 1044986 1045025) (-655 "LODOCAT.spad" 1042344 1042356 1043644 1043649) (-654 "LODO2.spad" 1041617 1041629 1042024 1042063) (-653 "LODO1.spad" 1041017 1041027 1041297 1041336) (-652 "LODEEF.spad" 1039789 1039807 1041007 1041012) (-651 "LNAGG.spad" 1035591 1035601 1039779 1039784) (-650 "LNAGG.spad" 1031357 1031369 1035547 1035552) (-649 "LMOPS.spad" 1028093 1028110 1031347 1031352) (-648 "LMODULE.spad" 1027861 1027871 1028083 1028088) (-647 "LMDICT.spad" 1027144 1027154 1027412 1027439) (-646 "LLINSET.spad" 1026541 1026551 1027134 1027139) (-645 "LITERAL.spad" 1026447 1026458 1026531 1026536) (-644 "LIST.spad" 1024165 1024175 1025594 1025621) (-643 "LIST3.spad" 1023456 1023470 1024155 1024160) (-642 "LIST2.spad" 1022096 1022108 1023446 1023451) (-641 "LIST2MAP.spad" 1018973 1018985 1022086 1022091) (-640 "LINSET.spad" 1018595 1018605 1018963 1018968) (-639 "LINEXP.spad" 1018027 1018037 1018575 1018590) (-638 "LINDEP.spad" 1016804 1016816 1017939 1017944) (-637 "LIMITRF.spad" 1014718 1014728 1016794 1016799) (-636 "LIMITPS.spad" 1013601 1013614 1014708 1014713) (-635 "LIE.spad" 1011615 1011627 1012891 1013036) (-634 "LIECAT.spad" 1011091 1011101 1011541 1011610) (-633 "LIECAT.spad" 1010595 1010607 1011047 1011052) (-632 "LIB.spad" 1008643 1008651 1009254 1009269) (-631 "LGROBP.spad" 1005996 1006015 1008633 1008638) (-630 "LF.spad" 1004915 1004931 1005986 1005991) (-629 "LFCAT.spad" 1003934 1003942 1004905 1004910) (-628 "LEXTRIPK.spad" 999437 999452 1003924 1003929) (-627 "LEXP.spad" 997440 997467 999417 999432) (-626 "LETAST.spad" 997139 997147 997430 997435) (-625 "LEADCDET.spad" 995523 995540 997129 997134) (-624 "LAZM3PK.spad" 994227 994249 995513 995518) (-623 "LAUPOL.spad" 992916 992929 993820 993889) (-622 "LAPLACE.spad" 992489 992505 992906 992911) (-621 "LA.spad" 991929 991943 992411 992450) (-620 "LALG.spad" 991705 991715 991909 991924) (-619 "LALG.spad" 991489 991501 991695 991700) (-618 "KVTFROM.spad" 991224 991234 991479 991484) (-617 "KTVLOGIC.spad" 990736 990744 991214 991219) (-616 "KRCFROM.spad" 990474 990484 990726 990731) (-615 "KOVACIC.spad" 989187 989204 990464 990469) (-614 "KONVERT.spad" 988909 988919 989177 989182) (-613 "KOERCE.spad" 988646 988656 988899 988904) (-612 "KERNEL.spad" 987265 987275 988430 988435) (-611 "KERNEL2.spad" 986968 986980 987255 987260) (-610 "KDAGG.spad" 986071 986093 986948 986963) (-609 "KDAGG.spad" 985182 985206 986061 986066) (-608 "KAFILE.spad" 984145 984161 984380 984407) (-607 "JORDAN.spad" 981972 981984 983435 983580) (-606 "JOINAST.spad" 981666 981674 981962 981967) (-605 "JAVACODE.spad" 981532 981540 981656 981661) (-604 "IXAGG.spad" 979655 979679 981522 981527) (-603 "IXAGG.spad" 977633 977659 979502 979507) (-602 "IVECTOR.spad" 976403 976418 976558 976585) (-601 "ITUPLE.spad" 975548 975558 976393 976398) (-600 "ITRIGMNP.spad" 974359 974378 975538 975543) (-599 "ITFUN3.spad" 973853 973867 974349 974354) (-598 "ITFUN2.spad" 973583 973595 973843 973848) (-597 "ITAYLOR.spad" 971375 971390 973419 973544) (-596 "ISUPS.spad" 963786 963801 970349 970446) (-595 "ISUMP.spad" 963283 963299 963776 963781) (-594 "ISTRING.spad" 962286 962299 962452 962479) (-593 "ISAST.spad" 962005 962013 962276 962281) (-592 "IRURPK.spad" 960718 960737 961995 962000) (-591 "IRSN.spad" 958678 958686 960708 960713) (-590 "IRRF2F.spad" 957153 957163 958634 958639) (-589 "IRREDFFX.spad" 956754 956765 957143 957148) (-588 "IROOT.spad" 955085 955095 956744 956749) (-587 "IR.spad" 952874 952888 954940 954967) (-586 "IR2.spad" 951894 951910 952864 952869) (-585 "IR2F.spad" 951094 951110 951884 951889) (-584 "IPRNTPK.spad" 950854 950862 951084 951089) (-583 "IPF.spad" 950419 950431 950659 950752) (-582 "IPADIC.spad" 950180 950206 950345 950414) (-581 "IP4ADDR.spad" 949737 949745 950170 950175) (-580 "IOMODE.spad" 949358 949366 949727 949732) (-579 "IOBFILE.spad" 948719 948727 949348 949353) (-578 "IOBCON.spad" 948584 948592 948709 948714) (-577 "INVLAPLA.spad" 948229 948245 948574 948579) (-576 "INTTR.spad" 941475 941492 948219 948224) (-575 "INTTOOLS.spad" 939186 939202 941049 941054) (-574 "INTSLPE.spad" 938492 938500 939176 939181) (-573 "INTRVL.spad" 938058 938068 938406 938487) (-572 "INTRF.spad" 936422 936436 938048 938053) (-571 "INTRET.spad" 935854 935864 936412 936417) (-570 "INTRAT.spad" 934529 934546 935844 935849) (-569 "INTPM.spad" 932892 932908 934172 934177) (-568 "INTPAF.spad" 930660 930678 932824 932829) (-567 "INTPACK.spad" 920970 920978 930650 930655) (-566 "INT.spad" 920331 920339 920824 920965) (-565 "INTHERTR.spad" 919597 919614 920321 920326) (-564 "INTHERAL.spad" 919263 919287 919587 919592) (-563 "INTHEORY.spad" 915676 915684 919253 919258) (-562 "INTG0.spad" 909139 909157 915608 915613) (-561 "INTFTBL.spad" 903168 903176 909129 909134) (-560 "INTFACT.spad" 902227 902237 903158 903163) (-559 "INTEF.spad" 900542 900558 902217 902222) (-558 "INTDOM.spad" 899157 899165 900468 900537) (-557 "INTDOM.spad" 897834 897844 899147 899152) (-556 "INTCAT.spad" 896087 896097 897748 897829) (-555 "INTBIT.spad" 895590 895598 896077 896082) (-554 "INTALG.spad" 894772 894799 895580 895585) (-553 "INTAF.spad" 894264 894280 894762 894767) (-552 "INTABL.spad" 892782 892813 892945 892972) (-551 "INT8.spad" 892662 892670 892772 892777) (-550 "INT64.spad" 892541 892549 892652 892657) (-549 "INT32.spad" 892420 892428 892531 892536) (-548 "INT16.spad" 892299 892307 892410 892415) (-547 "INS.spad" 889766 889774 892201 892294) (-546 "INS.spad" 887319 887329 889756 889761) (-545 "INPSIGN.spad" 886753 886766 887309 887314) (-544 "INPRODPF.spad" 885819 885838 886743 886748) (-543 "INPRODFF.spad" 884877 884901 885809 885814) (-542 "INNMFACT.spad" 883848 883865 884867 884872) (-541 "INMODGCD.spad" 883332 883362 883838 883843) (-540 "INFSP.spad" 881617 881639 883322 883327) (-539 "INFPROD0.spad" 880667 880686 881607 881612) (-538 "INFORM.spad" 877828 877836 880657 880662) (-537 "INFORM1.spad" 877453 877463 877818 877823) (-536 "INFINITY.spad" 877005 877013 877443 877448) (-535 "INETCLTS.spad" 876982 876990 876995 877000) (-534 "INEP.spad" 875514 875536 876972 876977) (-533 "INDE.spad" 875243 875260 875504 875509) (-532 "INCRMAPS.spad" 874664 874674 875233 875238) (-531 "INBFILE.spad" 873736 873744 874654 874659) (-530 "INBFF.spad" 869506 869517 873726 873731) (-529 "INBCON.spad" 867794 867802 869496 869501) (-528 "INBCON.spad" 866080 866090 867784 867789) (-527 "INAST.spad" 865741 865749 866070 866075) (-526 "IMPTAST.spad" 865449 865457 865731 865736) (-525 "IMATRIX.spad" 864394 864420 864906 864933) (-524 "IMATQF.spad" 863488 863532 864350 864355) (-523 "IMATLIN.spad" 862093 862117 863444 863449) (-522 "ILIST.spad" 860749 860764 861276 861303) (-521 "IIARRAY2.spad" 860137 860175 860356 860383) (-520 "IFF.spad" 859547 859563 859818 859911) (-519 "IFAST.spad" 859161 859169 859537 859542) (-518 "IFARRAY.spad" 856648 856663 858344 858371) (-517 "IFAMON.spad" 856510 856527 856604 856609) (-516 "IEVALAB.spad" 855899 855911 856500 856505) (-515 "IEVALAB.spad" 855286 855300 855889 855894) (-514 "IDPO.spad" 855084 855096 855276 855281) (-513 "IDPOAMS.spad" 854840 854852 855074 855079) (-512 "IDPOAM.spad" 854560 854572 854830 854835) (-511 "IDPC.spad" 853494 853506 854550 854555) (-510 "IDPAM.spad" 853239 853251 853484 853489) (-509 "IDPAG.spad" 852986 852998 853229 853234) (-508 "IDENT.spad" 852636 852644 852976 852981) (-507 "IDECOMP.spad" 849873 849891 852626 852631) (-506 "IDEAL.spad" 844796 844835 849808 849813) (-505 "ICDEN.spad" 843947 843963 844786 844791) (-504 "ICARD.spad" 843136 843144 843937 843942) (-503 "IBPTOOLS.spad" 841729 841746 843126 843131) (-502 "IBITS.spad" 840928 840941 841365 841392) (-501 "IBATOOL.spad" 837803 837822 840918 840923) (-500 "IBACHIN.spad" 836290 836305 837793 837798) (-499 "IARRAY2.spad" 835278 835304 835897 835924) (-498 "IARRAY1.spad" 834323 834338 834461 834488) (-497 "IAN.spad" 832536 832544 834139 834232) (-496 "IALGFACT.spad" 832137 832170 832526 832531) (-495 "HYPCAT.spad" 831561 831569 832127 832132) (-494 "HYPCAT.spad" 830983 830993 831551 831556) (-493 "HOSTNAME.spad" 830791 830799 830973 830978) (-492 "HOMOTOP.spad" 830534 830544 830781 830786) (-491 "HOAGG.spad" 827802 827812 830524 830529) (-490 "HOAGG.spad" 824845 824857 827569 827574) (-489 "HEXADEC.spad" 822947 822955 823312 823405) (-488 "HEUGCD.spad" 821962 821973 822937 822942) (-487 "HELLFDIV.spad" 821552 821576 821952 821957) (-486 "HEAP.spad" 820944 820954 821159 821186) (-485 "HEADAST.spad" 820475 820483 820934 820939) (-484 "HDP.spad" 810318 810334 810695 810826) (-483 "HDMP.spad" 807530 807545 808148 808275) (-482 "HB.spad" 805767 805775 807520 807525) (-481 "HASHTBL.spad" 804237 804268 804448 804475) (-480 "HASAST.spad" 803953 803961 804227 804232) (-479 "HACKPI.spad" 803436 803444 803855 803948) (-478 "GTSET.spad" 802375 802391 803082 803109) (-477 "GSTBL.spad" 800894 800929 801068 801083) (-476 "GSERIES.spad" 798061 798088 799026 799175) (-475 "GROUP.spad" 797330 797338 798041 798056) (-474 "GROUP.spad" 796607 796617 797320 797325) (-473 "GROEBSOL.spad" 795095 795116 796597 796602) (-472 "GRMOD.spad" 793666 793678 795085 795090) (-471 "GRMOD.spad" 792235 792249 793656 793661) (-470 "GRIMAGE.spad" 784840 784848 792225 792230) (-469 "GRDEF.spad" 783219 783227 784830 784835) (-468 "GRAY.spad" 781678 781686 783209 783214) (-467 "GRALG.spad" 780725 780737 781668 781673) (-466 "GRALG.spad" 779770 779784 780715 780720) (-465 "GPOLSET.spad" 779224 779247 779452 779479) (-464 "GOSPER.spad" 778489 778507 779214 779219) (-463 "GMODPOL.spad" 777627 777654 778457 778484) (-462 "GHENSEL.spad" 776696 776710 777617 777622) (-461 "GENUPS.spad" 772797 772810 776686 776691) (-460 "GENUFACT.spad" 772374 772384 772787 772792) (-459 "GENPGCD.spad" 771958 771975 772364 772369) (-458 "GENMFACT.spad" 771410 771429 771948 771953) (-457 "GENEEZ.spad" 769349 769362 771400 771405) (-456 "GDMP.spad" 766403 766420 767179 767306) (-455 "GCNAALG.spad" 760298 760325 766197 766264) (-454 "GCDDOM.spad" 759470 759478 760224 760293) (-453 "GCDDOM.spad" 758704 758714 759460 759465) (-452 "GB.spad" 756222 756260 758660 758665) (-451 "GBINTERN.spad" 752242 752280 756212 756217) (-450 "GBF.spad" 747999 748037 752232 752237) (-449 "GBEUCLID.spad" 745873 745911 747989 747994) (-448 "GAUSSFAC.spad" 745170 745178 745863 745868) (-447 "GALUTIL.spad" 743492 743502 745126 745131) (-446 "GALPOLYU.spad" 741938 741951 743482 743487) (-445 "GALFACTU.spad" 740103 740122 741928 741933) (-444 "GALFACT.spad" 730236 730247 740093 740098) (-443 "FVFUN.spad" 727259 727267 730226 730231) (-442 "FVC.spad" 726311 726319 727249 727254) (-441 "FUNDESC.spad" 725989 725997 726301 726306) (-440 "FUNCTION.spad" 725838 725850 725979 725984) (-439 "FT.spad" 724131 724139 725828 725833) (-438 "FTEM.spad" 723294 723302 724121 724126) (-437 "FSUPFACT.spad" 722194 722213 723230 723235) (-436 "FST.spad" 720280 720288 722184 722189) (-435 "FSRED.spad" 719758 719774 720270 720275) (-434 "FSPRMELT.spad" 718582 718598 719715 719720) (-433 "FSPECF.spad" 716659 716675 718572 718577) (-432 "FS.spad" 710721 710731 716434 716654) (-431 "FS.spad" 704561 704573 710276 710281) (-430 "FSINT.spad" 704219 704235 704551 704556) (-429 "FSERIES.spad" 703406 703418 704039 704138) (-428 "FSCINT.spad" 702719 702735 703396 703401) (-427 "FSAGG.spad" 701836 701846 702675 702714) (-426 "FSAGG.spad" 700915 700927 701756 701761) (-425 "FSAGG2.spad" 699614 699630 700905 700910) (-424 "FS2UPS.spad" 694097 694131 699604 699609) (-423 "FS2.spad" 693742 693758 694087 694092) (-422 "FS2EXPXP.spad" 692865 692888 693732 693737) (-421 "FRUTIL.spad" 691807 691817 692855 692860) (-420 "FR.spad" 685501 685511 690831 690900) (-419 "FRNAALG.spad" 680588 680598 685443 685496) (-418 "FRNAALG.spad" 675687 675699 680544 680549) (-417 "FRNAAF2.spad" 675141 675159 675677 675682) (-416 "FRMOD.spad" 674535 674565 675072 675077) (-415 "FRIDEAL.spad" 673730 673751 674515 674530) (-414 "FRIDEAL2.spad" 673332 673364 673720 673725) (-413 "FRETRCT.spad" 672843 672853 673322 673327) (-412 "FRETRCT.spad" 672220 672232 672701 672706) (-411 "FRAMALG.spad" 670548 670561 672176 672215) (-410 "FRAMALG.spad" 668908 668923 670538 670543) (-409 "FRAC.spad" 666007 666017 666410 666583) (-408 "FRAC2.spad" 665610 665622 665997 666002) (-407 "FR2.spad" 664944 664956 665600 665605) (-406 "FPS.spad" 661753 661761 664834 664939) (-405 "FPS.spad" 658590 658600 661673 661678) (-404 "FPC.spad" 657632 657640 658492 658585) (-403 "FPC.spad" 656760 656770 657622 657627) (-402 "FPATMAB.spad" 656522 656532 656750 656755) (-401 "FPARFRAC.spad" 654995 655012 656512 656517) (-400 "FORTRAN.spad" 653501 653544 654985 654990) (-399 "FORT.spad" 652430 652438 653491 653496) (-398 "FORTFN.spad" 649600 649608 652420 652425) (-397 "FORTCAT.spad" 649284 649292 649590 649595) (-396 "FORMULA.spad" 646748 646756 649274 649279) (-395 "FORMULA1.spad" 646227 646237 646738 646743) (-394 "FORDER.spad" 645918 645942 646217 646222) (-393 "FOP.spad" 645119 645127 645908 645913) (-392 "FNLA.spad" 644543 644565 645087 645114) (-391 "FNCAT.spad" 643130 643138 644533 644538) (-390 "FNAME.spad" 643022 643030 643120 643125) (-389 "FMTC.spad" 642820 642828 642948 643017) (-388 "FMONOID.spad" 639875 639885 642776 642781) (-387 "FM.spad" 639570 639582 639809 639836) (-386 "FMFUN.spad" 636600 636608 639560 639565) (-385 "FMC.spad" 635652 635660 636590 636595) (-384 "FMCAT.spad" 633306 633324 635620 635647) (-383 "FM1.spad" 632663 632675 633240 633267) (-382 "FLOATRP.spad" 630384 630398 632653 632658) (-381 "FLOAT.spad" 623672 623680 630250 630379) (-380 "FLOATCP.spad" 621089 621103 623662 623667) (-379 "FLINEXP.spad" 620801 620811 621069 621084) (-378 "FLINEXP.spad" 620467 620479 620737 620742) (-377 "FLASORT.spad" 619787 619799 620457 620462) (-376 "FLALG.spad" 617433 617452 619713 619782) (-375 "FLAGG.spad" 614451 614461 617413 617428) (-374 "FLAGG.spad" 611370 611382 614334 614339) (-373 "FLAGG2.spad" 610051 610067 611360 611365) (-372 "FINRALG.spad" 608080 608093 610007 610046) (-371 "FINRALG.spad" 606035 606050 607964 607969) (-370 "FINITE.spad" 605187 605195 606025 606030) (-369 "FINAALG.spad" 594168 594178 605129 605182) (-368 "FINAALG.spad" 583161 583173 594124 594129) (-367 "FILE.spad" 582744 582754 583151 583156) (-366 "FILECAT.spad" 581262 581279 582734 582739) (-365 "FIELD.spad" 580668 580676 581164 581257) (-364 "FIELD.spad" 580160 580170 580658 580663) (-363 "FGROUP.spad" 578769 578779 580140 580155) (-362 "FGLMICPK.spad" 577556 577571 578759 578764) (-361 "FFX.spad" 576931 576946 577272 577365) (-360 "FFSLPE.spad" 576420 576441 576921 576926) (-359 "FFPOLY.spad" 567672 567683 576410 576415) (-358 "FFPOLY2.spad" 566732 566749 567662 567667) (-357 "FFP.spad" 566129 566149 566448 566541) (-356 "FF.spad" 565577 565593 565810 565903) (-355 "FFNBX.spad" 564089 564109 565293 565386) (-354 "FFNBP.spad" 562602 562619 563805 563898) (-353 "FFNB.spad" 561067 561088 562283 562376) (-352 "FFINTBAS.spad" 558481 558500 561057 561062) (-351 "FFIELDC.spad" 556056 556064 558383 558476) (-350 "FFIELDC.spad" 553717 553727 556046 556051) (-349 "FFHOM.spad" 552465 552482 553707 553712) (-348 "FFF.spad" 549900 549911 552455 552460) (-347 "FFCGX.spad" 548747 548767 549616 549709) (-346 "FFCGP.spad" 547636 547656 548463 548556) (-345 "FFCG.spad" 546428 546449 547317 547410) (-344 "FFCAT.spad" 539455 539477 546267 546423) (-343 "FFCAT.spad" 532561 532585 539375 539380) (-342 "FFCAT2.spad" 532306 532346 532551 532556) (-341 "FEXPR.spad" 524015 524061 532062 532101) (-340 "FEVALAB.spad" 523721 523731 524005 524010) (-339 "FEVALAB.spad" 523212 523224 523498 523503) (-338 "FDIV.spad" 522654 522678 523202 523207) (-337 "FDIVCAT.spad" 520696 520720 522644 522649) (-336 "FDIVCAT.spad" 518736 518762 520686 520691) (-335 "FDIV2.spad" 518390 518430 518726 518731) (-334 "FCTRDATA.spad" 517422 517430 518380 518385) (-333 "FCPAK1.spad" 515975 515983 517412 517417) (-332 "FCOMP.spad" 515354 515364 515965 515970) (-331 "FC.spad" 505269 505277 515344 515349) (-330 "FAXF.spad" 498204 498218 505171 505264) (-329 "FAXF.spad" 491191 491207 498160 498165) (-328 "FARRAY.spad" 489337 489347 490374 490401) (-327 "FAMR.spad" 487457 487469 489235 489332) (-326 "FAMR.spad" 485561 485575 487341 487346) (-325 "FAMONOID.spad" 485211 485221 485515 485520) (-324 "FAMONC.spad" 483433 483445 485201 485206) (-323 "FAGROUP.spad" 483039 483049 483329 483356) (-322 "FACUTIL.spad" 481235 481252 483029 483034) (-321 "FACTFUNC.spad" 480411 480421 481225 481230) (-320 "EXPUPXS.spad" 477244 477267 478543 478692) (-319 "EXPRTUBE.spad" 474472 474480 477234 477239) (-318 "EXPRODE.spad" 471344 471360 474462 474467) (-317 "EXPR.spad" 466619 466629 467333 467740) (-316 "EXPR2UPS.spad" 462711 462724 466609 466614) (-315 "EXPR2.spad" 462414 462426 462701 462706) (-314 "EXPEXPAN.spad" 459352 459377 459986 460079) (-313 "EXIT.spad" 459023 459031 459342 459347) (-312 "EXITAST.spad" 458759 458767 459013 459018) (-311 "EVALCYC.spad" 458217 458231 458749 458754) (-310 "EVALAB.spad" 457781 457791 458207 458212) (-309 "EVALAB.spad" 457343 457355 457771 457776) (-308 "EUCDOM.spad" 454885 454893 457269 457338) (-307 "EUCDOM.spad" 452489 452499 454875 454880) (-306 "ESTOOLS.spad" 444329 444337 452479 452484) (-305 "ESTOOLS2.spad" 443930 443944 444319 444324) (-304 "ESTOOLS1.spad" 443615 443626 443920 443925) (-303 "ES.spad" 436162 436170 443605 443610) (-302 "ES.spad" 428615 428625 436060 436065) (-301 "ESCONT.spad" 425388 425396 428605 428610) (-300 "ESCONT1.spad" 425137 425149 425378 425383) (-299 "ES2.spad" 424632 424648 425127 425132) (-298 "ES1.spad" 424198 424214 424622 424627) (-297 "ERROR.spad" 421519 421527 424188 424193) (-296 "EQTBL.spad" 419991 420013 420200 420227) (-295 "EQ.spad" 414784 414794 417583 417695) (-294 "EQ2.spad" 414500 414512 414774 414779) (-293 "EP.spad" 410814 410824 414490 414495) (-292 "ENV.spad" 409466 409474 410804 410809) (-291 "ENTIRER.spad" 409134 409142 409410 409461) (-290 "EMR.spad" 408335 408376 409060 409129) (-289 "ELTAGG.spad" 406575 406594 408325 408330) (-288 "ELTAGG.spad" 404779 404800 406531 406536) (-287 "ELTAB.spad" 404226 404244 404769 404774) (-286 "ELFUTS.spad" 403605 403624 404216 404221) (-285 "ELEMFUN.spad" 403294 403302 403595 403600) (-284 "ELEMFUN.spad" 402981 402991 403284 403289) (-283 "ELAGG.spad" 400924 400934 402961 402976) (-282 "ELAGG.spad" 398804 398816 400843 400848) (-281 "ELABEXPR.spad" 397727 397735 398794 398799) (-280 "EFUPXS.spad" 394503 394533 397683 397688) (-279 "EFULS.spad" 391339 391362 394459 394464) (-278 "EFSTRUC.spad" 389294 389310 391329 391334) (-277 "EF.spad" 384060 384076 389284 389289) (-276 "EAB.spad" 382336 382344 384050 384055) (-275 "E04UCFA.spad" 381872 381880 382326 382331) (-274 "E04NAFA.spad" 381449 381457 381862 381867) (-273 "E04MBFA.spad" 381029 381037 381439 381444) (-272 "E04JAFA.spad" 380565 380573 381019 381024) (-271 "E04GCFA.spad" 380101 380109 380555 380560) (-270 "E04FDFA.spad" 379637 379645 380091 380096) (-269 "E04DGFA.spad" 379173 379181 379627 379632) (-268 "E04AGNT.spad" 375015 375023 379163 379168) (-267 "DVARCAT.spad" 371700 371710 375005 375010) (-266 "DVARCAT.spad" 368383 368395 371690 371695) (-265 "DSMP.spad" 365850 365864 366155 366282) (-264 "DROPT.spad" 359795 359803 365840 365845) (-263 "DROPT1.spad" 359458 359468 359785 359790) (-262 "DROPT0.spad" 354285 354293 359448 359453) (-261 "DRAWPT.spad" 352440 352448 354275 354280) (-260 "DRAW.spad" 345040 345053 352430 352435) (-259 "DRAWHACK.spad" 344348 344358 345030 345035) (-258 "DRAWCX.spad" 341790 341798 344338 344343) (-257 "DRAWCURV.spad" 341327 341342 341780 341785) (-256 "DRAWCFUN.spad" 330499 330507 341317 341322) (-255 "DQAGG.spad" 328667 328677 330467 330494) (-254 "DPOLCAT.spad" 324008 324024 328535 328662) (-253 "DPOLCAT.spad" 319435 319453 323964 323969) (-252 "DPMO.spad" 311661 311677 311799 312100) (-251 "DPMM.spad" 303900 303918 304025 304326) (-250 "DOMTMPLT.spad" 303560 303568 303890 303895) (-249 "DOMCTOR.spad" 303315 303323 303550 303555) (-248 "DOMAIN.spad" 302446 302454 303305 303310) (-247 "DMP.spad" 299704 299719 300276 300403) (-246 "DLP.spad" 299052 299062 299694 299699) (-245 "DLIST.spad" 297631 297641 298235 298262) (-244 "DLAGG.spad" 296042 296052 297621 297626) (-243 "DIVRING.spad" 295584 295592 295986 296037) (-242 "DIVRING.spad" 295170 295180 295574 295579) (-241 "DISPLAY.spad" 293350 293358 295160 295165) (-240 "DIRPROD.spad" 282930 282946 283570 283701) (-239 "DIRPROD2.spad" 281738 281756 282920 282925) (-238 "DIRPCAT.spad" 280680 280696 281602 281733) (-237 "DIRPCAT.spad" 279351 279369 280275 280280) (-236 "DIOSP.spad" 278176 278184 279341 279346) (-235 "DIOPS.spad" 277160 277170 278156 278171) (-234 "DIOPS.spad" 276118 276130 277116 277121) (-233 "DIFRING.spad" 275410 275418 276098 276113) (-232 "DIFRING.spad" 274710 274720 275400 275405) (-231 "DIFEXT.spad" 273869 273879 274690 274705) (-230 "DIFEXT.spad" 272945 272957 273768 273773) (-229 "DIAGG.spad" 272575 272585 272925 272940) (-228 "DIAGG.spad" 272213 272225 272565 272570) (-227 "DHMATRIX.spad" 270517 270527 271670 271697) (-226 "DFSFUN.spad" 263925 263933 270507 270512) (-225 "DFLOAT.spad" 260646 260654 263815 263920) (-224 "DFINTTLS.spad" 258855 258871 260636 260641) (-223 "DERHAM.spad" 256765 256797 258835 258850) (-222 "DEQUEUE.spad" 256083 256093 256372 256399) (-221 "DEGRED.spad" 255698 255712 256073 256078) (-220 "DEFINTRF.spad" 253223 253233 255688 255693) (-219 "DEFINTEF.spad" 251719 251735 253213 253218) (-218 "DEFAST.spad" 251087 251095 251709 251714) (-217 "DECIMAL.spad" 249193 249201 249554 249647) (-216 "DDFACT.spad" 246992 247009 249183 249188) (-215 "DBLRESP.spad" 246590 246614 246982 246987) (-214 "DBASE.spad" 245244 245254 246580 246585) (-213 "DATAARY.spad" 244706 244719 245234 245239) (-212 "D03FAFA.spad" 244534 244542 244696 244701) (-211 "D03EEFA.spad" 244354 244362 244524 244529) (-210 "D03AGNT.spad" 243434 243442 244344 244349) (-209 "D02EJFA.spad" 242896 242904 243424 243429) (-208 "D02CJFA.spad" 242374 242382 242886 242891) (-207 "D02BHFA.spad" 241864 241872 242364 242369) (-206 "D02BBFA.spad" 241354 241362 241854 241859) (-205 "D02AGNT.spad" 236158 236166 241344 241349) (-204 "D01WGTS.spad" 234477 234485 236148 236153) (-203 "D01TRNS.spad" 234454 234462 234467 234472) (-202 "D01GBFA.spad" 233976 233984 234444 234449) (-201 "D01FCFA.spad" 233498 233506 233966 233971) (-200 "D01ASFA.spad" 232966 232974 233488 233493) (-199 "D01AQFA.spad" 232412 232420 232956 232961) (-198 "D01APFA.spad" 231836 231844 232402 232407) (-197 "D01ANFA.spad" 231330 231338 231826 231831) (-196 "D01AMFA.spad" 230840 230848 231320 231325) (-195 "D01ALFA.spad" 230380 230388 230830 230835) (-194 "D01AKFA.spad" 229906 229914 230370 230375) (-193 "D01AJFA.spad" 229429 229437 229896 229901) (-192 "D01AGNT.spad" 225488 225496 229419 229424) (-191 "CYCLOTOM.spad" 224994 225002 225478 225483) (-190 "CYCLES.spad" 221826 221834 224984 224989) (-189 "CVMP.spad" 221243 221253 221816 221821) (-188 "CTRIGMNP.spad" 219733 219749 221233 221238) (-187 "CTOR.spad" 219424 219432 219723 219728) (-186 "CTORKIND.spad" 219027 219035 219414 219419) (-185 "CTORCAT.spad" 218276 218284 219017 219022) (-184 "CTORCAT.spad" 217523 217533 218266 218271) (-183 "CTORCALL.spad" 217103 217111 217513 217518) (-182 "CSTTOOLS.spad" 216346 216359 217093 217098) (-181 "CRFP.spad" 210050 210063 216336 216341) (-180 "CRCEAST.spad" 209770 209778 210040 210045) (-179 "CRAPACK.spad" 208813 208823 209760 209765) (-178 "CPMATCH.spad" 208313 208328 208738 208743) (-177 "CPIMA.spad" 208018 208037 208303 208308) (-176 "COORDSYS.spad" 202911 202921 208008 208013) (-175 "CONTOUR.spad" 202318 202326 202901 202906) (-174 "CONTFRAC.spad" 197930 197940 202220 202313) (-173 "CONDUIT.spad" 197688 197696 197920 197925) (-172 "COMRING.spad" 197362 197370 197626 197683) (-171 "COMPPROP.spad" 196876 196884 197352 197357) (-170 "COMPLPAT.spad" 196643 196658 196866 196871) (-169 "COMPLEX.spad" 190780 190790 191024 191285) (-168 "COMPLEX2.spad" 190493 190505 190770 190775) (-167 "COMPFACT.spad" 190095 190109 190483 190488) (-166 "COMPCAT.spad" 188163 188173 189829 190090) (-165 "COMPCAT.spad" 185959 185971 187627 187632) (-164 "COMMUPC.spad" 185705 185723 185949 185954) (-163 "COMMONOP.spad" 185238 185246 185695 185700) (-162 "COMM.spad" 185047 185055 185228 185233) (-161 "COMMAAST.spad" 184810 184818 185037 185042) (-160 "COMBOPC.spad" 183715 183723 184800 184805) (-159 "COMBINAT.spad" 182460 182470 183705 183710) (-158 "COMBF.spad" 179828 179844 182450 182455) (-157 "COLOR.spad" 178665 178673 179818 179823) (-156 "COLONAST.spad" 178331 178339 178655 178660) (-155 "CMPLXRT.spad" 178040 178057 178321 178326) (-154 "CLLCTAST.spad" 177702 177710 178030 178035) (-153 "CLIP.spad" 173794 173802 177692 177697) (-152 "CLIF.spad" 172433 172449 173750 173789) (-151 "CLAGG.spad" 168918 168928 172423 172428) (-150 "CLAGG.spad" 165274 165286 168781 168786) (-149 "CINTSLPE.spad" 164599 164612 165264 165269) (-148 "CHVAR.spad" 162677 162699 164589 164594) (-147 "CHARZ.spad" 162592 162600 162657 162672) (-146 "CHARPOL.spad" 162100 162110 162582 162587) (-145 "CHARNZ.spad" 161853 161861 162080 162095) (-144 "CHAR.spad" 159721 159729 161843 161848) (-143 "CFCAT.spad" 159037 159045 159711 159716) (-142 "CDEN.spad" 158195 158209 159027 159032) (-141 "CCLASS.spad" 156344 156352 157606 157645) (-140 "CATEGORY.spad" 155434 155442 156334 156339) (-139 "CATCTOR.spad" 155325 155333 155424 155429) (-138 "CATAST.spad" 154943 154951 155315 155320) (-137 "CASEAST.spad" 154657 154665 154933 154938) (-136 "CARTEN.spad" 149760 149784 154647 154652) (-135 "CARTEN2.spad" 149146 149173 149750 149755) (-134 "CARD.spad" 146435 146443 149120 149141) (-133 "CAPSLAST.spad" 146209 146217 146425 146430) (-132 "CACHSET.spad" 145831 145839 146199 146204) (-131 "CABMON.spad" 145384 145392 145821 145826) (-130 "BYTEORD.spad" 145059 145067 145374 145379) (-129 "BYTE.spad" 144484 144492 145049 145054) (-128 "BYTEBUF.spad" 142341 142349 143653 143680) (-127 "BTREE.spad" 141410 141420 141948 141975) (-126 "BTOURN.spad" 140413 140423 141017 141044) (-125 "BTCAT.spad" 139801 139811 140381 140408) (-124 "BTCAT.spad" 139209 139221 139791 139796) (-123 "BTAGG.spad" 138331 138339 139177 139204) (-122 "BTAGG.spad" 137473 137483 138321 138326) (-121 "BSTREE.spad" 136208 136218 137080 137107) (-120 "BRILL.spad" 134403 134414 136198 136203) (-119 "BRAGG.spad" 133327 133337 134393 134398) (-118 "BRAGG.spad" 132215 132227 133283 133288) (-117 "BPADICRT.spad" 130196 130208 130451 130544) (-116 "BPADIC.spad" 129860 129872 130122 130191) (-115 "BOUNDZRO.spad" 129516 129533 129850 129855) (-114 "BOP.spad" 124640 124648 129506 129511) (-113 "BOP1.spad" 122060 122070 124630 124635) (-112 "BOOLEAN.spad" 121492 121500 122050 122055) (-111 "BMODULE.spad" 121204 121216 121460 121487) (-110 "BITS.spad" 120623 120631 120840 120867) (-109 "BINDING.spad" 120034 120042 120613 120618) (-108 "BINARY.spad" 118145 118153 118501 118594) (-107 "BGAGG.spad" 117342 117352 118125 118140) (-106 "BGAGG.spad" 116547 116559 117332 117337) (-105 "BFUNCT.spad" 116111 116119 116527 116542) (-104 "BEZOUT.spad" 115245 115272 116061 116066) (-103 "BBTREE.spad" 112064 112074 114852 114879) (-102 "BASTYPE.spad" 111736 111744 112054 112059) (-101 "BASTYPE.spad" 111406 111416 111726 111731) (-100 "BALFACT.spad" 110845 110858 111396 111401) (-99 "AUTOMOR.spad" 110292 110301 110825 110840) (-98 "ATTREG.spad" 107011 107018 110044 110287) (-97 "ATTRBUT.spad" 103034 103041 106991 107006) (-96 "ATTRAST.spad" 102751 102758 103024 103029) (-95 "ATRIG.spad" 102221 102228 102741 102746) (-94 "ATRIG.spad" 101689 101698 102211 102216) (-93 "ASTCAT.spad" 101593 101600 101679 101684) (-92 "ASTCAT.spad" 101495 101504 101583 101588) (-91 "ASTACK.spad" 100828 100837 101102 101129) (-90 "ASSOCEQ.spad" 99628 99639 100784 100789) (-89 "ASP9.spad" 98709 98722 99618 99623) (-88 "ASP8.spad" 97752 97765 98699 98704) (-87 "ASP80.spad" 97074 97087 97742 97747) (-86 "ASP7.spad" 96234 96247 97064 97069) (-85 "ASP78.spad" 95685 95698 96224 96229) (-84 "ASP77.spad" 95054 95067 95675 95680) (-83 "ASP74.spad" 94146 94159 95044 95049) (-82 "ASP73.spad" 93417 93430 94136 94141) (-81 "ASP6.spad" 92284 92297 93407 93412) (-80 "ASP55.spad" 90793 90806 92274 92279) (-79 "ASP50.spad" 88610 88623 90783 90788) (-78 "ASP4.spad" 87905 87918 88600 88605) (-77 "ASP49.spad" 86904 86917 87895 87900) (-76 "ASP42.spad" 85311 85350 86894 86899) (-75 "ASP41.spad" 83890 83929 85301 85306) (-74 "ASP35.spad" 82878 82891 83880 83885) (-73 "ASP34.spad" 82179 82192 82868 82873) (-72 "ASP33.spad" 81739 81752 82169 82174) (-71 "ASP31.spad" 80879 80892 81729 81734) (-70 "ASP30.spad" 79771 79784 80869 80874) (-69 "ASP29.spad" 79237 79250 79761 79766) (-68 "ASP28.spad" 70510 70523 79227 79232) (-67 "ASP27.spad" 69407 69420 70500 70505) (-66 "ASP24.spad" 68494 68507 69397 69402) (-65 "ASP20.spad" 67958 67971 68484 68489) (-64 "ASP1.spad" 67339 67352 67948 67953) (-63 "ASP19.spad" 62025 62038 67329 67334) (-62 "ASP12.spad" 61439 61452 62015 62020) (-61 "ASP10.spad" 60710 60723 61429 61434) (-60 "ARRAY2.spad" 60070 60079 60317 60344) (-59 "ARRAY1.spad" 58905 58914 59253 59280) (-58 "ARRAY12.spad" 57574 57585 58895 58900) (-57 "ARR2CAT.spad" 53236 53257 57542 57569) (-56 "ARR2CAT.spad" 48918 48941 53226 53231) (-55 "ARITY.spad" 48290 48297 48908 48913) (-54 "APPRULE.spad" 47534 47556 48280 48285) (-53 "APPLYORE.spad" 47149 47162 47524 47529) (-52 "ANY.spad" 45491 45498 47139 47144) (-51 "ANY1.spad" 44562 44571 45481 45486) (-50 "ANTISYM.spad" 43001 43017 44542 44557) (-49 "ANON.spad" 42694 42701 42991 42996) (-48 "AN.spad" 40995 41002 42510 42603) (-47 "AMR.spad" 39174 39185 40893 40990) (-46 "AMR.spad" 37190 37203 38911 38916) (-45 "ALIST.spad" 34602 34623 34952 34979) (-44 "ALGSC.spad" 33725 33751 34474 34527) (-43 "ALGPKG.spad" 29434 29445 33681 33686) (-42 "ALGMFACT.spad" 28623 28637 29424 29429) (-41 "ALGMANIP.spad" 26079 26094 28456 28461) (-40 "ALGFF.spad" 24394 24421 24611 24767) (-39 "ALGFACT.spad" 23515 23525 24384 24389) (-38 "ALGEBRA.spad" 23348 23357 23471 23510) (-37 "ALGEBRA.spad" 23213 23224 23338 23343) (-36 "ALAGG.spad" 22723 22744 23181 23208) (-35 "AHYP.spad" 22104 22111 22713 22718) (-34 "AGG.spad" 20413 20420 22094 22099) (-33 "AGG.spad" 18686 18695 20369 20374) (-32 "AF.spad" 17111 17126 18621 18626) (-31 "ADDAST.spad" 16789 16796 17101 17106) (-30 "ACPLOT.spad" 15360 15367 16779 16784) (-29 "ACFS.spad" 13111 13120 15262 15355) (-28 "ACFS.spad" 10948 10959 13101 13106) (-27 "ACF.spad" 7550 7557 10850 10943) (-26 "ACF.spad" 4238 4247 7540 7545) (-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
author	dos-reis <gdr@axiomatics.org>	2009-06-11 23:00:40 +0000
committer	dos-reis <gdr@axiomatics.org>	2009-06-11 23:00:40 +0000
commit	9e07dcd91c45bf8b22d932321f5c97e931ffe8ac (patch)
tree	6d2174e90e5779b1b3ab4ae7df3ae6603b66c6c2 /src/share/algebra/browse.daase
parent	7bd82b57975bbc1ff5b87fed0739815c620ecdcc (diff)
download	open-axiom-9e07dcd91c45bf8b22d932321f5c97e931ffe8ac.tar.gz