* algebra/dpolcat.spad.pamphlet (DifferentialVariableCategory):

Extend DifferentialSpace.
author: dos-reis <gdr@axiomatics.org> 2010-06-16 03:19:56 +0000
committer: dos-reis <gdr@axiomatics.org> 2010-06-16 03:19:56 +0000
commit: 2bbc83eac50582a5ffab2860f4279aac28f9c429 (patch)
tree: b52e3554cb835b9bdea7b380c054283a0d1b3247 /src/share/algebra/browse.daase
parent: 5da51971d3bd899bb327021730a528de9107329d (diff)
download: open-axiom-2bbc83eac50582a5ffab2860f4279aac28f9c429.tar.gz
1 files changed, 57 insertions, 57 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 53ab59f1..85de97e3 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2268331 . 3485633349)       
+(2267929 . 3485644666)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
@@ -88,7 +88,7 @@ NIL
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -1386 UP UPUP -3201) 
+(-40 -1386 UP UPUP -2089) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4449 |has| (-417 |#2|) (-372)) (-4454 |has| (-417 |#2|) (-372)) (-4448 |has| (-417 |#2|) (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
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@@ -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."))) 
 ((-4456 . T) (-4457 . T)) 
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+((-2818 (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|))))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|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 
@@ -472,11 +472,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
 (((-4458 "*") . T)) 
 NIL 
-(-136 |minix| -4129 S T$) 
+(-136 |minix| -4132 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -4129 R) 
+(-137 |minix| -4132 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $) "\\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 
@@ -900,19 +900,19 @@ 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 
-(-243 S -4129 R) 
+(-243 S -4132 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 (-372))) (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-858))) (|HasAttribute| |#3| (QUOTE -4453)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (QUOTE (-1113)))) 
-(-244 -4129 R) 
+(-244 -4132 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"))) 
 ((-4450 |has| |#2| (-1062)) (-4451 |has| |#2| (-1062)) (-4453 |has| |#2| (-6 -4453)) ((-4458 "*") |has| |#2| (-174)) (-4456 . T)) 
 NIL 
-(-245 -4129 A B) 
+(-245 -4132 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 
-(-246 -4129 R) 
+(-246 -4132 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."))) 
 ((-4450 |has| |#2| (-1062)) (-4451 |has| |#2| (-1062)) (-4453 |has| |#2| (-6 -4453)) ((-4458 "*") |has| |#2| (-174)) (-4456 . T)) 
 ((-2818 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-372))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372)))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-803))) (-2818 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-736))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1062)))) (|HasCategory| |#2| (QUOTE (-377))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-239)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-377)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-736)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-803)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113))))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-2818 (|HasCategory| |#2| (QUOTE (-1062))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) 
@@ -958,11 +958,11 @@ NIL
 NIL 
 (-257 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4453 -2818 (-2088 (|has| |#4| (-1062)) (|has| |#4| (-239))) (|has| |#4| (-6 -4453)) (-2088 (|has| |#4| (-1062)) (|has| |#4| (-911 (-1190))))) (-4450 |has| |#4| (-1062)) (-4451 |has| |#4| (-1062)) ((-4458 "*") |has| |#4| (-174)) (-4456 . T)) 
+((-4453 -2818 (-2087 (|has| |#4| (-1062)) (|has| |#4| (-239))) (|has| |#4| (-6 -4453)) (-2087 (|has| |#4| (-1062)) (|has| |#4| (-911 (-1190))))) (-4450 |has| |#4| (-1062)) (-4451 |has| |#4| (-1062)) ((-4458 "*") |has| |#4| (-174)) (-4456 . T)) 
 ((-2818 (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-736))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-803))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-858))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#4| (QUOTE (-372))) (-2818 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (QUOTE (-1062)))) (-2818 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-372)))) (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-803))) (-2818 (|HasCategory| |#4| (QUOTE (-803))) (|HasCategory| |#4| (QUOTE (-858)))) (|HasCategory| |#4| (QUOTE (-858))) (|HasCategory| |#4| (QUOTE (-736))) (-2818 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-1062)))) (|HasCategory| |#4| (QUOTE (-377))) (-2818 (-12 (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-858))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574)))))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1062)))) (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-174)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-239)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-372)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-377)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-736)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-803)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-858)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-1062)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-1113))))) (-2818 (-12 (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-736))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-803))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-858))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-1062))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-736))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-803))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-858))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1062)))) (-2818 (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1062)))) (|HasCategory| |#4| (QUOTE (-736))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574))))) (-2818 (|HasCategory| |#4| (QUOTE (-1062))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (QUOTE (-1113)))) (-2818 (|HasAttribute| |#4| (QUOTE -4453)) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (QUOTE (-1062)))) (-12 (|HasCategory| |#4| (QUOTE (-1062))) (|HasCategory| |#4| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#4| (QUOTE (-132))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|))))) 
 (-258 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
-((-4453 -2818 (-2088 (|has| |#3| (-1062)) (|has| |#3| (-239))) (|has| |#3| (-6 -4453)) (-2088 (|has| |#3| (-1062)) (|has| |#3| (-911 (-1190))))) (-4450 |has| |#3| (-1062)) (-4451 |has| |#3| (-1062)) ((-4458 "*") |has| |#3| (-174)) (-4456 . T)) 
+((-4453 -2818 (-2087 (|has| |#3| (-1062)) (|has| |#3| (-239))) (|has| |#3| (-6 -4453)) (-2087 (|has| |#3| (-1062)) (|has| |#3| (-911 (-1190))))) (-4450 |has| |#3| (-1062)) (-4451 |has| |#3| (-1062)) ((-4458 "*") |has| |#3| (-174)) (-4456 . T)) 
 ((-2818 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#3| (QUOTE (-372))) (-2818 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-1062)))) (-2818 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372)))) (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-803))) (-2818 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-858)))) (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (QUOTE (-736))) (-2818 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1062)))) (|HasCategory| |#3| (QUOTE (-377))) (-2818 (-12 (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574)))))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1062)))) (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-239)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-372)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-377)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-736)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-803)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-858)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1062)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1113))))) (-2818 (-12 (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1062))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1062)))) (-2818 (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1062)))) (|HasCategory| |#3| (QUOTE (-736))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-2818 (|HasCategory| |#3| (QUOTE (-1062))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1113)))) (-2818 (|HasAttribute| |#3| (QUOTE -4453)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1062)))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) 
 (-259 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."))) 
@@ -1017,11 +1017,11 @@ NIL
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-920))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-272 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."))) 
+((|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}.")) (|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 
 NIL 
 (-273 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| (($ |#1|) "\\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| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
+((|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| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
 NIL 
 (-274) 
@@ -1116,7 +1116,7 @@ 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 
-(-297 S R |Mod| -2348 -2130 |exactQuo|) 
+(-297 S R |Mod| -2666 -4430 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
@@ -1143,7 +1143,7 @@ NIL
 (-303 |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."))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-304) 
 ((|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 
@@ -1239,7 +1239,7 @@ NIL
 (-327 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."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-328 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 
@@ -1560,7 +1560,7 @@ 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 
-(-408 -2032 |returnType| -1565 |symbols|) 
+(-408 -2032 |returnType| -1564 |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 
@@ -1867,11 +1867,11 @@ NIL
 (-484 |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."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-485 |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."))) 
 ((-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113)))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113)))) 
 (-486 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)}"))) 
 ((-4457 . T) (-4456 . T)) 
@@ -1887,7 +1887,7 @@ NIL
 (-489 |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."))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-490) 
 ((|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 
@@ -1896,7 +1896,7 @@ NIL
 ((|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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 ((|HasCategory| |#2| (QUOTE (-920))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4454)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-492 -4129 S) 
+(-492 -4132 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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-317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-372))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) 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(|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-239)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-377)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-736)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) 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(LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1062))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-2818 (|HasCategory| |#2| (QUOTE (-1062))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) 
@@ -2171,7 +2171,7 @@ NIL
 (-560 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-561 R -1386) 
 ((|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 
@@ -2398,12 +2398,12 @@ NIL
 NIL 
 (-617 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)."))) 
-((-4453 -2818 (-2088 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
+((-4453 -2818 (-2087 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
 ((-2818 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
 (-618 |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."))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-619 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 
@@ -2499,7 +2499,7 @@ NIL
 (-642) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1172) (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113)))) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1908) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1172) (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 (-52))) (QUOTE (-1113)))) 
 (-643 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2510,7 +2510,7 @@ NIL
 NIL 
 (-645 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4453 -2818 (-2088 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
+((-4453 -2818 (-2087 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
 ((-2818 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
 (-646 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))}."))) 
@@ -2523,7 +2523,7 @@ NIL
 (-648 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 
-((-2077 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) 
+((-2076 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) 
 (-649 R) 
 ((|constructor| (NIL "An extension of left-module 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}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
@@ -2600,7 +2600,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-668 A -3000) 
+(-668 A -2727) 
 ((|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}}"))) 
 ((-4450 . T) (-4451 . T) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
@@ -2792,7 +2792,7 @@ 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 
-(-716 S -3611 I) 
+(-716 S -3610 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 
@@ -2812,7 +2812,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-721 R |Mod| -2348 -2130 |exactQuo|) 
+(-721 R |Mod| -2666 -4430 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
@@ -2828,7 +2828,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-725 R |Mod| -2348 -2130 |exactQuo|) 
+(-725 R |Mod| -2666 -4430 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
 ((-4453 . T)) 
 NIL 
@@ -3091,7 +3091,7 @@ NIL
 (-790 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."))) 
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 (-791 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 
@@ -3228,7 +3228,7 @@ NIL
 ((|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(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(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 
-(-825 -4129 S |f|) 
+(-825 -4132 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}."))) 
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@@ -3348,7 +3348,7 @@ NIL
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-855 -4129 S) 
+(-855 -4132 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 
@@ -3384,11 +3384,11 @@ 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 (-372))) (|HasCategory| |#1| (QUOTE (-566)))) 
-(-864 R |sigma| -2076) 
+(-864 R |sigma| -2075) 
 ((|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."))) 
 ((-4450 . T) (-4451 . T) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
-(-865 |x| R |sigma| -2076) 
+(-865 |x| R |sigma| -2075) 
 ((|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}."))) 
 ((-4450 . T) (-4451 . T) (-4453 . T)) 
 ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-372)))) 
@@ -3523,7 +3523,7 @@ NIL
 (-898 |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 (-2077 (|HasCategory| |#2| (QUOTE (-1062)))) (-2077 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (-2077 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190))))) 
+((-12 (-2076 (|HasCategory| |#2| (QUOTE (-1062)))) (-2076 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (-2076 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190))))) 
 (-899 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 
@@ -3532,7 +3532,7 @@ 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 
-(-901 R -3611) 
+(-901 R -3610) 
 ((|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 
@@ -3720,11 +3720,11 @@ 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 -897) (|devaluate| |#1|)))) 
-(-948 R -1386 -3611) 
+(-948 R -1386 -3610) 
 ((|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 
-(-949 -3611) 
+(-949 -3610) 
 ((|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 
@@ -4123,7 +4123,7 @@ NIL
 (-1048) 
 ((|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.}"))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1908) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1049) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4235,7 +4235,7 @@ NIL
 (-1076) 
 ((|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}"))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1908) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1908 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1077 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 
@@ -4583,7 +4583,7 @@ NIL
 (-1163 |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."))) 
 ((-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113)))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113)))) 
 (-1164) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
@@ -4623,7 +4623,7 @@ NIL
 (-1173 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#1|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#1|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1908 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1174 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
@@ -4654,8 +4654,8 @@ NIL
 NIL 
 (-1181 |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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 ((|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 
@@ -4679,11 +4679,11 @@ NIL
 (-1187 |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}."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-1188 |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}."))) 
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-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-1189) 
 ((|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 
@@ -4743,7 +4743,7 @@ NIL
 (-1203 |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}"))) 
 ((-4456 . T) (-4457 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1908) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1908 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1204 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
@@ -4907,11 +4907,11 @@ NIL
 (-1244 |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)}."))) 
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 ((|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 
@@ -4991,11 +4991,11 @@ NIL
 (-1265 |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)}."))) 
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-((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
 (-1266 |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}."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-1267 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
 (((-4458 "*") |has| (-1266 |#2| |#3| |#4|) (-174)) (-4449 |has| (-1266 |#2| |#3| |#4|) (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
@@ -5015,7 +5015,7 @@ NIL
 (-1271 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-574)))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-1216))) (|HasSignature| |#2| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2968) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1190))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-1216))) (|HasSignature| |#2| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2379) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1190))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) 
 (-1272 |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."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
@@ -5023,7 +5023,7 @@ NIL
 (-1273 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
 (((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2379) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
 (-1274 |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 
@@ -5188,4 +5188,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2268311 2268316 2268321 2268326) (-2 NIL 2268291 2268296 2268301 2268306) (-1 NIL 2268271 2268276 2268281 2268286) (0 NIL 2268251 2268256 2268261 2268266) (-1310 "ZMOD.spad" 2268060 2268073 2268189 2268246) (-1309 "ZLINDEP.spad" 2267126 2267137 2268050 2268055) (-1308 "ZDSOLVE.spad" 2257071 2257093 2267116 2267121) (-1307 "YSTREAM.spad" 2256566 2256577 2257061 2257066) (-1306 "YDIAGRAM.spad" 2256200 2256209 2256556 2256561) (-1305 "XRPOLY.spad" 2255420 2255440 2256056 2256125) (-1304 "XPR.spad" 2253215 2253228 2255138 2255237) (-1303 "XPOLY.spad" 2252770 2252781 2253071 2253140) (-1302 "XPOLYC.spad" 2252089 2252105 2252696 2252765) (-1301 "XPBWPOLY.spad" 2250526 2250546 2251869 2251938) (-1300 "XF.spad" 2248989 2249004 2250428 2250521) (-1299 "XF.spad" 2247432 2247449 2248873 2248878) (-1298 "XFALG.spad" 2244480 2244496 2247358 2247427) (-1297 "XEXPPKG.spad" 2243731 2243757 2244470 2244475) (-1296 "XDPOLY.spad" 2243345 2243361 2243587 2243656) (-1295 "XALG.spad" 2243005 2243016 2243301 2243340) (-1294 "WUTSET.spad" 2238844 2238861 2242651 2242678) (-1293 "WP.spad" 2238043 2238087 2238702 2238769) (-1292 "WHILEAST.spad" 2237841 2237850 2238033 2238038) (-1291 "WHEREAST.spad" 2237512 2237521 2237831 2237836) (-1290 "WFFINTBS.spad" 2235175 2235197 2237502 2237507) (-1289 "WEIER.spad" 2233397 2233408 2235165 2235170) (-1288 "VSPACE.spad" 2233070 2233081 2233365 2233392) (-1287 "VSPACE.spad" 2232763 2232776 2233060 2233065) (-1286 "VOID.spad" 2232440 2232449 2232753 2232758) (-1285 "VIEW.spad" 2230120 2230129 2232430 2232435) (-1284 "VIEWDEF.spad" 2225321 2225330 2230110 2230115) (-1283 "VIEW3D.spad" 2209282 2209291 2225311 2225316) (-1282 "VIEW2D.spad" 2197173 2197182 2209272 2209277) (-1281 "VECTOR.spad" 2195847 2195858 2196098 2196125) (-1280 "VECTOR2.spad" 2194486 2194499 2195837 2195842) (-1279 "VECTCAT.spad" 2192390 2192401 2194454 2194481) (-1278 "VECTCAT.spad" 2190101 2190114 2192167 2192172) (-1277 "VARIABLE.spad" 2189881 2189896 2190091 2190096) (-1276 "UTYPE.spad" 2189525 2189534 2189871 2189876) (-1275 "UTSODETL.spad" 2188820 2188844 2189481 2189486) (-1274 "UTSODE.spad" 2187036 2187056 2188810 2188815) (-1273 "UTS.spad" 2181840 2181868 2185503 2185600) (-1272 "UTSCAT.spad" 2179319 2179335 2181738 2181835) (-1271 "UTSCAT.spad" 2176442 2176460 2178863 2178868) (-1270 "UTS2.spad" 2176037 2176072 2176432 2176437) (-1269 "URAGG.spad" 2170710 2170721 2176027 2176032) (-1268 "URAGG.spad" 2165347 2165360 2170666 2170671) (-1267 "UPXSSING.spad" 2162992 2163018 2164428 2164561) (-1266 "UPXS.spad" 2160146 2160174 2161124 2161273) (-1265 "UPXSCONS.spad" 2157905 2157925 2158278 2158427) (-1264 "UPXSCCA.spad" 2156476 2156496 2157751 2157900) (-1263 "UPXSCCA.spad" 2155189 2155211 2156466 2156471) (-1262 "UPXSCAT.spad" 2153778 2153794 2155035 2155184) (-1261 "UPXS2.spad" 2153321 2153374 2153768 2153773) (-1260 "UPSQFREE.spad" 2151735 2151749 2153311 2153316) (-1259 "UPSCAT.spad" 2149522 2149546 2151633 2151730) (-1258 "UPSCAT.spad" 2147015 2147041 2149128 2149133) (-1257 "UPOLYC.spad" 2142055 2142066 2146857 2147010) (-1256 "UPOLYC.spad" 2136987 2137000 2141791 2141796) (-1255 "UPOLYC2.spad" 2136458 2136477 2136977 2136982) (-1254 "UP.spad" 2133657 2133672 2134044 2134197) (-1253 "UPMP.spad" 2132557 2132570 2133647 2133652) (-1252 "UPDIVP.spad" 2132122 2132136 2132547 2132552) (-1251 "UPDECOMP.spad" 2130367 2130381 2132112 2132117) (-1250 "UPCDEN.spad" 2129576 2129592 2130357 2130362) (-1249 "UP2.spad" 2128940 2128961 2129566 2129571) (-1248 "UNISEG.spad" 2128293 2128304 2128859 2128864) (-1247 "UNISEG2.spad" 2127790 2127803 2128249 2128254) (-1246 "UNIFACT.spad" 2126893 2126905 2127780 2127785) (-1245 "ULS.spad" 2117451 2117479 2118538 2118967) (-1244 "ULSCONS.spad" 2109847 2109867 2110217 2110366) (-1243 "ULSCCAT.spad" 2107584 2107604 2109693 2109842) (-1242 "ULSCCAT.spad" 2105429 2105451 2107540 2107545) (-1241 "ULSCAT.spad" 2103661 2103677 2105275 2105424) (-1240 "ULS2.spad" 2103175 2103228 2103651 2103656) (-1239 "UINT8.spad" 2103052 2103061 2103165 2103170) (-1238 "UINT64.spad" 2102928 2102937 2103042 2103047) (-1237 "UINT32.spad" 2102804 2102813 2102918 2102923) (-1236 "UINT16.spad" 2102680 2102689 2102794 2102799) (-1235 "UFD.spad" 2101745 2101754 2102606 2102675) (-1234 "UFD.spad" 2100872 2100883 2101735 2101740) (-1233 "UDVO.spad" 2099753 2099762 2100862 2100867) (-1232 "UDPO.spad" 2097246 2097257 2099709 2099714) (-1231 "TYPE.spad" 2097178 2097187 2097236 2097241) (-1230 "TYPEAST.spad" 2097097 2097106 2097168 2097173) (-1229 "TWOFACT.spad" 2095749 2095764 2097087 2097092) (-1228 "TUPLE.spad" 2095235 2095246 2095648 2095653) (-1227 "TUBETOOL.spad" 2092102 2092111 2095225 2095230) (-1226 "TUBE.spad" 2090749 2090766 2092092 2092097) (-1225 "TS.spad" 2089348 2089364 2090314 2090411) (-1224 "TSETCAT.spad" 2076475 2076492 2089316 2089343) (-1223 "TSETCAT.spad" 2063588 2063607 2076431 2076436) (-1222 "TRMANIP.spad" 2057954 2057971 2063294 2063299) (-1221 "TRIMAT.spad" 2056917 2056942 2057944 2057949) (-1220 "TRIGMNIP.spad" 2055444 2055461 2056907 2056912) (-1219 "TRIGCAT.spad" 2054956 2054965 2055434 2055439) (-1218 "TRIGCAT.spad" 2054466 2054477 2054946 2054951) (-1217 "TREE.spad" 2053041 2053052 2054073 2054100) (-1216 "TRANFUN.spad" 2052880 2052889 2053031 2053036) (-1215 "TRANFUN.spad" 2052717 2052728 2052870 2052875) (-1214 "TOPSP.spad" 2052391 2052400 2052707 2052712) (-1213 "TOOLSIGN.spad" 2052054 2052065 2052381 2052386) (-1212 "TEXTFILE.spad" 2050615 2050624 2052044 2052049) (-1211 "TEX.spad" 2047761 2047770 2050605 2050610) (-1210 "TEX1.spad" 2047317 2047328 2047751 2047756) (-1209 "TEMUTL.spad" 2046872 2046881 2047307 2047312) (-1208 "TBCMPPK.spad" 2044965 2044988 2046862 2046867) (-1207 "TBAGG.spad" 2044015 2044038 2044945 2044960) (-1206 "TBAGG.spad" 2043073 2043098 2044005 2044010) (-1205 "TANEXP.spad" 2042481 2042492 2043063 2043068) (-1204 "TALGOP.spad" 2042205 2042216 2042471 2042476) (-1203 "TABLE.spad" 2040616 2040639 2040886 2040913) (-1202 "TABLEAU.spad" 2040097 2040108 2040606 2040611) (-1201 "TABLBUMP.spad" 2036900 2036911 2040087 2040092) (-1200 "SYSTEM.spad" 2036128 2036137 2036890 2036895) (-1199 "SYSSOLP.spad" 2033611 2033622 2036118 2036123) (-1198 "SYSPTR.spad" 2033510 2033519 2033601 2033606) (-1197 "SYSNNI.spad" 2032692 2032703 2033500 2033505) (-1196 "SYSINT.spad" 2032096 2032107 2032682 2032687) (-1195 "SYNTAX.spad" 2028302 2028311 2032086 2032091) (-1194 "SYMTAB.spad" 2026370 2026379 2028292 2028297) (-1193 "SYMS.spad" 2022393 2022402 2026360 2026365) (-1192 "SYMPOLY.spad" 2021400 2021411 2021482 2021609) (-1191 "SYMFUNC.spad" 2020901 2020912 2021390 2021395) (-1190 "SYMBOL.spad" 2018404 2018413 2020891 2020896) (-1189 "SWITCH.spad" 2015175 2015184 2018394 2018399) (-1188 "SUTS.spad" 2012080 2012108 2013642 2013739) (-1187 "SUPXS.spad" 2009221 2009249 2010212 2010361) (-1186 "SUP.spad" 2006034 2006045 2006807 2006960) (-1185 "SUPFRACF.spad" 2005139 2005157 2006024 2006029) (-1184 "SUP2.spad" 2004531 2004544 2005129 2005134) (-1183 "SUMRF.spad" 2003505 2003516 2004521 2004526) (-1182 "SUMFS.spad" 2003142 2003159 2003495 2003500) (-1181 "SULS.spad" 1993687 1993715 1994787 1995216) (-1180 "SUCHTAST.spad" 1993456 1993465 1993677 1993682) (-1179 "SUCH.spad" 1993138 1993153 1993446 1993451) (-1178 "SUBSPACE.spad" 1985253 1985268 1993128 1993133) (-1177 "SUBRESP.spad" 1984423 1984437 1985209 1985214) (-1176 "STTF.spad" 1980522 1980538 1984413 1984418) (-1175 "STTFNC.spad" 1976990 1977006 1980512 1980517) (-1174 "STTAYLOR.spad" 1969625 1969636 1976871 1976876) (-1173 "STRTBL.spad" 1968130 1968147 1968279 1968306) (-1172 "STRING.spad" 1967539 1967548 1967553 1967580) (-1171 "STRICAT.spad" 1967327 1967336 1967507 1967534) (-1170 "STREAM.spad" 1964245 1964256 1966852 1966867) (-1169 "STREAM3.spad" 1963818 1963833 1964235 1964240) (-1168 "STREAM2.spad" 1962946 1962959 1963808 1963813) (-1167 "STREAM1.spad" 1962652 1962663 1962936 1962941) (-1166 "STINPROD.spad" 1961588 1961604 1962642 1962647) (-1165 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(-1054 "RFFACT.spad" 1719952 1719964 1720207 1720212) (-1053 "RFDIST.spad" 1718948 1718957 1719942 1719947) (-1052 "RETSOL.spad" 1718367 1718380 1718938 1718943) (-1051 "RETRACT.spad" 1717795 1717806 1718357 1718362) (-1050 "RETRACT.spad" 1717221 1717234 1717785 1717790) (-1049 "RETAST.spad" 1717033 1717042 1717211 1717216) (-1048 "RESULT.spad" 1715093 1715102 1715680 1715707) (-1047 "RESRING.spad" 1714440 1714487 1715031 1715088) (-1046 "RESLATC.spad" 1713764 1713775 1714430 1714435) (-1045 "REPSQ.spad" 1713495 1713506 1713754 1713759) (-1044 "REP.spad" 1711049 1711058 1713485 1713490) (-1043 "REPDB.spad" 1710756 1710767 1711039 1711044) (-1042 "REP2.spad" 1700414 1700425 1710598 1710603) (-1041 "REP1.spad" 1694610 1694621 1700364 1700369) (-1040 "REGSET.spad" 1692407 1692424 1694256 1694283) (-1039 "REF.spad" 1691742 1691753 1692362 1692367) (-1038 "REDORDER.spad" 1690948 1690965 1691732 1691737) (-1037 "RECLOS.spad" 1689731 1689751 1690435 1690528) (-1036 "REALSOLV.spad" 1688871 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1561848) (-961 "POLYCATQ.spad" 1559236 1559258 1561108 1561113) (-960 "POLYCAT.spad" 1552706 1552727 1559104 1559231) (-959 "POLYCAT.spad" 1545514 1545537 1551914 1551919) (-958 "POLY2UP.spad" 1544966 1544980 1545504 1545509) (-957 "POLY2.spad" 1544563 1544575 1544956 1544961) (-956 "POLUTIL.spad" 1543504 1543533 1544519 1544524) (-955 "POLTOPOL.spad" 1542252 1542267 1543494 1543499) (-954 "POINT.spad" 1541090 1541100 1541177 1541204) (-953 "PNTHEORY.spad" 1537792 1537800 1541080 1541085) (-952 "PMTOOLS.spad" 1536567 1536581 1537782 1537787) (-951 "PMSYM.spad" 1536116 1536126 1536557 1536562) (-950 "PMQFCAT.spad" 1535707 1535721 1536106 1536111) (-949 "PMPRED.spad" 1535186 1535200 1535697 1535702) (-948 "PMPREDFS.spad" 1534640 1534662 1535176 1535181) (-947 "PMPLCAT.spad" 1533720 1533738 1534572 1534577) (-946 "PMLSAGG.spad" 1533305 1533319 1533710 1533715) (-945 "PMKERNEL.spad" 1532884 1532896 1533295 1533300) (-944 "PMINS.spad" 1532464 1532474 1532874 1532879) (-943 "PMFS.spad" 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1433265) (-886 "PARAMAST.spad" 1432189 1432197 1433051 1433056) (-885 "PAN2EXPR.spad" 1431601 1431609 1432179 1432184) (-884 "PALETTE.spad" 1430571 1430579 1431591 1431596) (-883 "PAIR.spad" 1429558 1429571 1430159 1430164) (-882 "PADICRC.spad" 1426892 1426910 1428063 1428156) (-881 "PADICRAT.spad" 1424907 1424919 1425128 1425221) (-880 "PADIC.spad" 1424602 1424614 1424833 1424902) (-879 "PADICCT.spad" 1423151 1423163 1424528 1424597) (-878 "PADEPAC.spad" 1421840 1421859 1423141 1423146) (-877 "PADE.spad" 1420592 1420608 1421830 1421835) (-876 "OWP.spad" 1419832 1419862 1420450 1420517) (-875 "OVERSET.spad" 1419405 1419413 1419822 1419827) (-874 "OVAR.spad" 1419186 1419209 1419395 1419400) (-873 "OUT.spad" 1418272 1418280 1419176 1419181) (-872 "OUTFORM.spad" 1407664 1407672 1418262 1418267) (-871 "OUTBFILE.spad" 1407082 1407090 1407654 1407659) (-870 "OUTBCON.spad" 1406088 1406096 1407072 1407077) (-869 "OUTBCON.spad" 1405092 1405102 1406078 1406083) (-868 "OSI.spad" 1404567 1404575 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"OPTCAT.spad" 1370186 1370194 1372497 1372502) (-848 "OPSIG.spad" 1369840 1369848 1370176 1370181) (-847 "OPQUERY.spad" 1369389 1369397 1369830 1369835) (-846 "OP.spad" 1369131 1369141 1369211 1369278) (-845 "OPERCAT.spad" 1368597 1368607 1369121 1369126) (-844 "OPERCAT.spad" 1368061 1368073 1368587 1368592) (-843 "ONECOMP.spad" 1366806 1366816 1367608 1367637) (-842 "ONECOMP2.spad" 1366230 1366242 1366796 1366801) (-841 "OMSERVER.spad" 1365236 1365244 1366220 1366225) (-840 "OMSAGG.spad" 1365024 1365034 1365192 1365231) (-839 "OMPKG.spad" 1363640 1363648 1365014 1365019) (-838 "OM.spad" 1362613 1362621 1363630 1363635) (-837 "OMLO.spad" 1362038 1362050 1362499 1362538) (-836 "OMEXPR.spad" 1361872 1361882 1362028 1362033) (-835 "OMERR.spad" 1361417 1361425 1361862 1361867) (-834 "OMERRK.spad" 1360451 1360459 1361407 1361412) (-833 "OMENC.spad" 1359795 1359803 1360441 1360446) (-832 "OMDEV.spad" 1354104 1354112 1359785 1359790) (-831 "OMCONN.spad" 1353513 1353521 1354094 1354099) (-830 "OINTDOM.spad" 1353276 1353284 1353439 1353508) (-829 "OFMONOID.spad" 1351399 1351409 1353232 1353237) (-828 "ODVAR.spad" 1350660 1350670 1351389 1351394) (-827 "ODR.spad" 1350304 1350330 1350472 1350621) (-826 "ODPOL.spad" 1347686 1347696 1348026 1348153) (-825 "ODP.spad" 1337456 1337476 1337829 1337960) (-824 "ODETOOLS.spad" 1336105 1336124 1337446 1337451) (-823 "ODESYS.spad" 1333799 1333816 1336095 1336100) (-822 "ODERTRIC.spad" 1329808 1329825 1333756 1333761) (-821 "ODERED.spad" 1329207 1329231 1329798 1329803) (-820 "ODERAT.spad" 1326822 1326839 1329197 1329202) (-819 "ODEPRRIC.spad" 1323859 1323881 1326812 1326817) (-818 "ODEPROB.spad" 1323116 1323124 1323849 1323854) (-817 "ODEPRIM.spad" 1320450 1320472 1323106 1323111) (-816 "ODEPAL.spad" 1319836 1319860 1320440 1320445) (-815 "ODEPACK.spad" 1306502 1306510 1319826 1319831) (-814 "ODEINT.spad" 1305937 1305953 1306492 1306497) (-813 "ODEIFTBL.spad" 1303332 1303340 1305927 1305932) (-812 "ODEEF.spad" 1298823 1298839 1303322 1303327) (-811 "ODECONST.spad" 1298360 1298378 1298813 1298818) (-810 "ODECAT.spad" 1296958 1296966 1298350 1298355) (-809 "OCT.spad" 1295094 1295104 1295808 1295847) (-808 "OCTCT2.spad" 1294740 1294761 1295084 1295089) (-807 "OC.spad" 1292536 1292546 1294696 1294735) (-806 "OC.spad" 1290057 1290069 1292219 1292224) (-805 "OCAMON.spad" 1289905 1289913 1290047 1290052) (-804 "OASGP.spad" 1289720 1289728 1289895 1289900) (-803 "OAMONS.spad" 1289242 1289250 1289710 1289715) (-802 "OAMON.spad" 1289103 1289111 1289232 1289237) (-801 "OAGROUP.spad" 1288965 1288973 1289093 1289098) (-800 "NUMTUBE.spad" 1288556 1288572 1288955 1288960) (-799 "NUMQUAD.spad" 1276532 1276540 1288546 1288551) (-798 "NUMODE.spad" 1267886 1267894 1276522 1276527) (-797 "NUMINT.spad" 1265452 1265460 1267876 1267881) (-796 "NUMFMT.spad" 1264292 1264300 1265442 1265447) (-795 "NUMERIC.spad" 1256406 1256416 1264097 1264102) (-794 "NTSCAT.spad" 1254914 1254930 1256374 1256401) (-793 "NTPOLFN.spad" 1254465 1254475 1254831 1254836) (-792 "NSUP.spad" 1247511 1247521 1252051 1252204) (-791 "NSUP2.spad" 1246903 1246915 1247501 1247506) (-790 "NSMP.spad" 1243133 1243152 1243441 1243568) (-789 "NREP.spad" 1241511 1241525 1243123 1243128) (-788 "NPCOEF.spad" 1240757 1240777 1241501 1241506) (-787 "NORMRETR.spad" 1240355 1240394 1240747 1240752) (-786 "NORMPK.spad" 1238257 1238276 1240345 1240350) (-785 "NORMMA.spad" 1237945 1237971 1238247 1238252) (-784 "NONE.spad" 1237686 1237694 1237935 1237940) (-783 "NONE1.spad" 1237362 1237372 1237676 1237681) (-782 "NODE1.spad" 1236849 1236865 1237352 1237357) (-781 "NNI.spad" 1235744 1235752 1236823 1236844) (-780 "NLINSOL.spad" 1234370 1234380 1235734 1235739) (-779 "NIPROB.spad" 1232911 1232919 1234360 1234365) (-778 "NFINTBAS.spad" 1230471 1230488 1232901 1232906) (-777 "NETCLT.spad" 1230445 1230456 1230461 1230466) (-776 "NCODIV.spad" 1228661 1228677 1230435 1230440) (-775 "NCNTFRAC.spad" 1228303 1228317 1228651 1228656) (-774 "NCEP.spad" 1226469 1226483 1228293 1228298) (-773 "NASRING.spad" 1226065 1226073 1226459 1226464) (-772 "NASRING.spad" 1225659 1225669 1226055 1226060) (-771 "NARNG.spad" 1225011 1225019 1225649 1225654) (-770 "NARNG.spad" 1224361 1224371 1225001 1225006) (-769 "NAGSP.spad" 1223438 1223446 1224351 1224356) (-768 "NAGS.spad" 1213099 1213107 1223428 1223433) (-767 "NAGF07.spad" 1211530 1211538 1213089 1213094) (-766 "NAGF04.spad" 1205932 1205940 1211520 1211525) (-765 "NAGF02.spad" 1200001 1200009 1205922 1205927) (-764 "NAGF01.spad" 1195762 1195770 1199991 1199996) (-763 "NAGE04.spad" 1189462 1189470 1195752 1195757) (-762 "NAGE02.spad" 1180122 1180130 1189452 1189457) (-761 "NAGE01.spad" 1176124 1176132 1180112 1180117) (-760 "NAGD03.spad" 1174128 1174136 1176114 1176119) (-759 "NAGD02.spad" 1166875 1166883 1174118 1174123) (-758 "NAGD01.spad" 1161168 1161176 1166865 1166870) (-757 "NAGC06.spad" 1157043 1157051 1161158 1161163) (-756 "NAGC05.spad" 1155544 1155552 1157033 1157038) (-755 "NAGC02.spad" 1154811 1154819 1155534 1155539) (-754 "NAALG.spad" 1154352 1154362 1154779 1154806) (-753 "NAALG.spad" 1153913 1153925 1154342 1154347) (-752 "MULTSQFR.spad" 1150871 1150888 1153903 1153908) (-751 "MULTFACT.spad" 1150254 1150271 1150861 1150866) (-750 "MTSCAT.spad" 1148348 1148369 1150152 1150249) (-749 "MTHING.spad" 1148007 1148017 1148338 1148343) (-748 "MSYSCMD.spad" 1147441 1147449 1147997 1148002) (-747 "MSET.spad" 1145399 1145409 1147147 1147186) (-746 "MSETAGG.spad" 1145244 1145254 1145367 1145394) (-745 "MRING.spad" 1142221 1142233 1144952 1145019) (-744 "MRF2.spad" 1141791 1141805 1142211 1142216) (-743 "MRATFAC.spad" 1141337 1141354 1141781 1141786) (-742 "MPRFF.spad" 1139377 1139396 1141327 1141332) (-741 "MPOLY.spad" 1136848 1136863 1137207 1137334) (-740 "MPCPF.spad" 1136112 1136131 1136838 1136843) (-739 "MPC3.spad" 1135929 1135969 1136102 1136107) (-738 "MPC2.spad" 1135575 1135608 1135919 1135924) (-737 "MONOTOOL.spad" 1133926 1133943 1135565 1135570) (-736 "MONOID.spad" 1133245 1133253 1133916 1133921) (-735 "MONOID.spad" 1132562 1132572 1133235 1133240) (-734 "MONOGEN.spad" 1131310 1131323 1132422 1132557) (-733 "MONOGEN.spad" 1130080 1130095 1131194 1131199) (-732 "MONADWU.spad" 1128110 1128118 1130070 1130075) (-731 "MONADWU.spad" 1126138 1126148 1128100 1128105) (-730 "MONAD.spad" 1125298 1125306 1126128 1126133) (-729 "MONAD.spad" 1124456 1124466 1125288 1125293) (-728 "MOEBIUS.spad" 1123192 1123206 1124436 1124451) (-727 "MODULE.spad" 1123062 1123072 1123160 1123187) (-726 "MODULE.spad" 1122952 1122964 1123052 1123057) (-725 "MODRING.spad" 1122287 1122326 1122932 1122947) (-724 "MODOP.spad" 1120952 1120964 1122109 1122176) (-723 "MODMONOM.spad" 1120683 1120701 1120942 1120947) (-722 "MODMON.spad" 1117478 1117494 1118197 1118350) (-721 "MODFIELD.spad" 1116840 1116879 1117380 1117473) (-720 "MMLFORM.spad" 1115700 1115708 1116830 1116835) (-719 "MMAP.spad" 1115442 1115476 1115690 1115695) (-718 "MLO.spad" 1113901 1113911 1115398 1115437) (-717 "MLIFT.spad" 1112513 1112530 1113891 1113896) (-716 "MKUCFUNC.spad" 1112048 1112066 1112503 1112508) (-715 "MKRECORD.spad" 1111652 1111665 1112038 1112043) (-714 "MKFUNC.spad" 1111059 1111069 1111642 1111647) (-713 "MKFLCFN.spad" 1110027 1110037 1111049 1111054) (-712 "MKBCFUNC.spad" 1109522 1109540 1110017 1110022) (-711 "MINT.spad" 1108961 1108969 1109424 1109517) (-710 "MHROWRED.spad" 1107472 1107482 1108951 1108956) (-709 "MFLOAT.spad" 1105992 1106000 1107362 1107467) (-708 "MFINFACT.spad" 1105392 1105414 1105982 1105987) (-707 "MESH.spad" 1103174 1103182 1105382 1105387) (-706 "MDDFACT.spad" 1101385 1101395 1103164 1103169) (-705 "MDAGG.spad" 1100676 1100686 1101365 1101380) (-704 "MCMPLX.spad" 1096687 1096695 1097301 1097502) (-703 "MCDEN.spad" 1095897 1095909 1096677 1096682) (-702 "MCALCFN.spad" 1093019 1093045 1095887 1095892) (-701 "MAYBE.spad" 1092303 1092314 1093009 1093014) (-700 "MATSTOR.spad" 1089611 1089621 1092293 1092298) (-699 "MATRIX.spad" 1088315 1088325 1088799 1088826) (-698 "MATLIN.spad" 1085659 1085683 1088199 1088204) (-697 "MATCAT.spad" 1077388 1077410 1085627 1085654) (-696 "MATCAT.spad" 1068989 1069013 1077230 1077235) (-695 "MATCAT2.spad" 1068271 1068319 1068979 1068984) (-694 "MAPPKG3.spad" 1067186 1067200 1068261 1068266) (-693 "MAPPKG2.spad" 1066524 1066536 1067176 1067181) (-692 "MAPPKG1.spad" 1065352 1065362 1066514 1066519) (-691 "MAPPAST.spad" 1064667 1064675 1065342 1065347) (-690 "MAPHACK3.spad" 1064479 1064493 1064657 1064662) (-689 "MAPHACK2.spad" 1064248 1064260 1064469 1064474) (-688 "MAPHACK1.spad" 1063892 1063902 1064238 1064243) (-687 "MAGMA.spad" 1061682 1061699 1063882 1063887) (-686 "MACROAST.spad" 1061261 1061269 1061672 1061677) (-685 "M3D.spad" 1058981 1058991 1060639 1060644) (-684 "LZSTAGG.spad" 1056219 1056229 1058971 1058976) (-683 "LZSTAGG.spad" 1053455 1053467 1056209 1056214) (-682 "LWORD.spad" 1050160 1050177 1053445 1053450) (-681 "LSTAST.spad" 1049944 1049952 1050150 1050155) (-680 "LSQM.spad" 1048230 1048244 1048624 1048675) (-679 "LSPP.spad" 1047765 1047782 1048220 1048225) (-678 "LSMP.spad" 1046615 1046643 1047755 1047760) (-677 "LSMP1.spad" 1044433 1044447 1046605 1046610) (-676 "LSAGG.spad" 1044102 1044112 1044401 1044428) (-675 "LSAGG.spad" 1043791 1043803 1044092 1044097) (-674 "LPOLY.spad" 1042745 1042764 1043647 1043716) (-673 "LPEFRAC.spad" 1042016 1042026 1042735 1042740) (-672 "LO.spad" 1041417 1041431 1041950 1041977) (-671 "LOGIC.spad" 1041019 1041027 1041407 1041412) (-670 "LOGIC.spad" 1040619 1040629 1041009 1041014) (-669 "LODOOPS.spad" 1039549 1039561 1040609 1040614) (-668 "LODO.spad" 1038933 1038949 1039229 1039268) (-667 "LODOF.spad" 1037979 1037996 1038890 1038895) (-666 "LODOCAT.spad" 1036645 1036655 1037935 1037974) (-665 "LODOCAT.spad" 1035309 1035321 1036601 1036606) (-664 "LODO2.spad" 1034582 1034594 1034989 1035028) (-663 "LODO1.spad" 1033982 1033992 1034262 1034301) (-662 "LODEEF.spad" 1032784 1032802 1033972 1033977) (-661 "LNAGG.spad" 1028931 1028941 1032774 1032779) (-660 "LNAGG.spad" 1025042 1025054 1028887 1028892) (-659 "LMOPS.spad" 1021810 1021827 1025032 1025037) (-658 "LMODULE.spad" 1021578 1021588 1021800 1021805) (-657 "LMDICT.spad" 1020865 1020875 1021129 1021156) (-656 "LLINSET.spad" 1020262 1020272 1020855 1020860) (-655 "LITERAL.spad" 1020168 1020179 1020252 1020257) (-654 "LIST.spad" 1017903 1017913 1019315 1019342) (-653 "LIST3.spad" 1017214 1017228 1017893 1017898) (-652 "LIST2.spad" 1015916 1015928 1017204 1017209) (-651 "LIST2MAP.spad" 1012819 1012831 1015906 1015911) (-650 "LINSET.spad" 1012441 1012451 1012809 1012814) (-649 "LINEXP.spad" 1011579 1011589 1012431 1012436) (-648 "LINDEP.spad" 1010388 1010400 1011491 1011496) (-647 "LIMITRF.spad" 1008316 1008326 1010378 1010383) (-646 "LIMITPS.spad" 1007219 1007232 1008306 1008311) (-645 "LIE.spad" 1005235 1005247 1006509 1006654) (-644 "LIECAT.spad" 1004711 1004721 1005161 1005230) (-643 "LIECAT.spad" 1004215 1004227 1004667 1004672) (-642 "LIB.spad" 1002428 1002436 1002874 1002889) (-641 "LGROBP.spad" 999781 999800 1002418 1002423) (-640 "LF.spad" 998736 998752 999771 999776) (-639 "LFCAT.spad" 997795 997803 998726 998731) (-638 "LEXTRIPK.spad" 993298 993313 997785 997790) (-637 "LEXP.spad" 991301 991328 993278 993293) (-636 "LETAST.spad" 991000 991008 991291 991296) (-635 "LEADCDET.spad" 989398 989415 990990 990995) (-634 "LAZM3PK.spad" 988102 988124 989388 989393) (-633 "LAUPOL.spad" 986795 986808 987695 987764) (-632 "LAPLACE.spad" 986378 986394 986785 986790) (-631 "LA.spad" 985818 985832 986300 986339) (-630 "LALG.spad" 985594 985604 985798 985813) (-629 "LALG.spad" 985378 985390 985584 985589) (-628 "KVTFROM.spad" 985113 985123 985368 985373) (-627 "KTVLOGIC.spad" 984625 984633 985103 985108) (-626 "KRCFROM.spad" 984363 984373 984615 984620) (-625 "KOVACIC.spad" 983086 983103 984353 984358) (-624 "KONVERT.spad" 982808 982818 983076 983081) (-623 "KOERCE.spad" 982545 982555 982798 982803) (-622 "KERNEL.spad" 981200 981210 982329 982334) (-621 "KERNEL2.spad" 980903 980915 981190 981195) (-620 "KDAGG.spad" 980012 980034 980883 980898) (-619 "KDAGG.spad" 979129 979153 980002 980007) (-618 "KAFILE.spad" 978092 978108 978327 978354) (-617 "JORDAN.spad" 975921 975933 977382 977527) (-616 "JOINAST.spad" 975615 975623 975911 975916) (-615 "JAVACODE.spad" 975481 975489 975605 975610) (-614 "IXAGG.spad" 973614 973638 975471 975476) (-613 "IXAGG.spad" 971602 971628 973461 973466) (-612 "IVECTOR.spad" 970372 970387 970527 970554) (-611 "ITUPLE.spad" 969533 969543 970362 970367) (-610 "ITRIGMNP.spad" 968372 968391 969523 969528) (-609 "ITFUN3.spad" 967878 967892 968362 968367) (-608 "ITFUN2.spad" 967622 967634 967868 967873) (-607 "ITFORM.spad" 966977 966985 967612 967617) (-606 "ITAYLOR.spad" 964971 964986 966841 966938) (-605 "ISUPS.spad" 957408 957423 963945 964042) (-604 "ISUMP.spad" 956909 956925 957398 957403) (-603 "ISTRING.spad" 955997 956010 956078 956105) (-602 "ISAST.spad" 955716 955724 955987 955992) (-601 "IRURPK.spad" 954433 954452 955706 955711) (-600 "IRSN.spad" 952405 952413 954423 954428) (-599 "IRRF2F.spad" 950890 950900 952361 952366) (-598 "IRREDFFX.spad" 950491 950502 950880 950885) (-597 "IROOT.spad" 948830 948840 950481 950486) (-596 "IR.spad" 946631 946645 948685 948712) (-595 "IRFORM.spad" 945955 945963 946621 946626) (-594 "IR2.spad" 944983 944999 945945 945950) (-593 "IR2F.spad" 944189 944205 944973 944978) (-592 "IPRNTPK.spad" 943949 943957 944179 944184) (-591 "IPF.spad" 943514 943526 943754 943847) (-590 "IPADIC.spad" 943275 943301 943440 943509) (-589 "IP4ADDR.spad" 942832 942840 943265 943270) (-588 "IOMODE.spad" 942354 942362 942822 942827) (-587 "IOBFILE.spad" 941715 941723 942344 942349) (-586 "IOBCON.spad" 941580 941588 941705 941710) (-585 "INVLAPLA.spad" 941229 941245 941570 941575) (-584 "INTTR.spad" 934611 934628 941219 941224) (-583 "INTTOOLS.spad" 932366 932382 934185 934190) (-582 "INTSLPE.spad" 931686 931694 932356 932361) (-581 "INTRVL.spad" 931252 931262 931600 931681) (-580 "INTRF.spad" 929676 929690 931242 931247) (-579 "INTRET.spad" 929108 929118 929666 929671) (-578 "INTRAT.spad" 927835 927852 929098 929103) (-577 "INTPM.spad" 926220 926236 927478 927483) (-576 "INTPAF.spad" 924084 924102 926152 926157) (-575 "INTPACK.spad" 914458 914466 924074 924079) (-574 "INT.spad" 913906 913914 914312 914453) (-573 "INTHERTR.spad" 913180 913197 913896 913901) (-572 "INTHERAL.spad" 912850 912874 913170 913175) (-571 "INTHEORY.spad" 909289 909297 912840 912845) (-570 "INTG0.spad" 903022 903040 909221 909226) (-569 "INTFTBL.spad" 897051 897059 903012 903017) (-568 "INTFACT.spad" 896110 896120 897041 897046) (-567 "INTEF.spad" 894495 894511 896100 896105) (-566 "INTDOM.spad" 893118 893126 894421 894490) (-565 "INTDOM.spad" 891803 891813 893108 893113) (-564 "INTCAT.spad" 890062 890072 891717 891798) (-563 "INTBIT.spad" 889569 889577 890052 890057) (-562 "INTALG.spad" 888757 888784 889559 889564) (-561 "INTAF.spad" 888257 888273 888747 888752) (-560 "INTABL.spad" 886775 886806 886938 886965) (-559 "INT8.spad" 886655 886663 886765 886770) (-558 "INT64.spad" 886534 886542 886645 886650) (-557 "INT32.spad" 886413 886421 886524 886529) (-556 "INT16.spad" 886292 886300 886403 886408) (-555 "INS.spad" 883795 883803 886194 886287) (-554 "INS.spad" 881384 881394 883785 883790) (-553 "INPSIGN.spad" 880832 880845 881374 881379) (-552 "INPRODPF.spad" 879928 879947 880822 880827) (-551 "INPRODFF.spad" 879016 879040 879918 879923) (-550 "INNMFACT.spad" 877991 878008 879006 879011) (-549 "INMODGCD.spad" 877479 877509 877981 877986) (-548 "INFSP.spad" 875776 875798 877469 877474) (-547 "INFPROD0.spad" 874856 874875 875766 875771) (-546 "INFORM.spad" 872055 872063 874846 874851) (-545 "INFORM1.spad" 871680 871690 872045 872050) (-544 "INFINITY.spad" 871232 871240 871670 871675) (-543 "INETCLTS.spad" 871209 871217 871222 871227) (-542 "INEP.spad" 869747 869769 871199 871204) (-541 "INDE.spad" 869476 869493 869737 869742) (-540 "INCRMAPS.spad" 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242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
-\ No newline at end of file
+((-3 NIL 2267909 2267914 2267919 2267924) (-2 NIL 2267889 2267894 2267899 2267904) (-1 NIL 2267869 2267874 2267879 2267884) (0 NIL 2267849 2267854 2267859 2267864) (-1310 "ZMOD.spad" 2267658 2267671 2267787 2267844) (-1309 "ZLINDEP.spad" 2266724 2266735 2267648 2267653) (-1308 "ZDSOLVE.spad" 2256669 2256691 2266714 2266719) (-1307 "YSTREAM.spad" 2256164 2256175 2256659 2256664) (-1306 "YDIAGRAM.spad" 2255798 2255807 2256154 2256159) (-1305 "XRPOLY.spad" 2255018 2255038 2255654 2255723) (-1304 "XPR.spad" 2252813 2252826 2254736 2254835) (-1303 "XPOLY.spad" 2252368 2252379 2252669 2252738) (-1302 "XPOLYC.spad" 2251687 2251703 2252294 2252363) (-1301 "XPBWPOLY.spad" 2250124 2250144 2251467 2251536) (-1300 "XF.spad" 2248587 2248602 2250026 2250119) (-1299 "XF.spad" 2247030 2247047 2248471 2248476) (-1298 "XFALG.spad" 2244078 2244094 2246956 2247025) (-1297 "XEXPPKG.spad" 2243329 2243355 2244068 2244073) (-1296 "XDPOLY.spad" 2242943 2242959 2243185 2243254) (-1295 "XALG.spad" 2242603 2242614 2242899 2242938) (-1294 "WUTSET.spad" 2238442 2238459 2242249 2242276) (-1293 "WP.spad" 2237641 2237685 2238300 2238367) (-1292 "WHILEAST.spad" 2237439 2237448 2237631 2237636) (-1291 "WHEREAST.spad" 2237110 2237119 2237429 2237434) (-1290 "WFFINTBS.spad" 2234773 2234795 2237100 2237105) (-1289 "WEIER.spad" 2232995 2233006 2234763 2234768) (-1288 "VSPACE.spad" 2232668 2232679 2232963 2232990) (-1287 "VSPACE.spad" 2232361 2232374 2232658 2232663) (-1286 "VOID.spad" 2232038 2232047 2232351 2232356) (-1285 "VIEW.spad" 2229718 2229727 2232028 2232033) (-1284 "VIEWDEF.spad" 2224919 2224928 2229708 2229713) (-1283 "VIEW3D.spad" 2208880 2208889 2224909 2224914) (-1282 "VIEW2D.spad" 2196771 2196780 2208870 2208875) (-1281 "VECTOR.spad" 2195445 2195456 2195696 2195723) (-1280 "VECTOR2.spad" 2194084 2194097 2195435 2195440) (-1279 "VECTCAT.spad" 2191988 2191999 2194052 2194079) (-1278 "VECTCAT.spad" 2189699 2189712 2191765 2191770) (-1277 "VARIABLE.spad" 2189479 2189494 2189689 2189694) (-1276 "UTYPE.spad" 2189123 2189132 2189469 2189474) (-1275 "UTSODETL.spad" 2188418 2188442 2189079 2189084) (-1274 "UTSODE.spad" 2186634 2186654 2188408 2188413) (-1273 "UTS.spad" 2181438 2181466 2185101 2185198) (-1272 "UTSCAT.spad" 2178917 2178933 2181336 2181433) (-1271 "UTSCAT.spad" 2176040 2176058 2178461 2178466) (-1270 "UTS2.spad" 2175635 2175670 2176030 2176035) (-1269 "URAGG.spad" 2170308 2170319 2175625 2175630) (-1268 "URAGG.spad" 2164945 2164958 2170264 2170269) (-1267 "UPXSSING.spad" 2162590 2162616 2164026 2164159) (-1266 "UPXS.spad" 2159744 2159772 2160722 2160871) (-1265 "UPXSCONS.spad" 2157503 2157523 2157876 2158025) (-1264 "UPXSCCA.spad" 2156074 2156094 2157349 2157498) (-1263 "UPXSCCA.spad" 2154787 2154809 2156064 2156069) (-1262 "UPXSCAT.spad" 2153376 2153392 2154633 2154782) (-1261 "UPXS2.spad" 2152919 2152972 2153366 2153371) (-1260 "UPSQFREE.spad" 2151333 2151347 2152909 2152914) (-1259 "UPSCAT.spad" 2149120 2149144 2151231 2151328) (-1258 "UPSCAT.spad" 2146613 2146639 2148726 2148731) (-1257 "UPOLYC.spad" 2141653 2141664 2146455 2146608) (-1256 "UPOLYC.spad" 2136585 2136598 2141389 2141394) (-1255 "UPOLYC2.spad" 2136056 2136075 2136575 2136580) (-1254 "UP.spad" 2133255 2133270 2133642 2133795) (-1253 "UPMP.spad" 2132155 2132168 2133245 2133250) (-1252 "UPDIVP.spad" 2131720 2131734 2132145 2132150) (-1251 "UPDECOMP.spad" 2129965 2129979 2131710 2131715) (-1250 "UPCDEN.spad" 2129174 2129190 2129955 2129960) (-1249 "UP2.spad" 2128538 2128559 2129164 2129169) (-1248 "UNISEG.spad" 2127891 2127902 2128457 2128462) (-1247 "UNISEG2.spad" 2127388 2127401 2127847 2127852) (-1246 "UNIFACT.spad" 2126491 2126503 2127378 2127383) (-1245 "ULS.spad" 2117049 2117077 2118136 2118565) (-1244 "ULSCONS.spad" 2109445 2109465 2109815 2109964) (-1243 "ULSCCAT.spad" 2107182 2107202 2109291 2109440) (-1242 "ULSCCAT.spad" 2105027 2105049 2107138 2107143) (-1241 "ULSCAT.spad" 2103259 2103275 2104873 2105022) (-1240 "ULS2.spad" 2102773 2102826 2103249 2103254) (-1239 "UINT8.spad" 2102650 2102659 2102763 2102768) (-1238 "UINT64.spad" 2102526 2102535 2102640 2102645) (-1237 "UINT32.spad" 2102402 2102411 2102516 2102521) (-1236 "UINT16.spad" 2102278 2102287 2102392 2102397) (-1235 "UFD.spad" 2101343 2101352 2102204 2102273) (-1234 "UFD.spad" 2100470 2100481 2101333 2101338) (-1233 "UDVO.spad" 2099351 2099360 2100460 2100465) (-1232 "UDPO.spad" 2096844 2096855 2099307 2099312) (-1231 "TYPE.spad" 2096776 2096785 2096834 2096839) (-1230 "TYPEAST.spad" 2096695 2096704 2096766 2096771) (-1229 "TWOFACT.spad" 2095347 2095362 2096685 2096690) (-1228 "TUPLE.spad" 2094833 2094844 2095246 2095251) (-1227 "TUBETOOL.spad" 2091700 2091709 2094823 2094828) (-1226 "TUBE.spad" 2090347 2090364 2091690 2091695) (-1225 "TS.spad" 2088946 2088962 2089912 2090009) (-1224 "TSETCAT.spad" 2076073 2076090 2088914 2088941) (-1223 "TSETCAT.spad" 2063186 2063205 2076029 2076034) (-1222 "TRMANIP.spad" 2057552 2057569 2062892 2062897) (-1221 "TRIMAT.spad" 2056515 2056540 2057542 2057547) (-1220 "TRIGMNIP.spad" 2055042 2055059 2056505 2056510) (-1219 "TRIGCAT.spad" 2054554 2054563 2055032 2055037) (-1218 "TRIGCAT.spad" 2054064 2054075 2054544 2054549) (-1217 "TREE.spad" 2052639 2052650 2053671 2053698) (-1216 "TRANFUN.spad" 2052478 2052487 2052629 2052634) (-1215 "TRANFUN.spad" 2052315 2052326 2052468 2052473) (-1214 "TOPSP.spad" 2051989 2051998 2052305 2052310) (-1213 "TOOLSIGN.spad" 2051652 2051663 2051979 2051984) (-1212 "TEXTFILE.spad" 2050213 2050222 2051642 2051647) (-1211 "TEX.spad" 2047359 2047368 2050203 2050208) (-1210 "TEX1.spad" 2046915 2046926 2047349 2047354) (-1209 "TEMUTL.spad" 2046470 2046479 2046905 2046910) (-1208 "TBCMPPK.spad" 2044563 2044586 2046460 2046465) (-1207 "TBAGG.spad" 2043613 2043636 2044543 2044558) (-1206 "TBAGG.spad" 2042671 2042696 2043603 2043608) (-1205 "TANEXP.spad" 2042079 2042090 2042661 2042666) (-1204 "TALGOP.spad" 2041803 2041814 2042069 2042074) (-1203 "TABLE.spad" 2040214 2040237 2040484 2040511) (-1202 "TABLEAU.spad" 2039695 2039706 2040204 2040209) (-1201 "TABLBUMP.spad" 2036498 2036509 2039685 2039690) (-1200 "SYSTEM.spad" 2035726 2035735 2036488 2036493) (-1199 "SYSSOLP.spad" 2033209 2033220 2035716 2035721) (-1198 "SYSPTR.spad" 2033108 2033117 2033199 2033204) (-1197 "SYSNNI.spad" 2032290 2032301 2033098 2033103) (-1196 "SYSINT.spad" 2031694 2031705 2032280 2032285) (-1195 "SYNTAX.spad" 2027900 2027909 2031684 2031689) (-1194 "SYMTAB.spad" 2025968 2025977 2027890 2027895) (-1193 "SYMS.spad" 2021991 2022000 2025958 2025963) (-1192 "SYMPOLY.spad" 2020998 2021009 2021080 2021207) (-1191 "SYMFUNC.spad" 2020499 2020510 2020988 2020993) (-1190 "SYMBOL.spad" 2018002 2018011 2020489 2020494) (-1189 "SWITCH.spad" 2014773 2014782 2017992 2017997) (-1188 "SUTS.spad" 2011678 2011706 2013240 2013337) (-1187 "SUPXS.spad" 2008819 2008847 2009810 2009959) (-1186 "SUP.spad" 2005632 2005643 2006405 2006558) (-1185 "SUPFRACF.spad" 2004737 2004755 2005622 2005627) (-1184 "SUP2.spad" 2004129 2004142 2004727 2004732) (-1183 "SUMRF.spad" 2003103 2003114 2004119 2004124) (-1182 "SUMFS.spad" 2002740 2002757 2003093 2003098) (-1181 "SULS.spad" 1993285 1993313 1994385 1994814) (-1180 "SUCHTAST.spad" 1993054 1993063 1993275 1993280) (-1179 "SUCH.spad" 1992736 1992751 1993044 1993049) (-1178 "SUBSPACE.spad" 1984851 1984866 1992726 1992731) (-1177 "SUBRESP.spad" 1984021 1984035 1984807 1984812) (-1176 "STTF.spad" 1980120 1980136 1984011 1984016) (-1175 "STTFNC.spad" 1976588 1976604 1980110 1980115) (-1174 "STTAYLOR.spad" 1969223 1969234 1976469 1976474) (-1173 "STRTBL.spad" 1967728 1967745 1967877 1967904) (-1172 "STRING.spad" 1967137 1967146 1967151 1967178) (-1171 "STRICAT.spad" 1966925 1966934 1967105 1967132) (-1170 "STREAM.spad" 1963843 1963854 1966450 1966465) (-1169 "STREAM3.spad" 1963416 1963431 1963833 1963838) (-1168 "STREAM2.spad" 1962544 1962557 1963406 1963411) (-1167 "STREAM1.spad" 1962250 1962261 1962534 1962539) (-1166 "STINPROD.spad" 1961186 1961202 1962240 1962245) (-1165 "STEP.spad" 1960387 1960396 1961176 1961181) (-1164 "STEPAST.spad" 1959621 1959630 1960377 1960382) (-1163 "STBL.spad" 1958147 1958175 1958314 1958329) (-1162 "STAGG.spad" 1957222 1957233 1958137 1958142) (-1161 "STAGG.spad" 1956295 1956308 1957212 1957217) (-1160 "STACK.spad" 1955652 1955663 1955902 1955929) (-1159 "SREGSET.spad" 1953356 1953373 1955298 1955325) (-1158 "SRDCMPK.spad" 1951917 1951937 1953346 1953351) (-1157 "SRAGG.spad" 1947060 1947069 1951885 1951912) (-1156 "SRAGG.spad" 1942223 1942234 1947050 1947055) (-1155 "SQMATRIX.spad" 1939895 1939913 1940811 1940898) (-1154 "SPLTREE.spad" 1934447 1934460 1939331 1939358) (-1153 "SPLNODE.spad" 1931035 1931048 1934437 1934442) (-1152 "SPFCAT.spad" 1929844 1929853 1931025 1931030) (-1151 "SPECOUT.spad" 1928396 1928405 1929834 1929839) (-1150 "SPADXPT.spad" 1919991 1920000 1928386 1928391) (-1149 "spad-parser.spad" 1919456 1919465 1919981 1919986) (-1148 "SPADAST.spad" 1919157 1919166 1919446 1919451) (-1147 "SPACEC.spad" 1903356 1903367 1919147 1919152) (-1146 "SPACE3.spad" 1903132 1903143 1903346 1903351) (-1145 "SORTPAK.spad" 1902681 1902694 1903088 1903093) (-1144 "SOLVETRA.spad" 1900444 1900455 1902671 1902676) (-1143 "SOLVESER.spad" 1898972 1898983 1900434 1900439) (-1142 "SOLVERAD.spad" 1894998 1895009 1898962 1898967) (-1141 "SOLVEFOR.spad" 1893460 1893478 1894988 1894993) (-1140 "SNTSCAT.spad" 1893060 1893077 1893428 1893455) (-1139 "SMTS.spad" 1891332 1891358 1892625 1892722) (-1138 "SMP.spad" 1888807 1888827 1889197 1889324) (-1137 "SMITH.spad" 1887652 1887677 1888797 1888802) (-1136 "SMATCAT.spad" 1885762 1885792 1887596 1887647) (-1135 "SMATCAT.spad" 1883804 1883836 1885640 1885645) (-1134 "SKAGG.spad" 1882767 1882778 1883772 1883799) (-1133 "SINT.spad" 1881707 1881716 1882633 1882762) (-1132 "SIMPAN.spad" 1881435 1881444 1881697 1881702) (-1131 "SIG.spad" 1880765 1880774 1881425 1881430) (-1130 "SIGNRF.spad" 1879883 1879894 1880755 1880760) (-1129 "SIGNEF.spad" 1879162 1879179 1879873 1879878) (-1128 "SIGAST.spad" 1878547 1878556 1879152 1879157) (-1127 "SHP.spad" 1876475 1876490 1878503 1878508) (-1126 "SHDP.spad" 1866109 1866136 1866618 1866749) (-1125 "SGROUP.spad" 1865717 1865726 1866099 1866104) (-1124 "SGROUP.spad" 1865323 1865334 1865707 1865712) (-1123 "SGCF.spad" 1858462 1858471 1865313 1865318) (-1122 "SFRTCAT.spad" 1857392 1857409 1858430 1858457) (-1121 "SFRGCD.spad" 1856455 1856475 1857382 1857387) (-1120 "SFQCMPK.spad" 1851092 1851112 1856445 1856450) (-1119 "SFORT.spad" 1850531 1850545 1851082 1851087) (-1118 "SEXOF.spad" 1850374 1850414 1850521 1850526) (-1117 "SEX.spad" 1850266 1850275 1850364 1850369) (-1116 "SEXCAT.spad" 1848047 1848087 1850256 1850261) (-1115 "SET.spad" 1846371 1846382 1847468 1847507) (-1114 "SETMN.spad" 1844821 1844838 1846361 1846366) (-1113 "SETCAT.spad" 1844143 1844152 1844811 1844816) (-1112 "SETCAT.spad" 1843463 1843474 1844133 1844138) (-1111 "SETAGG.spad" 1840012 1840023 1843443 1843458) (-1110 "SETAGG.spad" 1836569 1836582 1840002 1840007) (-1109 "SEQAST.spad" 1836272 1836281 1836559 1836564) (-1108 "SEGXCAT.spad" 1835428 1835441 1836262 1836267) (-1107 "SEG.spad" 1835241 1835252 1835347 1835352) (-1106 "SEGCAT.spad" 1834166 1834177 1835231 1835236) (-1105 "SEGBIND.spad" 1833924 1833935 1834113 1834118) (-1104 "SEGBIND2.spad" 1833622 1833635 1833914 1833919) (-1103 "SEGAST.spad" 1833336 1833345 1833612 1833617) (-1102 "SEG2.spad" 1832771 1832784 1833292 1833297) (-1101 "SDVAR.spad" 1832047 1832058 1832761 1832766) (-1100 "SDPOL.spad" 1829473 1829484 1829764 1829891) (-1099 "SCPKG.spad" 1827562 1827573 1829463 1829468) (-1098 "SCOPE.spad" 1826715 1826724 1827552 1827557) (-1097 "SCACHE.spad" 1825411 1825422 1826705 1826710) (-1096 "SASTCAT.spad" 1825320 1825329 1825401 1825406) (-1095 "SAOS.spad" 1825192 1825201 1825310 1825315) (-1094 "SAERFFC.spad" 1824905 1824925 1825182 1825187) (-1093 "SAE.spad" 1823080 1823096 1823691 1823826) (-1092 "SAEFACT.spad" 1822781 1822801 1823070 1823075) (-1091 "RURPK.spad" 1820440 1820456 1822771 1822776) (-1090 "RULESET.spad" 1819893 1819917 1820430 1820435) (-1089 "RULE.spad" 1818133 1818157 1819883 1819888) (-1088 "RULECOLD.spad" 1817985 1817998 1818123 1818128) (-1087 "RTVALUE.spad" 1817720 1817729 1817975 1817980) (-1086 "RSTRCAST.spad" 1817437 1817446 1817710 1817715) (-1085 "RSETGCD.spad" 1813815 1813835 1817427 1817432) (-1084 "RSETCAT.spad" 1803751 1803768 1813783 1813810) (-1083 "RSETCAT.spad" 1793707 1793726 1803741 1803746) (-1082 "RSDCMPK.spad" 1792159 1792179 1793697 1793702) (-1081 "RRCC.spad" 1790543 1790573 1792149 1792154) (-1080 "RRCC.spad" 1788925 1788957 1790533 1790538) (-1079 "RPTAST.spad" 1788627 1788636 1788915 1788920) (-1078 "RPOLCAT.spad" 1767987 1768002 1788495 1788622) (-1077 "RPOLCAT.spad" 1747060 1747077 1767570 1767575) (-1076 "ROUTINE.spad" 1742943 1742952 1745707 1745734) (-1075 "ROMAN.spad" 1742271 1742280 1742809 1742938) (-1074 "ROIRC.spad" 1741351 1741383 1742261 1742266) (-1073 "RNS.spad" 1740254 1740263 1741253 1741346) (-1072 "RNS.spad" 1739243 1739254 1740244 1740249) (-1071 "RNG.spad" 1738978 1738987 1739233 1739238) (-1070 "RNGBIND.spad" 1738138 1738152 1738933 1738938) (-1069 "RMODULE.spad" 1737903 1737914 1738128 1738133) (-1068 "RMCAT2.spad" 1737323 1737380 1737893 1737898) (-1067 "RMATRIX.spad" 1736147 1736166 1736490 1736529) (-1066 "RMATCAT.spad" 1731726 1731757 1736103 1736142) (-1065 "RMATCAT.spad" 1727195 1727228 1731574 1731579) (-1064 "RLINSET.spad" 1726589 1726600 1727185 1727190) (-1063 "RINTERP.spad" 1726477 1726497 1726579 1726584) (-1062 "RING.spad" 1725947 1725956 1726457 1726472) (-1061 "RING.spad" 1725425 1725436 1725937 1725942) (-1060 "RIDIST.spad" 1724817 1724826 1725415 1725420) (-1059 "RGCHAIN.spad" 1723400 1723416 1724302 1724329) (-1058 "RGBCSPC.spad" 1723181 1723193 1723390 1723395) (-1057 "RGBCMDL.spad" 1722711 1722723 1723171 1723176) (-1056 "RF.spad" 1720353 1720364 1722701 1722706) (-1055 "RFFACTOR.spad" 1719815 1719826 1720343 1720348) (-1054 "RFFACT.spad" 1719550 1719562 1719805 1719810) (-1053 "RFDIST.spad" 1718546 1718555 1719540 1719545) (-1052 "RETSOL.spad" 1717965 1717978 1718536 1718541) (-1051 "RETRACT.spad" 1717393 1717404 1717955 1717960) (-1050 "RETRACT.spad" 1716819 1716832 1717383 1717388) (-1049 "RETAST.spad" 1716631 1716640 1716809 1716814) (-1048 "RESULT.spad" 1714691 1714700 1715278 1715305) (-1047 "RESRING.spad" 1714038 1714085 1714629 1714686) (-1046 "RESLATC.spad" 1713362 1713373 1714028 1714033) (-1045 "REPSQ.spad" 1713093 1713104 1713352 1713357) (-1044 "REP.spad" 1710647 1710656 1713083 1713088) (-1043 "REPDB.spad" 1710354 1710365 1710637 1710642) (-1042 "REP2.spad" 1700012 1700023 1710196 1710201) (-1041 "REP1.spad" 1694208 1694219 1699962 1699967) (-1040 "REGSET.spad" 1692005 1692022 1693854 1693881) (-1039 "REF.spad" 1691340 1691351 1691960 1691965) (-1038 "REDORDER.spad" 1690546 1690563 1691330 1691335) (-1037 "RECLOS.spad" 1689329 1689349 1690033 1690126) (-1036 "REALSOLV.spad" 1688469 1688478 1689319 1689324) (-1035 "REAL.spad" 1688341 1688350 1688459 1688464) (-1034 "REAL0Q.spad" 1685639 1685654 1688331 1688336) (-1033 "REAL0.spad" 1682483 1682498 1685629 1685634) (-1032 "RDUCEAST.spad" 1682204 1682213 1682473 1682478) (-1031 "RDIV.spad" 1681859 1681884 1682194 1682199) (-1030 "RDIST.spad" 1681426 1681437 1681849 1681854) (-1029 "RDETRS.spad" 1680290 1680308 1681416 1681421) (-1028 "RDETR.spad" 1678429 1678447 1680280 1680285) (-1027 "RDEEFS.spad" 1677528 1677545 1678419 1678424) (-1026 "RDEEF.spad" 1676538 1676555 1677518 1677523) (-1025 "RCFIELD.spad" 1673724 1673733 1676440 1676533) (-1024 "RCFIELD.spad" 1670996 1671007 1673714 1673719) (-1023 "RCAGG.spad" 1668924 1668935 1670986 1670991) (-1022 "RCAGG.spad" 1666779 1666792 1668843 1668848) (-1021 "RATRET.spad" 1666139 1666150 1666769 1666774) (-1020 "RATFACT.spad" 1665831 1665843 1666129 1666134) (-1019 "RANDSRC.spad" 1665150 1665159 1665821 1665826) (-1018 "RADUTIL.spad" 1664906 1664915 1665140 1665145) (-1017 "RADIX.spad" 1661827 1661841 1663373 1663466) (-1016 "RADFF.spad" 1660240 1660277 1660359 1660515) (-1015 "RADCAT.spad" 1659835 1659844 1660230 1660235) (-1014 "RADCAT.spad" 1659428 1659439 1659825 1659830) (-1013 "QUEUE.spad" 1658776 1658787 1659035 1659062) (-1012 "QUAT.spad" 1657234 1657245 1657577 1657642) (-1011 "QUATCT2.spad" 1656854 1656873 1657224 1657229) (-1010 "QUATCAT.spad" 1655024 1655035 1656784 1656849) (-1009 "QUATCAT.spad" 1652945 1652958 1654707 1654712) (-1008 "QUAGG.spad" 1651772 1651783 1652913 1652940) (-1007 "QQUTAST.spad" 1651540 1651549 1651762 1651767) (-1006 "QFORM.spad" 1651158 1651173 1651530 1651535) (-1005 "QFCAT.spad" 1649860 1649871 1651060 1651153) (-1004 "QFCAT.spad" 1648153 1648166 1649355 1649360) (-1003 "QFCAT2.spad" 1647845 1647862 1648143 1648148) (-1002 "QEQUAT.spad" 1647403 1647412 1647835 1647840) (-1001 "QCMPACK.spad" 1642149 1642169 1647393 1647398) (-1000 "QALGSET.spad" 1638227 1638260 1642063 1642068) (-999 "QALGSET2.spad" 1636223 1636241 1638217 1638222) (-998 "PWFFINTB.spad" 1633639 1633660 1636213 1636218) (-997 "PUSHVAR.spad" 1632978 1632997 1633629 1633634) (-996 "PTRANFN.spad" 1629106 1629116 1632968 1632973) (-995 "PTPACK.spad" 1626194 1626204 1629096 1629101) (-994 "PTFUNC2.spad" 1626017 1626031 1626184 1626189) (-993 "PTCAT.spad" 1625272 1625282 1625985 1626012) (-992 "PSQFR.spad" 1624579 1624603 1625262 1625267) (-991 "PSEUDLIN.spad" 1623465 1623475 1624569 1624574) (-990 "PSETPK.spad" 1608898 1608914 1623343 1623348) (-989 "PSETCAT.spad" 1602818 1602841 1608878 1608893) (-988 "PSETCAT.spad" 1596712 1596737 1602774 1602779) (-987 "PSCURVE.spad" 1595695 1595703 1596702 1596707) (-986 "PSCAT.spad" 1594478 1594507 1595593 1595690) (-985 "PSCAT.spad" 1593351 1593382 1594468 1594473) (-984 "PRTITION.spad" 1592049 1592057 1593341 1593346) (-983 "PRTDAST.spad" 1591768 1591776 1592039 1592044) (-982 "PRS.spad" 1581330 1581347 1591724 1591729) (-981 "PRQAGG.spad" 1580765 1580775 1581298 1581325) (-980 "PROPLOG.spad" 1580337 1580345 1580755 1580760) (-979 "PROPFUN2.spad" 1579960 1579973 1580327 1580332) (-978 "PROPFUN1.spad" 1579358 1579369 1579950 1579955) (-977 "PROPFRML.spad" 1577926 1577937 1579348 1579353) (-976 "PROPERTY.spad" 1577414 1577422 1577916 1577921) (-975 "PRODUCT.spad" 1575096 1575108 1575380 1575435) (-974 "PR.spad" 1573488 1573500 1574187 1574314) (-973 "PRINT.spad" 1573240 1573248 1573478 1573483) (-972 "PRIMES.spad" 1571493 1571503 1573230 1573235) (-971 "PRIMELT.spad" 1569574 1569588 1571483 1571488) (-970 "PRIMCAT.spad" 1569201 1569209 1569564 1569569) (-969 "PRIMARR.spad" 1568206 1568216 1568384 1568411) (-968 "PRIMARR2.spad" 1566973 1566985 1568196 1568201) (-967 "PREASSOC.spad" 1566355 1566367 1566963 1566968) (-966 "PPCURVE.spad" 1565492 1565500 1566345 1566350) (-965 "PORTNUM.spad" 1565267 1565275 1565482 1565487) (-964 "POLYROOT.spad" 1564116 1564138 1565223 1565228) (-963 "POLY.spad" 1561451 1561461 1561966 1562093) (-962 "POLYLIFT.spad" 1560716 1560739 1561441 1561446) (-961 "POLYCATQ.spad" 1558834 1558856 1560706 1560711) (-960 "POLYCAT.spad" 1552304 1552325 1558702 1558829) (-959 "POLYCAT.spad" 1545112 1545135 1551512 1551517) (-958 "POLY2UP.spad" 1544564 1544578 1545102 1545107) (-957 "POLY2.spad" 1544161 1544173 1544554 1544559) (-956 "POLUTIL.spad" 1543102 1543131 1544117 1544122) (-955 "POLTOPOL.spad" 1541850 1541865 1543092 1543097) (-954 "POINT.spad" 1540688 1540698 1540775 1540802) (-953 "PNTHEORY.spad" 1537390 1537398 1540678 1540683) (-952 "PMTOOLS.spad" 1536165 1536179 1537380 1537385) (-951 "PMSYM.spad" 1535714 1535724 1536155 1536160) (-950 "PMQFCAT.spad" 1535305 1535319 1535704 1535709) (-949 "PMPRED.spad" 1534784 1534798 1535295 1535300) (-948 "PMPREDFS.spad" 1534238 1534260 1534774 1534779) (-947 "PMPLCAT.spad" 1533318 1533336 1534170 1534175) (-946 "PMLSAGG.spad" 1532903 1532917 1533308 1533313) (-945 "PMKERNEL.spad" 1532482 1532494 1532893 1532898) (-944 "PMINS.spad" 1532062 1532072 1532472 1532477) (-943 "PMFS.spad" 1531639 1531657 1532052 1532057) (-942 "PMDOWN.spad" 1530929 1530943 1531629 1531634) (-941 "PMASS.spad" 1529939 1529947 1530919 1530924) (-940 "PMASSFS.spad" 1528906 1528922 1529929 1529934) (-939 "PLOTTOOL.spad" 1528686 1528694 1528896 1528901) (-938 "PLOT.spad" 1523609 1523617 1528676 1528681) (-937 "PLOT3D.spad" 1520073 1520081 1523599 1523604) (-936 "PLOT1.spad" 1519230 1519240 1520063 1520068) (-935 "PLEQN.spad" 1506520 1506547 1519220 1519225) (-934 "PINTERP.spad" 1506142 1506161 1506510 1506515) (-933 "PINTERPA.spad" 1505926 1505942 1506132 1506137) (-932 "PI.spad" 1505535 1505543 1505900 1505921) (-931 "PID.spad" 1504505 1504513 1505461 1505530) (-930 "PICOERCE.spad" 1504162 1504172 1504495 1504500) (-929 "PGROEB.spad" 1502763 1502777 1504152 1504157) (-928 "PGE.spad" 1494380 1494388 1502753 1502758) (-927 "PGCD.spad" 1493270 1493287 1494370 1494375) (-926 "PFRPAC.spad" 1492419 1492429 1493260 1493265) (-925 "PFR.spad" 1489082 1489092 1492321 1492414) (-924 "PFOTOOLS.spad" 1488340 1488356 1489072 1489077) (-923 "PFOQ.spad" 1487710 1487728 1488330 1488335) (-922 "PFO.spad" 1487129 1487156 1487700 1487705) (-921 "PF.spad" 1486703 1486715 1486934 1487027) (-920 "PFECAT.spad" 1484385 1484393 1486629 1486698) (-919 "PFECAT.spad" 1482095 1482105 1484341 1484346) (-918 "PFBRU.spad" 1479983 1479995 1482085 1482090) (-917 "PFBR.spad" 1477543 1477566 1479973 1479978) (-916 "PERM.spad" 1473350 1473360 1477373 1477388) (-915 "PERMGRP.spad" 1468120 1468130 1473340 1473345) (-914 "PERMCAT.spad" 1466781 1466791 1468100 1468115) (-913 "PERMAN.spad" 1465313 1465327 1466771 1466776) (-912 "PENDTREE.spad" 1464654 1464664 1464942 1464947) (-911 "PDRING.spad" 1463205 1463215 1464634 1464649) (-910 "PDRING.spad" 1461764 1461776 1463195 1463200) (-909 "PDEPROB.spad" 1460779 1460787 1461754 1461759) (-908 "PDEPACK.spad" 1454819 1454827 1460769 1460774) (-907 "PDECOMP.spad" 1454289 1454306 1454809 1454814) (-906 "PDECAT.spad" 1452645 1452653 1454279 1454284) (-905 "PCOMP.spad" 1452498 1452511 1452635 1452640) (-904 "PBWLB.spad" 1451086 1451103 1452488 1452493) (-903 "PATTERN.spad" 1445625 1445635 1451076 1451081) (-902 "PATTERN2.spad" 1445363 1445375 1445615 1445620) (-901 "PATTERN1.spad" 1443699 1443715 1445353 1445358) (-900 "PATRES.spad" 1441274 1441286 1443689 1443694) (-899 "PATRES2.spad" 1440946 1440960 1441264 1441269) (-898 "PATMATCH.spad" 1439143 1439174 1440654 1440659) (-897 "PATMAB.spad" 1438572 1438582 1439133 1439138) (-896 "PATLRES.spad" 1437658 1437672 1438562 1438567) (-895 "PATAB.spad" 1437422 1437432 1437648 1437653) (-894 "PARTPERM.spad" 1435430 1435438 1437412 1437417) (-893 "PARSURF.spad" 1434864 1434892 1435420 1435425) (-892 "PARSU2.spad" 1434661 1434677 1434854 1434859) (-891 "script-parser.spad" 1434181 1434189 1434651 1434656) (-890 "PARSCURV.spad" 1433615 1433643 1434171 1434176) (-889 "PARSC2.spad" 1433406 1433422 1433605 1433610) (-888 "PARPCURV.spad" 1432868 1432896 1433396 1433401) (-887 "PARPC2.spad" 1432659 1432675 1432858 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242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
+\ No newline at end of file
author	dos-reis <gdr@axiomatics.org>	2010-06-16 03:19:56 +0000
committer	dos-reis <gdr@axiomatics.org>	2010-06-16 03:19:56 +0000
commit	2bbc83eac50582a5ffab2860f4279aac28f9c429 (patch)
tree	b52e3554cb835b9bdea7b380c054283a0d1b3247 /src/share/algebra/browse.daase
parent	5da51971d3bd899bb327021730a528de9107329d (diff)
download	open-axiom-2bbc83eac50582a5ffab2860f4279aac28f9c429.tar.gz