diff options
Diffstat (limited to 'src/share/algebra/browse.daase')
| -rw-r--r-- | src/share/algebra/browse.daase | 58 |
1 files changed, 29 insertions, 29 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 2eff267f..cd8ab950 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294147 . 3486848000) +(2294307 . 3486852427) (-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 -2119 UP UPUP -2094) +(-40 -2119 UP UPUP -1488) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3795 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3795 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3795 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) @@ -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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4466 "*") . T)) NIL -(-136 |minix| -1914 S T$) +(-136 |minix| -1913 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -1914 R) +(-137 |minix| -1913 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -896,19 +896,19 @@ 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 -(-242 S -1914 R) +(-242 S -1913 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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 (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1121)))) -(-243 -1914 R) +(-243 -1913 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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"))) ((-4458 |has| |#2| (-1070)) (-4459 |has| |#2| (-1070)) (-4461 |has| |#2| (-6 -4461)) (-4464 . T)) NIL -(-244 -1914 A B) +(-244 -1913 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 -(-245 -1914 R) +(-245 -1913 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."))) ((-4458 |has| |#2| (-1070)) (-4459 |has| |#2| (-1070)) (-4461 |has| |#2| (-6 -4461)) (-4464 . T)) ((-3795 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST (QUOTE 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(QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasAttribute| |#2| (QUOTE -4461)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) @@ -1124,7 +1124,7 @@ 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 -(-299 S R |Mod| -3381 -3046 |exactQuo|) +(-299 S R |Mod| -1767 -2748 |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"))) ((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL @@ -1247,7 +1247,7 @@ NIL (-329 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."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . 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(|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 @@ -1515,7 +1515,7 @@ NIL (-396 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) ((-4459 . T) (-4458 . T)) -((|HasCategory| |#1| (QUOTE (-174)))) +((|HasCategory| |#1| (QUOTE (-174))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121))))) (-397 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL @@ -1875,7 +1875,7 @@ NIL (-486 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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(-576))))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| (-576) (QUOTE (-861))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197))))) (-3795 (|HasCategory| |#2| (QUOTE (-1070))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasAttribute| |#2| (QUOTE -4461)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) @@ -2103,7 +2103,7 @@ NIL (-543 |Varset|) ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL -NIL +((-12 (|HasCategory| (-783) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1121))))) (-544 K -2119 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL @@ -2608,7 +2608,7 @@ 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)))) -(-670 A -2973) +(-670 A -3304) ((|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}}"))) ((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) @@ -2820,7 +2820,7 @@ 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 -(-723 R |Mod| -3381 -3046 |exactQuo|) +(-723 R |Mod| -1767 -2748 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL @@ -2836,7 +2836,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -3381 -3046 |exactQuo|) +(-727 R |Mod| -1767 -2748 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4461 . T)) NIL @@ -3236,7 +3236,7 @@ NIL ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -1914 S) +(-857 -1913 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL @@ -4707,11 +4707,11 @@ NIL (-1194 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . 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We may integrate a series when we can divide coefficients by integers.")) (|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}."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . 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(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}.")) 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -5019,11 +5019,11 @@ NIL (-1272 |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)}."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1759) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1584) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4412) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1585) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-1273 |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."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1759) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1584) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3795 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4412) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1585) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-1274 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4466 "*") |has| (-1273 |#2| |#3| |#4|) (-174)) (-4457 |has| (-1273 |#2| |#3| |#4|) (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) @@ -5043,7 +5043,7 @@ NIL (-1278 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1584) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1759) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1585) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4412) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) (-1279 |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."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) @@ -5051,7 +5051,7 @@ NIL (-1280 |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))}.}")) (|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}."))) (((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -1759) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1584) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3795 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -4113) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3795 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4412) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1585) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-1281 |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 @@ -5216,4 +5216,4 @@ NIL NIL NIL NIL -((-3 NIL 2294127 2294132 2294137 2294142) (-2 NIL 2294107 2294112 2294117 2294122) (-1 NIL 2294087 2294092 2294097 2294102) (0 NIL 2294067 2294072 2294077 2294082) (-1317 "ZMOD.spad" 2293876 2293889 2294005 2294062) (-1316 "ZLINDEP.spad" 2292942 2292953 2293866 2293871) (-1315 "ZDSOLVE.spad" 2282887 2282909 2292932 2292937) (-1314 "YSTREAM.spad" 2282382 2282393 2282877 2282882) (-1313 "YDIAGRAM.spad" 2282016 2282025 2282372 2282377) (-1312 "XRPOLY.spad" 2281236 2281256 2281872 2281941) (-1311 "XPR.spad" 2279031 2279044 2280954 2281053) (-1310 "XPOLY.spad" 2278586 2278597 2278887 2278956) (-1309 "XPOLYC.spad" 2277905 2277921 2278512 2278581) (-1308 "XPBWPOLY.spad" 2276342 2276362 2277685 2277754) (-1307 "XF.spad" 2274805 2274820 2276244 2276337) (-1306 "XF.spad" 2273248 2273265 2274689 2274694) (-1305 "XFALG.spad" 2270296 2270312 2273174 2273243) (-1304 "XEXPPKG.spad" 2269547 2269573 2270286 2270291) (-1303 "XDPOLY.spad" 2269161 2269177 2269403 2269472) (-1302 "XALG.spad" 2268821 2268832 2269117 2269156) (-1301 "WUTSET.spad" 2264624 2264641 2268431 2268458) (-1300 "WP.spad" 2263823 2263867 2264482 2264549) (-1299 "WHILEAST.spad" 2263621 2263630 2263813 2263818) (-1298 "WHEREAST.spad" 2263292 2263301 2263611 2263616) (-1297 "WFFINTBS.spad" 2260955 2260977 2263282 2263287) (-1296 "WEIER.spad" 2259177 2259188 2260945 2260950) (-1295 "VSPACE.spad" 2258850 2258861 2259145 2259172) (-1294 "VSPACE.spad" 2258543 2258556 2258840 2258845) (-1293 "VOID.spad" 2258220 2258229 2258533 2258538) (-1292 "VIEW.spad" 2255900 2255909 2258210 2258215) (-1291 "VIEWDEF.spad" 2251101 2251110 2255890 2255895) (-1290 "VIEW3D.spad" 2235062 2235071 2251091 2251096) (-1289 "VIEW2D.spad" 2222953 2222962 2235052 2235057) (-1288 "VECTOR.spad" 2221474 2221485 2221725 2221752) (-1287 "VECTOR2.spad" 2220113 2220126 2221464 2221469) (-1286 "VECTCAT.spad" 2218017 2218028 2220081 2220108) (-1285 "VECTCAT.spad" 2215728 2215741 2217794 2217799) (-1284 "VARIABLE.spad" 2215508 2215523 2215718 2215723) (-1283 "UTYPE.spad" 2215152 2215161 2215498 2215503) (-1282 "UTSODETL.spad" 2214447 2214471 2215108 2215113) (-1281 "UTSODE.spad" 2212663 2212683 2214437 2214442) (-1280 "UTS.spad" 2207610 2207638 2211130 2211227) (-1279 "UTSCAT.spad" 2205089 2205105 2207508 2207605) (-1278 "UTSCAT.spad" 2202212 2202230 2204633 2204638) (-1277 "UTS2.spad" 2201807 2201842 2202202 2202207) (-1276 "URAGG.spad" 2196480 2196491 2201797 2201802) (-1275 "URAGG.spad" 2191117 2191130 2196436 2196441) (-1274 "UPXSSING.spad" 2188762 2188788 2190198 2190331) (-1273 "UPXS.spad" 2186058 2186086 2186894 2187043) (-1272 "UPXSCONS.spad" 2183817 2183837 2184190 2184339) (-1271 "UPXSCCA.spad" 2182388 2182408 2183663 2183812) (-1270 "UPXSCCA.spad" 2181101 2181123 2182378 2182383) (-1269 "UPXSCAT.spad" 2179690 2179706 2180947 2181096) (-1268 "UPXS2.spad" 2179233 2179286 2179680 2179685) (-1267 "UPSQFREE.spad" 2177647 2177661 2179223 2179228) (-1266 "UPSCAT.spad" 2175434 2175458 2177545 2177642) (-1265 "UPSCAT.spad" 2172927 2172953 2175040 2175045) (-1264 "UPOLYC.spad" 2167967 2167978 2172769 2172922) (-1263 "UPOLYC.spad" 2162899 2162912 2167703 2167708) (-1262 "UPOLYC2.spad" 2162370 2162389 2162889 2162894) (-1261 "UP.spad" 2159476 2159491 2159863 2160016) (-1260 "UPMP.spad" 2158376 2158389 2159466 2159471) (-1259 "UPDIVP.spad" 2157941 2157955 2158366 2158371) (-1258 "UPDECOMP.spad" 2156186 2156200 2157931 2157936) (-1257 "UPCDEN.spad" 2155395 2155411 2156176 2156181) (-1256 "UP2.spad" 2154759 2154780 2155385 2155390) (-1255 "UNISEG.spad" 2154112 2154123 2154678 2154683) (-1254 "UNISEG2.spad" 2153609 2153622 2154068 2154073) (-1253 "UNIFACT.spad" 2152712 2152724 2153599 2153604) (-1252 "ULS.spad" 2142496 2142524 2143441 2143870) (-1251 "ULSCONS.spad" 2133630 2133650 2134000 2134149) (-1250 "ULSCCAT.spad" 2131367 2131387 2133476 2133625) (-1249 "ULSCCAT.spad" 2129212 2129234 2131323 2131328) (-1248 "ULSCAT.spad" 2127444 2127460 2129058 2129207) (-1247 "ULS2.spad" 2126958 2127011 2127434 2127439) (-1246 "UINT8.spad" 2126835 2126844 2126948 2126953) (-1245 "UINT64.spad" 2126711 2126720 2126825 2126830) (-1244 "UINT32.spad" 2126587 2126596 2126701 2126706) (-1243 "UINT16.spad" 2126463 2126472 2126577 2126582) (-1242 "UFD.spad" 2125528 2125537 2126389 2126458) (-1241 "UFD.spad" 2124655 2124666 2125518 2125523) (-1240 "UDVO.spad" 2123536 2123545 2124645 2124650) (-1239 "UDPO.spad" 2121029 2121040 2123492 2123497) (-1238 "TYPE.spad" 2120961 2120970 2121019 2121024) (-1237 "TYPEAST.spad" 2120880 2120889 2120951 2120956) (-1236 "TWOFACT.spad" 2119532 2119547 2120870 2120875) (-1235 "TUPLE.spad" 2119018 2119029 2119431 2119436) (-1234 "TUBETOOL.spad" 2115885 2115894 2119008 2119013) (-1233 "TUBE.spad" 2114532 2114549 2115875 2115880) (-1232 "TS.spad" 2113131 2113147 2114097 2114194) (-1231 "TSETCAT.spad" 2100258 2100275 2113099 2113126) (-1230 "TSETCAT.spad" 2087371 2087390 2100214 2100219) (-1229 "TRMANIP.spad" 2081737 2081754 2087077 2087082) (-1228 "TRIMAT.spad" 2080700 2080725 2081727 2081732) (-1227 "TRIGMNIP.spad" 2079227 2079244 2080690 2080695) (-1226 "TRIGCAT.spad" 2078739 2078748 2079217 2079222) (-1225 "TRIGCAT.spad" 2078249 2078260 2078729 2078734) (-1224 "TREE.spad" 2076707 2076718 2077739 2077766) (-1223 "TRANFUN.spad" 2076546 2076555 2076697 2076702) (-1222 "TRANFUN.spad" 2076383 2076394 2076536 2076541) (-1221 "TOPSP.spad" 2076057 2076066 2076373 2076378) (-1220 "TOOLSIGN.spad" 2075720 2075731 2076047 2076052) (-1219 "TEXTFILE.spad" 2074281 2074290 2075710 2075715) (-1218 "TEX.spad" 2071427 2071436 2074271 2074276) (-1217 "TEX1.spad" 2070983 2070994 2071417 2071422) (-1216 "TEMUTL.spad" 2070538 2070547 2070973 2070978) (-1215 "TBCMPPK.spad" 2068631 2068654 2070528 2070533) (-1214 "TBAGG.spad" 2067681 2067704 2068611 2068626) (-1213 "TBAGG.spad" 2066739 2066764 2067671 2067676) (-1212 "TANEXP.spad" 2066147 2066158 2066729 2066734) (-1211 "TALGOP.spad" 2065871 2065882 2066137 2066142) (-1210 "TABLE.spad" 2063840 2063863 2064110 2064137) (-1209 "TABLEAU.spad" 2063321 2063332 2063830 2063835) (-1208 "TABLBUMP.spad" 2060124 2060135 2063311 2063316) (-1207 "SYSTEM.spad" 2059352 2059361 2060114 2060119) (-1206 "SYSSOLP.spad" 2056835 2056846 2059342 2059347) (-1205 "SYSPTR.spad" 2056734 2056743 2056825 2056830) (-1204 "SYSNNI.spad" 2055916 2055927 2056724 2056729) (-1203 "SYSINT.spad" 2055320 2055331 2055906 2055911) (-1202 "SYNTAX.spad" 2051526 2051535 2055310 2055315) (-1201 "SYMTAB.spad" 2049594 2049603 2051516 2051521) (-1200 "SYMS.spad" 2045617 2045626 2049584 2049589) (-1199 "SYMPOLY.spad" 2044624 2044635 2044706 2044833) (-1198 "SYMFUNC.spad" 2044125 2044136 2044614 2044619) (-1197 "SYMBOL.spad" 2041628 2041637 2044115 2044120) (-1196 "SWITCH.spad" 2038399 2038408 2041618 2041623) (-1195 "SUTS.spad" 2035447 2035475 2036866 2036963) (-1194 "SUPXS.spad" 2032730 2032758 2033579 2033728) (-1193 "SUP.spad" 2029450 2029461 2030223 2030376) (-1192 "SUPFRACF.spad" 2028555 2028573 2029440 2029445) (-1191 "SUP2.spad" 2027947 2027960 2028545 2028550) (-1190 "SUMRF.spad" 2026921 2026932 2027937 2027942) (-1189 "SUMFS.spad" 2026558 2026575 2026911 2026916) (-1188 "SULS.spad" 2016329 2016357 2017287 2017716) (-1187 "SUCHTAST.spad" 2016098 2016107 2016319 2016324) (-1186 "SUCH.spad" 2015780 2015795 2016088 2016093) (-1185 "SUBSPACE.spad" 2007895 2007910 2015770 2015775) (-1184 "SUBRESP.spad" 2007065 2007079 2007851 2007856) (-1183 "STTF.spad" 2003164 2003180 2007055 2007060) (-1182 "STTFNC.spad" 1999632 1999648 2003154 2003159) (-1181 "STTAYLOR.spad" 1992267 1992278 1999513 1999518) (-1180 "STRTBL.spad" 1990318 1990335 1990467 1990494) (-1179 "STRING.spad" 1989105 1989114 1989326 1989353) (-1178 "STREAM.spad" 1985906 1985917 1988513 1988528) (-1177 "STREAM3.spad" 1985479 1985494 1985896 1985901) (-1176 "STREAM2.spad" 1984607 1984620 1985469 1985474) (-1175 "STREAM1.spad" 1984313 1984324 1984597 1984602) (-1174 "STINPROD.spad" 1983249 1983265 1984303 1984308) (-1173 "STEP.spad" 1982450 1982459 1983239 1983244) (-1172 "STEPAST.spad" 1981684 1981693 1982440 1982445) (-1171 "STBL.spad" 1979768 1979796 1979935 1979950) (-1170 "STAGG.spad" 1978843 1978854 1979758 1979763) (-1169 "STAGG.spad" 1977916 1977929 1978833 1978838) (-1168 "STACK.spad" 1977156 1977167 1977406 1977433) (-1167 "SREGSET.spad" 1974824 1974841 1976766 1976793) (-1166 "SRDCMPK.spad" 1973385 1973405 1974814 1974819) (-1165 "SRAGG.spad" 1968528 1968537 1973353 1973380) (-1164 "SRAGG.spad" 1963691 1963702 1968518 1968523) (-1163 "SQMATRIX.spad" 1961234 1961252 1962150 1962237) (-1162 "SPLTREE.spad" 1955630 1955643 1960514 1960541) (-1161 "SPLNODE.spad" 1952218 1952231 1955620 1955625) (-1160 "SPFCAT.spad" 1951027 1951036 1952208 1952213) (-1159 "SPECOUT.spad" 1949579 1949588 1951017 1951022) (-1158 "SPADXPT.spad" 1941174 1941183 1949569 1949574) (-1157 "spad-parser.spad" 1940639 1940648 1941164 1941169) (-1156 "SPADAST.spad" 1940340 1940349 1940629 1940634) (-1155 "SPACEC.spad" 1924539 1924550 1940330 1940335) (-1154 "SPACE3.spad" 1924315 1924326 1924529 1924534) (-1153 "SORTPAK.spad" 1923864 1923877 1924271 1924276) (-1152 "SOLVETRA.spad" 1921627 1921638 1923854 1923859) (-1151 "SOLVESER.spad" 1920155 1920166 1921617 1921622) (-1150 "SOLVERAD.spad" 1916181 1916192 1920145 1920150) (-1149 "SOLVEFOR.spad" 1914643 1914661 1916171 1916176) (-1148 "SNTSCAT.spad" 1914243 1914260 1914611 1914638) (-1147 "SMTS.spad" 1912515 1912541 1913808 1913905) (-1146 "SMP.spad" 1909990 1910010 1910380 1910507) (-1145 "SMITH.spad" 1908835 1908860 1909980 1909985) (-1144 "SMATCAT.spad" 1906945 1906975 1908779 1908830) (-1143 "SMATCAT.spad" 1904987 1905019 1906823 1906828) (-1142 "SKAGG.spad" 1903950 1903961 1904955 1904982) (-1141 "SINT.spad" 1902890 1902899 1903816 1903945) (-1140 "SIMPAN.spad" 1902618 1902627 1902880 1902885) (-1139 "SIG.spad" 1901948 1901957 1902608 1902613) (-1138 "SIGNRF.spad" 1901066 1901077 1901938 1901943) (-1137 "SIGNEF.spad" 1900345 1900362 1901056 1901061) (-1136 "SIGAST.spad" 1899730 1899739 1900335 1900340) (-1135 "SHP.spad" 1897658 1897673 1899686 1899691) (-1134 "SHDP.spad" 1885336 1885363 1885845 1885944) (-1133 "SGROUP.spad" 1884944 1884953 1885326 1885331) (-1132 "SGROUP.spad" 1884550 1884561 1884934 1884939) (-1131 "SGCF.spad" 1877689 1877698 1884540 1884545) (-1130 "SFRTCAT.spad" 1876619 1876636 1877657 1877684) (-1129 "SFRGCD.spad" 1875682 1875702 1876609 1876614) (-1128 "SFQCMPK.spad" 1870319 1870339 1875672 1875677) (-1127 "SFORT.spad" 1869758 1869772 1870309 1870314) (-1126 "SEXOF.spad" 1869601 1869641 1869748 1869753) (-1125 "SEX.spad" 1869493 1869502 1869591 1869596) (-1124 "SEXCAT.spad" 1867265 1867305 1869483 1869488) (-1123 "SET.spad" 1865553 1865564 1866650 1866689) (-1122 "SETMN.spad" 1864003 1864020 1865543 1865548) (-1121 "SETCAT.spad" 1863488 1863497 1863993 1863998) (-1120 "SETCAT.spad" 1862971 1862982 1863478 1863483) (-1119 "SETAGG.spad" 1859520 1859531 1862951 1862966) (-1118 "SETAGG.spad" 1856077 1856090 1859510 1859515) (-1117 "SEQAST.spad" 1855780 1855789 1856067 1856072) (-1116 "SEGXCAT.spad" 1854936 1854949 1855770 1855775) (-1115 "SEG.spad" 1854749 1854760 1854855 1854860) (-1114 "SEGCAT.spad" 1853674 1853685 1854739 1854744) (-1113 "SEGBIND.spad" 1853432 1853443 1853621 1853626) (-1112 "SEGBIND2.spad" 1853130 1853143 1853422 1853427) (-1111 "SEGAST.spad" 1852844 1852853 1853120 1853125) (-1110 "SEG2.spad" 1852279 1852292 1852800 1852805) (-1109 "SDVAR.spad" 1851555 1851566 1852269 1852274) (-1108 "SDPOL.spad" 1848888 1848899 1849179 1849306) (-1107 "SCPKG.spad" 1846977 1846988 1848878 1848883) (-1106 "SCOPE.spad" 1846130 1846139 1846967 1846972) (-1105 "SCACHE.spad" 1844826 1844837 1846120 1846125) (-1104 "SASTCAT.spad" 1844735 1844744 1844816 1844821) (-1103 "SAOS.spad" 1844607 1844616 1844725 1844730) (-1102 "SAERFFC.spad" 1844320 1844340 1844597 1844602) (-1101 "SAE.spad" 1841790 1841806 1842401 1842536) (-1100 "SAEFACT.spad" 1841491 1841511 1841780 1841785) (-1099 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1578391 1578396) (-969 "POLYCATQ.spad" 1575784 1575806 1577656 1577661) (-968 "POLYCAT.spad" 1569254 1569275 1575652 1575779) (-967 "POLYCAT.spad" 1562062 1562085 1568462 1568467) (-966 "POLY2UP.spad" 1561514 1561528 1562052 1562057) (-965 "POLY2.spad" 1561111 1561123 1561504 1561509) (-964 "POLUTIL.spad" 1560052 1560081 1561067 1561072) (-963 "POLTOPOL.spad" 1558800 1558815 1560042 1560047) (-962 "POINT.spad" 1557485 1557495 1557572 1557599) (-961 "PNTHEORY.spad" 1554187 1554195 1557475 1557480) (-960 "PMTOOLS.spad" 1552962 1552976 1554177 1554182) (-959 "PMSYM.spad" 1552511 1552521 1552952 1552957) (-958 "PMQFCAT.spad" 1552102 1552116 1552501 1552506) (-957 "PMPRED.spad" 1551581 1551595 1552092 1552097) (-956 "PMPREDFS.spad" 1551035 1551057 1551571 1551576) (-955 "PMPLCAT.spad" 1550115 1550133 1550967 1550972) (-954 "PMLSAGG.spad" 1549700 1549714 1550105 1550110) (-953 "PMKERNEL.spad" 1549279 1549291 1549690 1549695) (-952 "PMINS.spad" 1548859 1548869 1549269 1549274) (-951 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1450377 1450382) (-894 "PARSCURV.spad" 1449341 1449369 1449897 1449902) (-893 "PARSC2.spad" 1449132 1449148 1449331 1449336) (-892 "PARPCURV.spad" 1448594 1448622 1449122 1449127) (-891 "PARPC2.spad" 1448385 1448401 1448584 1448589) (-890 "PARAMAST.spad" 1447513 1447521 1448375 1448380) (-889 "PAN2EXPR.spad" 1446925 1446933 1447503 1447508) (-888 "PALETTE.spad" 1445895 1445903 1446915 1446920) (-887 "PAIR.spad" 1444882 1444895 1445483 1445488) (-886 "PADICRC.spad" 1442123 1442141 1443294 1443387) (-885 "PADICRAT.spad" 1440031 1440043 1440252 1440345) (-884 "PADIC.spad" 1439726 1439738 1439957 1440026) (-883 "PADICCT.spad" 1438275 1438287 1439652 1439721) (-882 "PADEPAC.spad" 1436964 1436983 1438265 1438270) (-881 "PADE.spad" 1435716 1435732 1436954 1436959) (-880 "OWP.spad" 1434956 1434986 1435574 1435641) (-879 "OVERSET.spad" 1434529 1434537 1434946 1434951) (-878 "OVAR.spad" 1434310 1434333 1434519 1434524) (-877 "OUT.spad" 1433396 1433404 1434300 1434305) (-876 "OUTFORM.spad" 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(-857 "ORDFUNS.spad" 1398663 1398679 1399521 1399526) (-856 "ORDFIN.spad" 1398483 1398491 1398653 1398658) (-855 "ORDCOMP.spad" 1396948 1396958 1398030 1398059) (-854 "ORDCOMP2.spad" 1396241 1396253 1396938 1396943) (-853 "OPTPROB.spad" 1394879 1394887 1396231 1396236) (-852 "OPTPACK.spad" 1387288 1387296 1394869 1394874) (-851 "OPTCAT.spad" 1384967 1384975 1387278 1387283) (-850 "OPSIG.spad" 1384621 1384629 1384957 1384962) (-849 "OPQUERY.spad" 1384170 1384178 1384611 1384616) (-848 "OP.spad" 1383912 1383922 1383992 1384059) (-847 "OPERCAT.spad" 1383378 1383388 1383902 1383907) (-846 "OPERCAT.spad" 1382842 1382854 1383368 1383373) (-845 "ONECOMP.spad" 1381587 1381597 1382389 1382418) (-844 "ONECOMP2.spad" 1381011 1381023 1381577 1381582) (-843 "OMSERVER.spad" 1380017 1380025 1381001 1381006) (-842 "OMSAGG.spad" 1379805 1379815 1379973 1380012) (-841 "OMPKG.spad" 1378421 1378429 1379795 1379800) (-840 "OM.spad" 1377394 1377402 1378411 1378416) (-839 "OMLO.spad" 1376819 1376831 1377280 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233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-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 2294287 2294292 2294297 2294302) (-2 NIL 2294267 2294272 2294277 2294282) (-1 NIL 2294247 2294252 2294257 2294262) (0 NIL 2294227 2294232 2294237 2294242) (-1317 "ZMOD.spad" 2294036 2294049 2294165 2294222) (-1316 "ZLINDEP.spad" 2293102 2293113 2294026 2294031) (-1315 "ZDSOLVE.spad" 2283047 2283069 2293092 2293097) (-1314 "YSTREAM.spad" 2282542 2282553 2283037 2283042) (-1313 "YDIAGRAM.spad" 2282176 2282185 2282532 2282537) (-1312 "XRPOLY.spad" 2281396 2281416 2282032 2282101) (-1311 "XPR.spad" 2279191 2279204 2281114 2281213) (-1310 "XPOLY.spad" 2278746 2278757 2279047 2279116) (-1309 "XPOLYC.spad" 2278065 2278081 2278672 2278741) (-1308 "XPBWPOLY.spad" 2276502 2276522 2277845 2277914) (-1307 "XF.spad" 2274965 2274980 2276404 2276497) (-1306 "XF.spad" 2273408 2273425 2274849 2274854) (-1305 "XFALG.spad" 2270456 2270472 2273334 2273403) (-1304 "XEXPPKG.spad" 2269707 2269733 2270446 2270451) (-1303 "XDPOLY.spad" 2269321 2269337 2269563 2269632) (-1302 "XALG.spad" 2268981 2268992 2269277 2269316) (-1301 "WUTSET.spad" 2264784 2264801 2268591 2268618) (-1300 "WP.spad" 2263983 2264027 2264642 2264709) (-1299 "WHILEAST.spad" 2263781 2263790 2263973 2263978) (-1298 "WHEREAST.spad" 2263452 2263461 2263771 2263776) (-1297 "WFFINTBS.spad" 2261115 2261137 2263442 2263447) (-1296 "WEIER.spad" 2259337 2259348 2261105 2261110) (-1295 "VSPACE.spad" 2259010 2259021 2259305 2259332) (-1294 "VSPACE.spad" 2258703 2258716 2259000 2259005) (-1293 "VOID.spad" 2258380 2258389 2258693 2258698) (-1292 "VIEW.spad" 2256060 2256069 2258370 2258375) (-1291 "VIEWDEF.spad" 2251261 2251270 2256050 2256055) (-1290 "VIEW3D.spad" 2235222 2235231 2251251 2251256) (-1289 "VIEW2D.spad" 2223113 2223122 2235212 2235217) (-1288 "VECTOR.spad" 2221634 2221645 2221885 2221912) (-1287 "VECTOR2.spad" 2220273 2220286 2221624 2221629) (-1286 "VECTCAT.spad" 2218177 2218188 2220241 2220268) (-1285 "VECTCAT.spad" 2215888 2215901 2217954 2217959) (-1284 "VARIABLE.spad" 2215668 2215683 2215878 2215883) (-1283 "UTYPE.spad" 2215312 2215321 2215658 2215663) (-1282 "UTSODETL.spad" 2214607 2214631 2215268 2215273) (-1281 "UTSODE.spad" 2212823 2212843 2214597 2214602) (-1280 "UTS.spad" 2207770 2207798 2211290 2211387) (-1279 "UTSCAT.spad" 2205249 2205265 2207668 2207765) (-1278 "UTSCAT.spad" 2202372 2202390 2204793 2204798) (-1277 "UTS2.spad" 2201967 2202002 2202362 2202367) (-1276 "URAGG.spad" 2196640 2196651 2201957 2201962) (-1275 "URAGG.spad" 2191277 2191290 2196596 2196601) (-1274 "UPXSSING.spad" 2188922 2188948 2190358 2190491) (-1273 "UPXS.spad" 2186218 2186246 2187054 2187203) (-1272 "UPXSCONS.spad" 2183977 2183997 2184350 2184499) (-1271 "UPXSCCA.spad" 2182548 2182568 2183823 2183972) (-1270 "UPXSCCA.spad" 2181261 2181283 2182538 2182543) (-1269 "UPXSCAT.spad" 2179850 2179866 2181107 2181256) (-1268 "UPXS2.spad" 2179393 2179446 2179840 2179845) (-1267 "UPSQFREE.spad" 2177807 2177821 2179383 2179388) (-1266 "UPSCAT.spad" 2175594 2175618 2177705 2177802) (-1265 "UPSCAT.spad" 2173087 2173113 2175200 2175205) (-1264 "UPOLYC.spad" 2168127 2168138 2172929 2173082) (-1263 "UPOLYC.spad" 2163059 2163072 2167863 2167868) (-1262 "UPOLYC2.spad" 2162530 2162549 2163049 2163054) (-1261 "UP.spad" 2159636 2159651 2160023 2160176) (-1260 "UPMP.spad" 2158536 2158549 2159626 2159631) (-1259 "UPDIVP.spad" 2158101 2158115 2158526 2158531) (-1258 "UPDECOMP.spad" 2156346 2156360 2158091 2158096) (-1257 "UPCDEN.spad" 2155555 2155571 2156336 2156341) (-1256 "UP2.spad" 2154919 2154940 2155545 2155550) (-1255 "UNISEG.spad" 2154272 2154283 2154838 2154843) (-1254 "UNISEG2.spad" 2153769 2153782 2154228 2154233) (-1253 "UNIFACT.spad" 2152872 2152884 2153759 2153764) (-1252 "ULS.spad" 2142656 2142684 2143601 2144030) (-1251 "ULSCONS.spad" 2133790 2133810 2134160 2134309) (-1250 "ULSCCAT.spad" 2131527 2131547 2133636 2133785) (-1249 "ULSCCAT.spad" 2129372 2129394 2131483 2131488) (-1248 "ULSCAT.spad" 2127604 2127620 2129218 2129367) (-1247 "ULS2.spad" 2127118 2127171 2127594 2127599) (-1246 "UINT8.spad" 2126995 2127004 2127108 2127113) (-1245 "UINT64.spad" 2126871 2126880 2126985 2126990) (-1244 "UINT32.spad" 2126747 2126756 2126861 2126866) (-1243 "UINT16.spad" 2126623 2126632 2126737 2126742) (-1242 "UFD.spad" 2125688 2125697 2126549 2126618) (-1241 "UFD.spad" 2124815 2124826 2125678 2125683) (-1240 "UDVO.spad" 2123696 2123705 2124805 2124810) (-1239 "UDPO.spad" 2121189 2121200 2123652 2123657) (-1238 "TYPE.spad" 2121121 2121130 2121179 2121184) (-1237 "TYPEAST.spad" 2121040 2121049 2121111 2121116) (-1236 "TWOFACT.spad" 2119692 2119707 2121030 2121035) (-1235 "TUPLE.spad" 2119178 2119189 2119591 2119596) (-1234 "TUBETOOL.spad" 2116045 2116054 2119168 2119173) (-1233 "TUBE.spad" 2114692 2114709 2116035 2116040) (-1232 "TS.spad" 2113291 2113307 2114257 2114354) (-1231 "TSETCAT.spad" 2100418 2100435 2113259 2113286) (-1230 "TSETCAT.spad" 2087531 2087550 2100374 2100379) (-1229 "TRMANIP.spad" 2081897 2081914 2087237 2087242) (-1228 "TRIMAT.spad" 2080860 2080885 2081887 2081892) (-1227 "TRIGMNIP.spad" 2079387 2079404 2080850 2080855) (-1226 "TRIGCAT.spad" 2078899 2078908 2079377 2079382) (-1225 "TRIGCAT.spad" 2078409 2078420 2078889 2078894) (-1224 "TREE.spad" 2076867 2076878 2077899 2077926) (-1223 "TRANFUN.spad" 2076706 2076715 2076857 2076862) (-1222 "TRANFUN.spad" 2076543 2076554 2076696 2076701) (-1221 "TOPSP.spad" 2076217 2076226 2076533 2076538) (-1220 "TOOLSIGN.spad" 2075880 2075891 2076207 2076212) (-1219 "TEXTFILE.spad" 2074441 2074450 2075870 2075875) (-1218 "TEX.spad" 2071587 2071596 2074431 2074436) (-1217 "TEX1.spad" 2071143 2071154 2071577 2071582) (-1216 "TEMUTL.spad" 2070698 2070707 2071133 2071138) (-1215 "TBCMPPK.spad" 2068791 2068814 2070688 2070693) (-1214 "TBAGG.spad" 2067841 2067864 2068771 2068786) (-1213 "TBAGG.spad" 2066899 2066924 2067831 2067836) (-1212 "TANEXP.spad" 2066307 2066318 2066889 2066894) (-1211 "TALGOP.spad" 2066031 2066042 2066297 2066302) (-1210 "TABLE.spad" 2064000 2064023 2064270 2064297) (-1209 "TABLEAU.spad" 2063481 2063492 2063990 2063995) (-1208 "TABLBUMP.spad" 2060284 2060295 2063471 2063476) (-1207 "SYSTEM.spad" 2059512 2059521 2060274 2060279) (-1206 "SYSSOLP.spad" 2056995 2057006 2059502 2059507) (-1205 "SYSPTR.spad" 2056894 2056903 2056985 2056990) (-1204 "SYSNNI.spad" 2056076 2056087 2056884 2056889) (-1203 "SYSINT.spad" 2055480 2055491 2056066 2056071) (-1202 "SYNTAX.spad" 2051686 2051695 2055470 2055475) (-1201 "SYMTAB.spad" 2049754 2049763 2051676 2051681) (-1200 "SYMS.spad" 2045777 2045786 2049744 2049749) (-1199 "SYMPOLY.spad" 2044784 2044795 2044866 2044993) (-1198 "SYMFUNC.spad" 2044285 2044296 2044774 2044779) (-1197 "SYMBOL.spad" 2041788 2041797 2044275 2044280) (-1196 "SWITCH.spad" 2038559 2038568 2041778 2041783) (-1195 "SUTS.spad" 2035607 2035635 2037026 2037123) (-1194 "SUPXS.spad" 2032890 2032918 2033739 2033888) (-1193 "SUP.spad" 2029610 2029621 2030383 2030536) (-1192 "SUPFRACF.spad" 2028715 2028733 2029600 2029605) (-1191 "SUP2.spad" 2028107 2028120 2028705 2028710) (-1190 "SUMRF.spad" 2027081 2027092 2028097 2028102) (-1189 "SUMFS.spad" 2026718 2026735 2027071 2027076) (-1188 "SULS.spad" 2016489 2016517 2017447 2017876) (-1187 "SUCHTAST.spad" 2016258 2016267 2016479 2016484) (-1186 "SUCH.spad" 2015940 2015955 2016248 2016253) (-1185 "SUBSPACE.spad" 2008055 2008070 2015930 2015935) (-1184 "SUBRESP.spad" 2007225 2007239 2008011 2008016) (-1183 "STTF.spad" 2003324 2003340 2007215 2007220) (-1182 "STTFNC.spad" 1999792 1999808 2003314 2003319) (-1181 "STTAYLOR.spad" 1992427 1992438 1999673 1999678) (-1180 "STRTBL.spad" 1990478 1990495 1990627 1990654) (-1179 "STRING.spad" 1989265 1989274 1989486 1989513) (-1178 "STREAM.spad" 1986066 1986077 1988673 1988688) (-1177 "STREAM3.spad" 1985639 1985654 1986056 1986061) (-1176 "STREAM2.spad" 1984767 1984780 1985629 1985634) (-1175 "STREAM1.spad" 1984473 1984484 1984757 1984762) (-1174 "STINPROD.spad" 1983409 1983425 1984463 1984468) (-1173 "STEP.spad" 1982610 1982619 1983399 1983404) (-1172 "STEPAST.spad" 1981844 1981853 1982600 1982605) (-1171 "STBL.spad" 1979928 1979956 1980095 1980110) (-1170 "STAGG.spad" 1979003 1979014 1979918 1979923) (-1169 "STAGG.spad" 1978076 1978089 1978993 1978998) (-1168 "STACK.spad" 1977316 1977327 1977566 1977593) (-1167 "SREGSET.spad" 1974984 1975001 1976926 1976953) (-1166 "SRDCMPK.spad" 1973545 1973565 1974974 1974979) (-1165 "SRAGG.spad" 1968688 1968697 1973513 1973540) (-1164 "SRAGG.spad" 1963851 1963862 1968678 1968683) (-1163 "SQMATRIX.spad" 1961394 1961412 1962310 1962397) (-1162 "SPLTREE.spad" 1955790 1955803 1960674 1960701) (-1161 "SPLNODE.spad" 1952378 1952391 1955780 1955785) (-1160 "SPFCAT.spad" 1951187 1951196 1952368 1952373) (-1159 "SPECOUT.spad" 1949739 1949748 1951177 1951182) (-1158 "SPADXPT.spad" 1941334 1941343 1949729 1949734) (-1157 "spad-parser.spad" 1940799 1940808 1941324 1941329) (-1156 "SPADAST.spad" 1940500 1940509 1940789 1940794) (-1155 "SPACEC.spad" 1924699 1924710 1940490 1940495) (-1154 "SPACE3.spad" 1924475 1924486 1924689 1924694) (-1153 "SORTPAK.spad" 1924024 1924037 1924431 1924436) (-1152 "SOLVETRA.spad" 1921787 1921798 1924014 1924019) (-1151 "SOLVESER.spad" 1920315 1920326 1921777 1921782) (-1150 "SOLVERAD.spad" 1916341 1916352 1920305 1920310) (-1149 "SOLVEFOR.spad" 1914803 1914821 1916331 1916336) (-1148 "SNTSCAT.spad" 1914403 1914420 1914771 1914798) (-1147 "SMTS.spad" 1912675 1912701 1913968 1914065) (-1146 "SMP.spad" 1910150 1910170 1910540 1910667) (-1145 "SMITH.spad" 1908995 1909020 1910140 1910145) (-1144 "SMATCAT.spad" 1907105 1907135 1908939 1908990) (-1143 "SMATCAT.spad" 1905147 1905179 1906983 1906988) (-1142 "SKAGG.spad" 1904110 1904121 1905115 1905142) (-1141 "SINT.spad" 1903050 1903059 1903976 1904105) (-1140 "SIMPAN.spad" 1902778 1902787 1903040 1903045) (-1139 "SIG.spad" 1902108 1902117 1902768 1902773) (-1138 "SIGNRF.spad" 1901226 1901237 1902098 1902103) (-1137 "SIGNEF.spad" 1900505 1900522 1901216 1901221) (-1136 "SIGAST.spad" 1899890 1899899 1900495 1900500) (-1135 "SHP.spad" 1897818 1897833 1899846 1899851) (-1134 "SHDP.spad" 1885496 1885523 1886005 1886104) (-1133 "SGROUP.spad" 1885104 1885113 1885486 1885491) (-1132 "SGROUP.spad" 1884710 1884721 1885094 1885099) (-1131 "SGCF.spad" 1877849 1877858 1884700 1884705) (-1130 "SFRTCAT.spad" 1876779 1876796 1877817 1877844) (-1129 "SFRGCD.spad" 1875842 1875862 1876769 1876774) (-1128 "SFQCMPK.spad" 1870479 1870499 1875832 1875837) (-1127 "SFORT.spad" 1869918 1869932 1870469 1870474) (-1126 "SEXOF.spad" 1869761 1869801 1869908 1869913) (-1125 "SEX.spad" 1869653 1869662 1869751 1869756) (-1124 "SEXCAT.spad" 1867425 1867465 1869643 1869648) (-1123 "SET.spad" 1865713 1865724 1866810 1866849) (-1122 "SETMN.spad" 1864163 1864180 1865703 1865708) (-1121 "SETCAT.spad" 1863648 1863657 1864153 1864158) (-1120 "SETCAT.spad" 1863131 1863142 1863638 1863643) (-1119 "SETAGG.spad" 1859680 1859691 1863111 1863126) (-1118 "SETAGG.spad" 1856237 1856250 1859670 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1839310 1839326 1841641 1841646) (-1098 "RULESET.spad" 1838763 1838787 1839300 1839305) (-1097 "RULE.spad" 1837003 1837027 1838753 1838758) (-1096 "RULECOLD.spad" 1836855 1836868 1836993 1836998) (-1095 "RTVALUE.spad" 1836590 1836599 1836845 1836850) (-1094 "RSTRCAST.spad" 1836307 1836316 1836580 1836585) (-1093 "RSETGCD.spad" 1832685 1832705 1836297 1836302) (-1092 "RSETCAT.spad" 1822621 1822638 1832653 1832680) (-1091 "RSETCAT.spad" 1812577 1812596 1822611 1822616) (-1090 "RSDCMPK.spad" 1811029 1811049 1812567 1812572) (-1089 "RRCC.spad" 1809413 1809443 1811019 1811024) (-1088 "RRCC.spad" 1807795 1807827 1809403 1809408) (-1087 "RPTAST.spad" 1807497 1807506 1807785 1807790) (-1086 "RPOLCAT.spad" 1786857 1786872 1807365 1807492) (-1085 "RPOLCAT.spad" 1765930 1765947 1786440 1786445) (-1084 "ROUTINE.spad" 1761351 1761360 1764115 1764142) (-1083 "ROMAN.spad" 1760679 1760688 1761217 1761346) (-1082 "ROIRC.spad" 1759759 1759791 1760669 1760674) (-1081 "RNS.spad" 1758662 1758671 1759661 1759754) (-1080 "RNS.spad" 1757651 1757662 1758652 1758657) (-1079 "RNG.spad" 1757386 1757395 1757641 1757646) (-1078 "RNGBIND.spad" 1756546 1756560 1757341 1757346) (-1077 "RMODULE.spad" 1756311 1756322 1756536 1756541) (-1076 "RMCAT2.spad" 1755731 1755788 1756301 1756306) (-1075 "RMATRIX.spad" 1754519 1754538 1754862 1754901) (-1074 "RMATCAT.spad" 1750098 1750129 1754475 1754514) (-1073 "RMATCAT.spad" 1745567 1745600 1749946 1749951) (-1072 "RLINSET.spad" 1745271 1745282 1745557 1745562) (-1071 "RINTERP.spad" 1745159 1745179 1745261 1745266) (-1070 "RING.spad" 1744629 1744638 1745139 1745154) (-1069 "RING.spad" 1744107 1744118 1744619 1744624) (-1068 "RIDIST.spad" 1743499 1743508 1744097 1744102) (-1067 "RGCHAIN.spad" 1742027 1742043 1742929 1742956) (-1066 "RGBCSPC.spad" 1741808 1741820 1742017 1742022) (-1065 "RGBCMDL.spad" 1741338 1741350 1741798 1741803) (-1064 "RF.spad" 1738980 1738991 1741328 1741333) (-1063 "RFFACTOR.spad" 1738442 1738453 1738970 1738975) (-1062 "RFFACT.spad" 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(-1043 "REAL.spad" 1706470 1706479 1706588 1706593) (-1042 "REAL0Q.spad" 1703768 1703783 1706460 1706465) (-1041 "REAL0.spad" 1700612 1700627 1703758 1703763) (-1040 "RDUCEAST.spad" 1700333 1700342 1700602 1700607) (-1039 "RDIV.spad" 1699988 1700013 1700323 1700328) (-1038 "RDIST.spad" 1699555 1699566 1699978 1699983) (-1037 "RDETRS.spad" 1698419 1698437 1699545 1699550) (-1036 "RDETR.spad" 1696558 1696576 1698409 1698414) (-1035 "RDEEFS.spad" 1695657 1695674 1696548 1696553) (-1034 "RDEEF.spad" 1694667 1694684 1695647 1695652) (-1033 "RCFIELD.spad" 1691853 1691862 1694569 1694662) (-1032 "RCFIELD.spad" 1689125 1689136 1691843 1691848) (-1031 "RCAGG.spad" 1687053 1687064 1689115 1689120) (-1030 "RCAGG.spad" 1684908 1684921 1686972 1686977) (-1029 "RATRET.spad" 1684268 1684279 1684898 1684903) (-1028 "RATFACT.spad" 1683960 1683972 1684258 1684263) (-1027 "RANDSRC.spad" 1683279 1683288 1683950 1683955) (-1026 "RADUTIL.spad" 1683035 1683044 1683269 1683274) (-1025 "RADIX.spad" 1679859 1679873 1681405 1681498) (-1024 "RADFF.spad" 1677598 1677635 1677717 1677873) (-1023 "RADCAT.spad" 1677193 1677202 1677588 1677593) (-1022 "RADCAT.spad" 1676786 1676797 1677183 1677188) (-1021 "QUEUE.spad" 1676017 1676028 1676276 1676303) (-1020 "QUAT.spad" 1674505 1674516 1674848 1674913) (-1019 "QUATCT2.spad" 1674125 1674144 1674495 1674500) (-1018 "QUATCAT.spad" 1672295 1672306 1674055 1674120) (-1017 "QUATCAT.spad" 1670216 1670229 1671978 1671983) (-1016 "QUAGG.spad" 1669043 1669054 1670184 1670211) (-1015 "QQUTAST.spad" 1668811 1668820 1669033 1669038) (-1014 "QFORM.spad" 1668429 1668444 1668801 1668806) (-1013 "QFCAT.spad" 1667131 1667142 1668331 1668424) (-1012 "QFCAT.spad" 1665424 1665437 1666626 1666631) (-1011 "QFCAT2.spad" 1665116 1665133 1665414 1665419) (-1010 "QEQUAT.spad" 1664674 1664683 1665106 1665111) (-1009 "QCMPACK.spad" 1659420 1659440 1664664 1664669) (-1008 "QALGSET.spad" 1655498 1655531 1659334 1659339) (-1007 "QALGSET2.spad" 1653493 1653512 1655488 1655493) (-1006 "PWFFINTB.spad" 1650908 1650930 1653483 1653488) (-1005 "PUSHVAR.spad" 1650246 1650266 1650898 1650903) (-1004 "PTRANFN.spad" 1646373 1646384 1650236 1650241) (-1003 "PTPACK.spad" 1643460 1643471 1646363 1646368) (-1002 "PTFUNC2.spad" 1643282 1643297 1643450 1643455) (-1001 "PTCAT.spad" 1642536 1642547 1643250 1643277) (-1000 "PSQFR.spad" 1641842 1641867 1642526 1642531) (-999 "PSEUDLIN.spad" 1640728 1640738 1641832 1641837) (-998 "PSETPK.spad" 1626161 1626177 1640606 1640611) (-997 "PSETCAT.spad" 1620081 1620104 1626141 1626156) (-996 "PSETCAT.spad" 1613975 1614000 1620037 1620042) (-995 "PSCURVE.spad" 1612958 1612966 1613965 1613970) (-994 "PSCAT.spad" 1611741 1611770 1612856 1612953) (-993 "PSCAT.spad" 1610614 1610645 1611731 1611736) (-992 "PRTITION.spad" 1609312 1609320 1610604 1610609) (-991 "PRTDAST.spad" 1609031 1609039 1609302 1609307) (-990 "PRS.spad" 1598593 1598610 1608987 1608992) (-989 "PRQAGG.spad" 1598028 1598038 1598561 1598588) (-988 "PROPLOG.spad" 1597600 1597608 1598018 1598023) (-987 "PROPFUN2.spad" 1597223 1597236 1597590 1597595) (-986 "PROPFUN1.spad" 1596621 1596632 1597213 1597218) (-985 "PROPFRML.spad" 1595189 1595200 1596611 1596616) (-984 "PROPERTY.spad" 1594677 1594685 1595179 1595184) (-983 "PRODUCT.spad" 1592359 1592371 1592643 1592698) (-982 "PR.spad" 1590751 1590763 1591450 1591577) (-981 "PRINT.spad" 1590503 1590511 1590741 1590746) (-980 "PRIMES.spad" 1588756 1588766 1590493 1590498) (-979 "PRIMELT.spad" 1586837 1586851 1588746 1588751) (-978 "PRIMCAT.spad" 1586464 1586472 1586827 1586832) (-977 "PRIMARR.spad" 1585316 1585326 1585494 1585521) (-976 "PRIMARR2.spad" 1584083 1584095 1585306 1585311) (-975 "PREASSOC.spad" 1583465 1583477 1584073 1584078) (-974 "PPCURVE.spad" 1582602 1582610 1583455 1583460) (-973 "PORTNUM.spad" 1582377 1582385 1582592 1582597) (-972 "POLYROOT.spad" 1581226 1581248 1582333 1582338) (-971 "POLY.spad" 1578561 1578571 1579076 1579203) (-970 "POLYLIFT.spad" 1577826 1577849 1578551 1578556) (-969 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1549009 1549014) (-950 "PMDOWN.spad" 1547886 1547900 1548586 1548591) (-949 "PMASS.spad" 1546896 1546904 1547876 1547881) (-948 "PMASSFS.spad" 1545863 1545879 1546886 1546891) (-947 "PLOTTOOL.spad" 1545643 1545651 1545853 1545858) (-946 "PLOT.spad" 1540566 1540574 1545633 1545638) (-945 "PLOT3D.spad" 1537030 1537038 1540556 1540561) (-944 "PLOT1.spad" 1536187 1536197 1537020 1537025) (-943 "PLEQN.spad" 1523477 1523504 1536177 1536182) (-942 "PINTERP.spad" 1523099 1523118 1523467 1523472) (-941 "PINTERPA.spad" 1522883 1522899 1523089 1523094) (-940 "PI.spad" 1522492 1522500 1522857 1522878) (-939 "PID.spad" 1521462 1521470 1522418 1522487) (-938 "PICOERCE.spad" 1521119 1521129 1521452 1521457) (-937 "PGROEB.spad" 1519720 1519734 1521109 1521114) (-936 "PGE.spad" 1511337 1511345 1519710 1519715) (-935 "PGCD.spad" 1510227 1510244 1511327 1511332) (-934 "PFRPAC.spad" 1509376 1509386 1510217 1510222) (-933 "PFR.spad" 1506039 1506049 1509278 1509371) (-932 "PFOTOOLS.spad" 1505297 1505313 1506029 1506034) (-931 "PFOQ.spad" 1504667 1504685 1505287 1505292) (-930 "PFO.spad" 1504086 1504113 1504657 1504662) (-929 "PF.spad" 1503660 1503672 1503891 1503984) (-928 "PFECAT.spad" 1501342 1501350 1503586 1503655) (-927 "PFECAT.spad" 1499052 1499062 1501298 1501303) (-926 "PFBRU.spad" 1496940 1496952 1499042 1499047) (-925 "PFBR.spad" 1494500 1494523 1496930 1496935) (-924 "PERM.spad" 1490307 1490317 1494330 1494345) (-923 "PERMGRP.spad" 1485077 1485087 1490297 1490302) (-922 "PERMCAT.spad" 1483738 1483748 1485057 1485072) (-921 "PERMAN.spad" 1482270 1482284 1483728 1483733) (-920 "PENDTREE.spad" 1481494 1481504 1481782 1481787) (-919 "PDSPC.spad" 1480307 1480317 1481484 1481489) (-918 "PDSPC.spad" 1479118 1479130 1480297 1480302) (-917 "PDRING.spad" 1478960 1478970 1479098 1479113) (-916 "PDMOD.spad" 1478776 1478788 1478928 1478955) (-915 "PDEPROB.spad" 1477791 1477799 1478766 1478771) (-914 "PDEPACK.spad" 1471831 1471839 1477781 1477786) (-913 "PDECOMP.spad" 1471301 1471318 1471821 1471826) (-912 "PDECAT.spad" 1469657 1469665 1471291 1471296) (-911 "PDDOM.spad" 1469095 1469108 1469647 1469652) (-910 "PDDOM.spad" 1468531 1468546 1469085 1469090) (-909 "PCOMP.spad" 1468384 1468397 1468521 1468526) (-908 "PBWLB.spad" 1466972 1466989 1468374 1468379) (-907 "PATTERN.spad" 1461511 1461521 1466962 1466967) (-906 "PATTERN2.spad" 1461249 1461261 1461501 1461506) (-905 "PATTERN1.spad" 1459585 1459601 1461239 1461244) (-904 "PATRES.spad" 1457160 1457172 1459575 1459580) (-903 "PATRES2.spad" 1456832 1456846 1457150 1457155) (-902 "PATMATCH.spad" 1455029 1455060 1456540 1456545) (-901 "PATMAB.spad" 1454458 1454468 1455019 1455024) (-900 "PATLRES.spad" 1453544 1453558 1454448 1454453) (-899 "PATAB.spad" 1453308 1453318 1453534 1453539) (-898 "PARTPERM.spad" 1451316 1451324 1453298 1453303) (-897 "PARSURF.spad" 1450750 1450778 1451306 1451311) (-896 "PARSU2.spad" 1450547 1450563 1450740 1450745) (-895 "script-parser.spad" 1450067 1450075 1450537 1450542) (-894 "PARSCURV.spad" 1449501 1449529 1450057 1450062) (-893 "PARSC2.spad" 1449292 1449308 1449491 1449496) (-892 "PARPCURV.spad" 1448754 1448782 1449282 1449287) (-891 "PARPC2.spad" 1448545 1448561 1448744 1448749) (-890 "PARAMAST.spad" 1447673 1447681 1448535 1448540) (-889 "PAN2EXPR.spad" 1447085 1447093 1447663 1447668) (-888 "PALETTE.spad" 1446055 1446063 1447075 1447080) (-887 "PAIR.spad" 1445042 1445055 1445643 1445648) (-886 "PADICRC.spad" 1442283 1442301 1443454 1443547) (-885 "PADICRAT.spad" 1440191 1440203 1440412 1440505) (-884 "PADIC.spad" 1439886 1439898 1440117 1440186) (-883 "PADICCT.spad" 1438435 1438447 1439812 1439881) (-882 "PADEPAC.spad" 1437124 1437143 1438425 1438430) (-881 "PADE.spad" 1435876 1435892 1437114 1437119) (-880 "OWP.spad" 1435116 1435146 1435734 1435801) (-879 "OVERSET.spad" 1434689 1434697 1435106 1435111) (-878 "OVAR.spad" 1434470 1434493 1434679 1434684) (-877 "OUT.spad" 1433556 1433564 1434460 1434465) (-876 "OUTFORM.spad" 1422948 1422956 1433546 1433551) (-875 "OUTBFILE.spad" 1422366 1422374 1422938 1422943) (-874 "OUTBCON.spad" 1421372 1421380 1422356 1422361) (-873 "OUTBCON.spad" 1420376 1420386 1421362 1421367) (-872 "OSI.spad" 1419851 1419859 1420366 1420371) (-871 "OSGROUP.spad" 1419769 1419777 1419841 1419846) (-870 "ORTHPOL.spad" 1418254 1418264 1419686 1419691) (-869 "OREUP.spad" 1417707 1417735 1417934 1417973) (-868 "ORESUP.spad" 1417008 1417032 1417387 1417426) (-867 "OREPCTO.spad" 1414865 1414877 1416928 1416933) (-866 "OREPCAT.spad" 1409012 1409022 1414821 1414860) (-865 "OREPCAT.spad" 1403049 1403061 1408860 1408865) (-864 "ORDTYPE.spad" 1402286 1402294 1403039 1403044) (-863 "ORDTYPE.spad" 1401521 1401531 1402276 1402281) (-862 "ORDSTRCT.spad" 1401348 1401363 1401511 1401516) (-861 "ORDSET.spad" 1401048 1401056 1401338 1401343) (-860 "ORDRING.spad" 1400438 1400446 1401028 1401043) (-859 "ORDRING.spad" 1399836 1399846 1400428 1400433) (-858 "ORDMON.spad" 1399691 1399699 1399826 1399831) (-857 "ORDFUNS.spad" 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"DIRPCAT.spad" 278892 278910 279597 279602) (-241 "DIOSP.spad" 277717 277725 278882 278887) (-240 "DIOPS.spad" 276713 276723 277697 277712) (-239 "DIOPS.spad" 275683 275695 276669 276674) (-238 "DIFRING.spad" 275521 275529 275663 275678) (-237 "DIFFSPC.spad" 275100 275108 275511 275516) (-236 "DIFFSPC.spad" 274677 274687 275090 275095) (-235 "DIFFMOD.spad" 274166 274176 274645 274672) (-234 "DIFFDOM.spad" 273331 273342 274156 274161) (-233 "DIFFDOM.spad" 272494 272507 273321 273326) (-232 "DIFEXT.spad" 272313 272323 272474 272489) (-231 "DIAGG.spad" 271943 271953 272293 272308) (-230 "DIAGG.spad" 271581 271593 271933 271938) (-229 "DHMATRIX.spad" 269776 269786 270921 270948) (-228 "DFSFUN.spad" 263416 263424 269766 269771) (-227 "DFLOAT.spad" 260147 260155 263306 263411) (-226 "DFINTTLS.spad" 258378 258394 260137 260142) (-225 "DERHAM.spad" 256292 256324 258358 258373) (-224 "DEQUEUE.spad" 255499 255509 255782 255809) (-223 "DEGRED.spad" 255116 255130 255489 255494) (-222 "DEFINTRF.spad" 252653 252663 255106 255111) (-221 "DEFINTEF.spad" 251163 251179 252643 252648) (-220 "DEFAST.spad" 250531 250539 251153 251158) (-219 "DECIMAL.spad" 248540 248548 248901 248994) (-218 "DDFACT.spad" 246353 246370 248530 248535) (-217 "DBLRESP.spad" 245953 245977 246343 246348) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-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))
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